text:
#
# 1. 1.9.2020 Managed to convert ODE models for economic extension to transition model ready for stochastic simulation, using separate birth death list
#             See section on SC2UIR model. Not done for other two economic extensions yet
# 2. 1.9.2020 Implemented stochastic simulation (Tau-leap method) using PyGom inbuilt capabilities: for SCIR simulation only so far
#             Neeed to use integer N>>1, not 1.0, for stochastic simulation. Calculates in a few minutes for N=10000, rescaled ICUfrac to 0.02 (x10). N=100000 didn't finish in 10m.

# # Model Definitions

# import required packages
import os
import csv
from sympy import symbols, init_printing
import numpy as np
import matplotlib
get_ipython().run_line_magic('matplotlib', 'inline')
import seaborn as sb
from matplotlib import pyplot as plt
import sympy
import itertools
import scipy
import datetime
import matplotlib.dates as mdates
from pygom import DeterministicOde, Transition, SimulateOde, TransitionType, SquareLoss
from scipy.optimize import minimize,brentq

import pickle as pk
import jsonpickle as jpk

from cycler import cycler
import datetime
import matplotlib.dates as mdates
from pandas.plotting import register_matplotlib_converters
register_matplotlib_converters()
import pwlf
import sys
import copy
#from IPython.core.display import display, HTML
#display(HTML("<style>.container { width:100% !important; }</style>"))

import pprint
ppr = pprint.PrettyPrinter()

import data_config
if not data_config.data_loaded:
    print('loading data.py...(set data_config.data_loaded=True to avoid, if this already done)')
    from data import *
    print('done with data.py.')
else:
    print('data already loaded, so no "from data import *" required.')

savefigs = False # whether to save specific figures for paper to .../figures directory

def Float(x):
    try:
        rtn = float(x)
    except:
        rtn = float('NaN')
    return rtn

###########################################################
# to get ModelFit class definition:

possmodels = ['SIR','SCIR','SC2IR','SC2FIR','SC2UIR','SC2FUIR',    'SEIR','SCEIR','SC3EIR','SC3FEIR','SC3UEIR',  'SEI3R','SCEI3R','SC3EI3R','SC3FEI3R','SC3UEI3R','SC3FUEI3R'] # full root model set
agemodels =  ['SIR',       'SC2IR','SC2FIR',                       'SEIR',        'SC3EIR','SC3FEIR',            'SEI3R',         'SC3EI3R','SC3FEI3R','SC3UEI3R','SC3FUEI3R']
# exec(open('ModelFit.py','r').read())
###########################################################

C_2s = 1000.   # scaling factor for c_2, to allow fit parameter c_2 to be of commensurate magnitude to other parameters

def state_age(state0,age_structure):
    state = []
    sa = {}                                               # state age dictionary
    for s in state0:
        state_tmp = []
        for i in range(age_structure):
            state_tmp.append(s+'_'+str(i))

        state.extend(state_tmp)
        sa.update({s:state_tmp.copy()})
    return sa,state

def param_list_age(param_list,age_structure):
    contact = [[None]*age_structure]*age_structure         # add contact matrix to parameters {µ_i_j}
    for i in range(age_structure):
        contact[i] = ['m'+'_'+str(i)+'_'+str(j) for j in range(age_structure)]  # this should be set to M_i_j/N_j where N_j is normalized by N
        param_list.extend(contact[i])
    return param_list,contact

def phi_age(contact,sa,s,age_structure):
    phi = [None]*age_structure                             # contact matrix weighted contacts per day for age groups
    for i in range(age_structure):
        tmp = '('
        plus = ''
        for j in range(age_structure):
            tmp= tmp+plus+contact[i][j]+'*'+sa[s][j]      # note that division by N_j is assumed subsumed into contact matrix elt normalization
            plus = '+'
        tmp = tmp+')'
        phi[i]=tmp[:]               # Note that strings are treated like arrays and need to be copied elementwise
    return phi

def state_sum_age(s,sa,age_structure):
    for i in range(age_structure):
        state_sum = '('
        plus = ''
        for j in range(age_structure):
            state_sum= state_sum+plus+sa[s][j]
            plus = '+'
        state_sum = state_sum+')'
    return state_sum

def transition_age(transition,src,dest,factor,dept,sa,ttype,age_structure,phi=None,yfactor=None):
    youngmax = int(age_structure//3)
    for i in range(age_structure):
        if yfactor and i < youngmax:
                afactor = yfactor
        else:
            afactor = factor
        if phi is not None:
            transition.append(Transition(origin=sa[src][i],destination=sa[dest][i], equation = afactor+phi[i]+'*'+sa[dept][i],
                transition_type=TransitionType.T))
        else:
            transition.append(Transition(origin=sa[src][i],destination=sa[dest][i], equation = afactor+sa[dept][i],
                transition_type=TransitionType.T))
    return transition

def initial_state_age(I_0,state0,s_init,first_infected_agegroup,age_structure):
    x0 = []
    for s in state0:
        state_tmp = []
        for i in range(age_structure):
            if i == first_infected_agegroup and s == 'S':    # always subtract initial diseased from one age group of susceptibles
                x0.append(1.0-I_0)
            elif i == first_infected_agegroup and s == s_init:  # depending on model the s_init state is 'E' or 'I'
                x0.append(I_0)
            else:
                x0.append(0.)
    return x0

def make_model(mod_name,age_structure=None):
    """ make models of types ['SIR','SCIR','SC2IR','SEIR','SCEIR','SC3EIR','SEI3R','SCEI3R','SC3EI3R','SC2UIR','SC3UEIR','SC3UEI3R']"""
    global C_2s           # scaling factor for c_2 (1000) to allow c_2 parameter to be same order of magnitude as other parameters
    rtn = {}
    I_0 =  0.00003
    c_2s = '%f*' % C_2s   # string equation substitute scaled constant

    if mod_name == 'SIR':
        if age_structure:                                         # age_structure is integer number of age compartments
            state0 = ['S', 'I', 'R', 'D']
            sa,state = state_age(state0,age_structure)

            param_list0 = ['beta', 'gamma','mu','N']
            param_list,contact = param_list_age(param_list0.copy(),age_structure)

            phi = phi_age(contact,sa,'I',age_structure)

            transition = []
            transition = transition_age(transition,'S','I','beta*','S',sa,TransitionType.T,age_structure,phi=phi)
            transition = transition_age(transition,'I','R','gamma*','I',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I','D','mu*','I',sa,TransitionType.T,age_structure)

            model = DeterministicOde(state, param_list, transition=transition)
            if model == None:
                print('Error in make_model constructing DeterministicOde (in pygom)')
            model.modelname='SIR'+'_A'+str(age_structure)
            model.ei=slice(1*age_structure,2*age_structure)
            model.confirmed=slice(1*age_structure,4*age_structure)  # cases 1-3 i.e. I, R and D
            model.recovered=slice(2*age_structure,3*age_structure)
            model.deaths=slice(3*age_structure,4*age_structure)

            first_infected_agegroup = int(age_structure//4)       # first approximation : would give 20-25 year olds for 16 group 0-80 in 5 year intervals
            model.I_1 = 1*age_structure + first_infected_agegroup
            #x0 = [1.0-I_0, I_0, 0.0, 0.0]
            x0 = initial_state_age(I_0,state0,'I',first_infected_agegroup,age_structure)
            model.initial_values = (x0, 0) # 0 for t[0]

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn
        else:
            seasonal = False
            if seasonal:               # implement time-dependent beta via dervied parameter, using TransitionType.ODE ... code still needs supporting superstructure
                pi = 3.14159
                param_list = ['beta', 'gamma','mu','N','beta_p']    # new parameter beta_p as seasonal variation amplitude of beta - also need phase - for this need year-registered time
                state = ['S', 'I', 'R', 'D', 'tau']
                derived_param = [('betaT', 'beta*(1+betap*sin(2*pi*tau/365.)')]
                transition = [
                    Transition(origin='S', equation='-betaT*I*S',transition_type=TransitionType.ODE),
                    Transition(origin='I', equation='betaT*I*S-gamma*I-mu*I',transition_type=TransitionType.ODE),
                    Transition(origin='tau',equation='1',transition_type=TransitionType.ODE)
                ]
                model = DeterministicOde(state, param_list, derived_param=derived_param, transition=transition)
                model.tau=slice(4,5)
            else:
                param_list = ['beta', 'gamma','mu','N']
                state = ['S', 'I', 'R', 'D']
                transition = [
                    Transition(origin='S', destination='I', equation='beta*I*S',
                               transition_type=TransitionType.T),
                    Transition(origin='I', destination='R', equation='gamma*I',
                               transition_type=TransitionType.T),
                    Transition(origin='I', destination='D', equation='mu*I',
                               transition_type=TransitionType.T)
                ]
                model = DeterministicOde(state, param_list, transition=transition)
            model.modelname='SIR'
            model.ei=1
            model.confirmed=slice(1,4)  # cases 1-3 i.e. I, R and D
            model.recovered=slice(2,3)
            model.deaths=slice(3,4)
            model.I_1 = 1
            x0 = [1.0-I_0, I_0, 0.0, 0.0]
            model.initial_values = (x0, 0) # 0 for t[0]

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn

    if mod_name == 'SCIR': # this is a simpler version of the caution extension, not extended to U,F, or _A
        if age_structure:  # age_structure is integer number of age compartments
            print('Error: Age structure NYI for model',mod_name)
        else:
            state = ['S', 'I', 'R', 'D', 'S_c']
            param_list = ['beta', 'gamma', 'mu', 'c_0', 'c_1', 'c_2', 'N']

            transition = [
                Transition(origin='S', destination='I', equation='beta*I*S',
                           transition_type=TransitionType.T),
                Transition(origin='S', destination='S_c', equation=c_2s+'c_2*I*S',
                           transition_type=TransitionType.T),
                Transition(origin='S_c', destination='S', equation='c_1*S_c',
                           transition_type=TransitionType.T),
                Transition(origin='S_c', destination='I', equation='c_0*beta*I*S_c',
                           transition_type=TransitionType.T),
                Transition(origin='I', destination='R', equation='gamma*I',
                           transition_type=TransitionType.T),
                Transition(origin='I', destination='D', equation='mu*I',
                           transition_type=TransitionType.T)
                ]

            model = DeterministicOde(state, param_list, transition=transition)
            global SCIR_modelS
            SCIR_modelS = SimulateOde(state, param_list , transition=transition)
            model.modelname='SCIR'
            model.ei=1
            model.confirmed=slice(1,4)  # cases 1-3 i.e. I, R and D
            model.recovered=slice(2,3)
            model.deaths=slice(3,4)
            model.all_susceptibles=[0,4]
            model.S_c=4
            model.I_1 = 1
            x0_SCIR = [1.0-I_0, I_0, 0.0, 0.0, 0.0]
            model.initial_values = (x0_SCIR, 0)

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn

    if mod_name == 'SC2IR':
        if age_structure:                                         # age_structure is integer number of age compartments
            state0 = ['S', 'I', 'R', 'D', 'I_c', 'S_c']
            sa,state = state_age(state0,age_structure)

            param_list0 = ['beta', 'gamma', 'mu', 'c_0', 'c_1', 'c_2', 'c_3', 'N']
            param_list,contact = param_list_age(param_list0.copy(),age_structure)

            phi = phi_age(contact,sa,'I',age_structure)
            phi_c = phi_age(contact,sa,'I_c',age_structure)
            phi_1c = [p[0]+'+c_0*'+p[1] for p in zip(phi,phi_c)]   # '(I_1+c_0*I_c)' to corresponding phi combination
            sumI = state_sum_age('I',sa,age_structure)
            sumI_c = state_sum_age('I_c',sa,age_structure)

            transition = []
            transition = transition_age(transition,'S','I','beta*','S',sa,TransitionType.T,age_structure,phi=phi_1c)
            transition = transition_age(transition,'S','S_c',c_2s+'c_2*('+sumI+'+'+sumI_c+')'+'*','S',sa,TransitionType.T,age_structure,
                                        yfactor=c_2s+'c_3*('+sumI+'+'+sumI_c+')'+'*')
            transition = transition_age(transition,'S_c','S','c_1*','S_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'S_c','I_c','c_0*beta*','S_c',sa,TransitionType.T,age_structure,phi=phi_1c)
            transition = transition_age(transition,'I','R','gamma*','I',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I','D','mu*','I',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I','I_c',c_2s+'c_2*('+sumI+'+'+sumI_c+')'+'*','I',sa,TransitionType.T,age_structure,
                                        yfactor=c_2s+'c_3*('+sumI+'+'+sumI_c+')'+'*')
            transition = transition_age(transition,'I_c','R','gamma*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','D','mu*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','I','c_1*','I_c',sa,TransitionType.T,age_structure)

            model = DeterministicOde(state, param_list, transition=transition)
            if model == None:
                print('Error in make_model constructing DeterministicOde (in pygom)')
            model.modelname=mod_name+'_A'+str(age_structure)
            model.ei=slice(1*age_structure,2*age_structure)
            model.confirmed=slice(1*age_structure,5*age_structure)
            model.recovered=slice(2*age_structure,3*age_structure)
            model.deaths=slice(3*age_structure,4*age_structure)
            model.all_susceptibles=[slice(0,1*age_structure),slice(5*age_structure,6*age_structure)]
            model.S_c=slice(5*age_structure,6*age_structure)

            first_infected_agegroup = int(age_structure//4)       # first approximation : would give 20-25 year olds for 16 group 0-80 in 5 year intervals
            model.I_1 = 1*age_structure + first_infected_agegroup
            #x0 = [1.0-I_0, I_0, 0.0, 0.0]
            x0_SC2IR = initial_state_age(I_0,state0,'I',first_infected_agegroup,age_structure)
            model.initial_values = (x0_SC2IR, 0) # 0 for t[0]

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn
        else:
            state = ['S', 'I', 'R', 'D', 'I_c', 'S_c']
            param_list = ['beta', 'gamma', 'mu', 'c_0', 'c_1', 'c_2', 'N']

            transition = [
                Transition(origin='S', destination='I', equation='beta*(I+c_0*I_c)*S',
                           transition_type=TransitionType.T),
                Transition(origin='S', destination='S_c', equation=c_2s+'c_2*(I+I_c)*S',
                           transition_type=TransitionType.T),
                Transition(origin='S_c', destination='S', equation='c_1*S_c',
                           transition_type=TransitionType.T),
                Transition(origin='S_c', destination='I_c', equation='c_0*beta*(I+c_0*I_c)*S_c',
                           transition_type=TransitionType.T),
                Transition(origin='I', destination='R', equation='gamma*I',
                           transition_type=TransitionType.T),
                Transition(origin='I', destination='D', equation='mu*I',
                           transition_type=TransitionType.T),
                Transition(origin='I', destination='I_c', equation=c_2s+'c_2*(I+I_c)*I',
                           transition_type=TransitionType.T),
                Transition(origin='I_c', destination='R', equation='gamma*I_c',
                           transition_type=TransitionType.T),
                Transition(origin='I_c', destination='I', equation='c_1*I_c',
                           transition_type=TransitionType.T),
                Transition(origin='I_c', destination='D', equation='mu*I_c',
                           transition_type=TransitionType.T)  #,
                ]

            model = DeterministicOde(state, param_list, transition=transition)
            model.modelname='SC2IR'

            model.ei=1
            model.confirmed=slice(1,5)  # cases 1-3 i.e. I, R and D
            model.recovered=slice(2,3)
            model.deaths=slice(3,4)
            model.all_susceptibles=[0,5]
            model.S_c=5
            model.I_1 = 1
            x0_SC2IR = [1.0-I_0, I_0, 0.0, 0.0, 0.0, 0.0]
            model.initial_values = (x0_SC2IR, 0)

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn

    if mod_name == 'SC2FIR':
        if age_structure:                                         # age_structure is integer number of age compartments
            state0 = ['S', 'I', 'R', 'D', 'I_c', 'S_c', 'S_f']
            sa,state = state_age(state0,age_structure)

            param_list0 = ['beta', 'gamma', 'mu', 'c_0', 'c_1', 'c_2', 'c_3', 'c_4', 'N']
            param_list,contact = param_list_age(param_list0.copy(),age_structure)

            phi = phi_age(contact,sa,'I',age_structure)
            phi_c = phi_age(contact,sa,'I_c',age_structure)
            phi_1c = [p[0]+'+c_0*'+p[1] for p in zip(phi,phi_c)]   # '(I_1+c_0*I_c)' to corresponding phi combination
            sumI = state_sum_age('I',sa,age_structure)
            sumI_c = state_sum_age('I_c',sa,age_structure)

            transition = []
            transition = transition_age(transition,'S','I','beta*','S',sa,TransitionType.T,age_structure,phi=phi_1c)
            transition = transition_age(transition,'S_f','I','beta*','S_f',sa,TransitionType.T,age_structure,phi=phi_1c)
            transition = transition_age(transition,'S','S_c',c_2s+'c_2*('+sumI+'+'+sumI_c+')'+'*','S',sa,TransitionType.T,age_structure,
                                        yfactor=c_2s+'c_3*('+sumI+'+'+sumI_c+')'+'*')
            transition = transition_age(transition,'S_c','S_f','c_1*','S_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'S_f','S','c_4*','S_f',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'S_c','I_c','c_0*beta*','S_c',sa,TransitionType.T,age_structure,phi=phi_1c)
            transition = transition_age(transition,'I','R','gamma*','I',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I','D','mu*','I',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I','I_c',c_2s+'c_2*('+sumI+'+'+sumI_c+')'+'*','I',sa,TransitionType.T,age_structure,
                                        yfactor=c_2s+'c_3*('+sumI+'+'+sumI_c+')'+'*')
            transition = transition_age(transition,'I_c','R','gamma*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','D','mu*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','I','c_1*','I_c',sa,TransitionType.T,age_structure)

            model = DeterministicOde(state, param_list, transition=transition)
            if model == None:
                print('Error in make_model constructing DeterministicOde (in pygom)')
            model.modelname=mod_name+'_A'+str(age_structure)
            model.ei=slice(1*age_structure,2*age_structure)
            model.confirmed=slice(1*age_structure,5*age_structure)
            model.recovered=slice(2*age_structure,3*age_structure)
            model.deaths=slice(3*age_structure,4*age_structure)
            model.all_susceptibles=[slice(0,1*age_structure),slice(5*age_structure,7*age_structure)]
            model.S_c=slice(5*age_structure,6*age_structure)

            first_infected_agegroup = int(age_structure//4)       # first approximation : would give 20-25 year olds for 16 group 0-80 in 5 year intervals
            model.I_1 = 1*age_structure + first_infected_agegroup
            #x0 = [1.0-I_0, I_0, 0.0, 0.0]
            x0_SC2FIR = initial_state_age(I_0,state0,'I',first_infected_agegroup,age_structure)
            model.initial_values = (x0_SC2FIR, 0) # 0 for t[0]

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn
        else:
            state = ['S', 'I', 'R', 'D', 'I_c', 'S_c', 'S_f']
            param_list = ['beta', 'gamma', 'mu', 'c_0', 'c_1', 'c_2', 'c_4', 'N']

            transition = [
                Transition(origin='S', destination='I', equation='beta*(I+c_0*I_c)*S',transition_type=TransitionType.T),
                Transition(origin='S_f', destination='I', equation='beta*(I+c_0*I_c)*S_f',transition_type=TransitionType.T),
                Transition(origin='S', destination='S_c', equation=c_2s+'c_2*(I+I_c)*S',transition_type=TransitionType.T),
                Transition(origin='S_c', destination='S_f', equation='c_1*S_c',transition_type=TransitionType.T),
                Transition(origin='S_f', destination='S', equation='c_4*S_f',transition_type=TransitionType.T),
                Transition(origin='S_c', destination='I_c', equation='c_0*beta*(I+c_0*I_c)*S_c',transition_type=TransitionType.T),
                Transition(origin='I', destination='R', equation='gamma*I',transition_type=TransitionType.T),
                Transition(origin='I', destination='D', equation='mu*I',transition_type=TransitionType.T),
                Transition(origin='I', destination='I_c', equation=c_2s+'c_2*(I+I_c)*I',transition_type=TransitionType.T),
                Transition(origin='I_c', destination='R', equation='gamma*I_c',transition_type=TransitionType.T),
                Transition(origin='I_c', destination='I', equation='c_1*I_c',transition_type=TransitionType.T),
                Transition(origin='I_c', destination='D', equation='mu*I_c',transition_type=TransitionType.T)
                ]

            model = DeterministicOde(state, param_list, transition=transition)
            model.modelname='SC2FIR'

            model.ei=1
            model.confirmed=slice(1,5)  # cases 1-3 i.e. I, R and D
            model.recovered=slice(2,3)
            model.deaths=slice(3,4)
            model.all_susceptibles=[0,5,6]
            model.S_c=5
            model.I_1 = 1
            x0_SC2FIR = [1.0-I_0, I_0, 0.0, 0.0, 0.0, 0.0, 0.0]
            model.initial_values = (x0_SC2FIR, 0)

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn

    if mod_name == 'SEIR':
        if age_structure:                                         # age_structure is integer number of age compartments
            state0 = ['S', 'E', 'I', 'R', 'D']
            sa,state = state_age(state0,age_structure)

            param_list0 = ['beta','alpha', 'gamma','mu','N']
            param_list,contact = param_list_age(param_list0.copy(),age_structure)

            phi = phi_age(contact,sa,'I',age_structure)
            # note that beta_2 and beta_3 are set to zero in default installation, and with age-dept I3 models we enforce this
            transition = []
            transition = transition_age(transition,'S','E','beta *','S',sa,TransitionType.T,age_structure,phi=phi)
            transition = transition_age(transition,'E','I','alpha * ','E',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I','R','gamma * ','I',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I','D','mu * ','I',sa,TransitionType.T,age_structure)

            model = DeterministicOde(state, param_list, transition=transition)
            if model == None:
                print('Error in make_model constructing DeterministicOde (in pygom)')
            model.modelname=mod_name+'_A'+str(age_structure)
            model.ei=slice(1*age_structure,3*age_structure)
            model.confirmed=slice(2*age_structure,5*age_structure)
            model.recovered=slice(3*age_structure,4*age_structure)
            model.deaths=slice(4*age_structure,5*age_structure)

            first_infected_agegroup = int(age_structure//4)       # first approximation : would give 20-25 year olds for 16 group 0-80 in 5 year intervals
            model.I_1 = 2*age_structure + first_infected_agegroup
            x0_SEIR = initial_state_age(I_0,state0,'E',first_infected_agegroup,age_structure)
            model.initial_values = (x0_SEIR, 0) # 0 for t[0]

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn
        else:
            state = ['S', 'E', 'I', 'R', 'D']
            param_list = ['beta', 'alpha', 'gamma', 'mu', 'N']

            transition = [
                Transition(origin='S', destination='E', equation='beta*I*S',
                           transition_type=TransitionType.T),
                Transition(origin='E', destination='I', equation='alpha*E',
                           transition_type=TransitionType.T),
                Transition(origin='I', destination='R', equation='gamma*I',
                           transition_type=TransitionType.T),
                Transition(origin='I', destination='D', equation='mu*I',
                           transition_type=TransitionType.T)
                ]

            model = DeterministicOde(state, param_list, transition=transition)
            model.modelname='SEIR'
            model.ei=slice(1,3) # cases 1,2 i.e. E and I
            model.confirmed=slice(2,5)  # cases 2-4 i.e. I, R and D, not E
            model.recovered=slice(3,4)
            model.deaths=slice(4,5)
            model.I_1 = 2
            x0_SEIR = [1.0-I_0, 0.0, I_0, 0.0, 0.0]
            model.initial_values = (x0_SEIR, 0)

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn

    if mod_name == 'SCEIR': # this is a simpler version of the caution extension, not extended to U,F, or _A
        if age_structure:  # age_structure is integer number of age compartments
            print('Error: Age structure NYI for model',mod_name)
        else:
            state = ['S', 'E', 'I', 'R', 'D', 'S_c']
            param_list = ['beta', 'alpha', 'gamma', 'mu', 'c_0', 'c_1', 'c_2', 'N']

            transition = [
                Transition(origin='S', destination='E', equation='beta*I*S',
                           transition_type=TransitionType.T),
                Transition(origin='S', destination='S_c', equation=c_2s+'c_2*I*S',
                           transition_type=TransitionType.T),
                Transition(origin='S_c', destination='S', equation='c_1*S_c',
                           transition_type=TransitionType.T),
                Transition(origin='S_c', destination='E', equation='c_0*beta*I*S_c',
                           transition_type=TransitionType.T),
                Transition(origin='E', destination='I', equation='alpha*E',
                           transition_type=TransitionType.T),
                Transition(origin='I', destination='R', equation='gamma*I',
                           transition_type=TransitionType.T),
                Transition(origin='I', destination='D', equation='mu*I',
                           transition_type=TransitionType.T)
                ]

            model = DeterministicOde(state, param_list, transition=transition)
            model.modelname='SCEIR'
            model.ei=slice(1,3) # cases 1,2 i.e. E,I
            model.confirmed=slice(2,5)  # cases 2-4 i.e. I, R and D, not E
            model.recovered=slice(3,4)
            model.deaths=slice(4,5)
            model.all_susceptibles=[0,5]
            model.S_c=5
            model.I_1 = 2
            x0_SCEIR = [1.0-I_0, 0.0, I_0, 0.0, 0.0, 0.0]
            model.initial_values = (x0_SCEIR, 0)
            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn
    """
    if mod_name == 'SCFEIR':  # extension suppressed because C version too simple : use C3
        if age_structure:  # age_structure is integer number of age compartments
            print('Error: Age structure NYI for model',mod_name)
        else:
            state = ['S', 'E', 'I', 'R', 'D', 'S_c', 'S_f']
            param_list = ['beta', 'alpha', 'gamma', 'mu', 'c_0', 'c_1', 'c_2', 'N']

            transition = [
                Transition(origin='S', destination='E', equation='beta*I*S',
                           transition_type=TransitionType.T),
                Transition(origin='S_f', destination='E', equation='beta*I*S_f',
                           transition_type=TransitionType.T),
                Transition(origin='S', destination='S_c', equation=c_2s+'c_2*I*S',
                           transition_type=TransitionType.T),
                Transition(origin='S_c', destination='S_f', equation='c_1*S_c',
                           transition_type=TransitionType.T),
                Transition(origin='S_f', destination='S', equation='c_1*S_f',
                           transition_type=TransitionType.T),
                Transition(origin='S_c', destination='E', equation='c_0*beta*I*S_c',
                           transition_type=TransitionType.T),
                Transition(origin='E', destination='I', equation='alpha*E',
                           transition_type=TransitionType.T),
                Transition(origin='I', destination='R', equation='gamma*I',
                           transition_type=TransitionType.T),
                Transition(origin='I', destination='D', equation='mu*I',
                           transition_type=TransitionType.T)
                ]

            model = DeterministicOde(state, param_list, transition=transition)
            model.modelname='SCFEIR'
            model.ei=slice(1,3) # cases 1,2 i.e. E,I
            model.confirmed=slice(2,5)  # cases 2-4 i.e. I, R and D, not E
            model.recovered=slice(3,4)
            model.deaths=slice(4,5)
            model.all_susceptibles=[0,5,6]
            model.S_c=5
            model.I_1 = 2
            x0_SCFEIR = [1.0-I_0, 0.0, I_0, 0.0, 0.0, 0.0, 0.0]
            model.initial_values = (x0_SCFEIR, 0)
            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn
    """

    if mod_name == 'SC3EIR':
        if age_structure:  # age_structure is integer number of age compartments
            state0 = ['S', 'E', 'I', 'R', 'D', 'I_c', 'S_c', 'E_c']
            sa,state = state_age(state0,age_structure)

            param_list0 = ['beta_1', 'beta','alpha', 'gamma','mu','c_0','c_1','c_2','c_3','N']
            param_list,contact = param_list_age(param_list0.copy(),age_structure)

            phi = phi_age(contact,sa,'I',age_structure)
            phi_c = phi_age(contact,sa,'I_c',age_structure)
            phi_1c = [p[0]+'+c_0*'+p[1] for p in zip(phi,phi_c)]   # '(I_1+c_0*I_c)' to corresponding phi combination
            sumI = state_sum_age('I',sa,age_structure)

            transition = []
            transition = transition_age(transition,'S','E','beta*','S',sa,TransitionType.T,age_structure,phi=phi_1c)
            transition = transition_age(transition,'S','S_c',c_2s+'c_2*'+sumI_3+'*','S',sa,TransitionType.T,age_structure,
                                        yfactor=c_2s+'c_3*'+sumI_3+'*')  # c_2s+'c_2*I*S'
            transition = transition_age(transition,'S_c','S','c_1*','S_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'S_c','E_c','c_0*beta*','S_c',sa,TransitionType.T,age_structure,phi=phi_1c) # 'c_0*beta*(I+c_0*I_c)*S_c'
            transition = transition_age(transition,'E','I','alpha*','E',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E','E_c',c_2s+'c_2*'+sumI_3+'*','E',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E_c','I_c','alpha*','E_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E_c','E','c_1*','E_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I','R','gamma*','I',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I','I_c',c_2s+'c_2*'+sumI+'*','I',sa,TransitionType.T,age_structure,
                                        yfactor=c_2s+'c_3*'+sumI+'*')  # c_2s+'c_2*I*I'
            transition = transition_age(transition,'I','D','mu*','I',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','R','gamma*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','I','c_1*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','D','mu*','I_c',sa,TransitionType.T,age_structure)

            model = DeterministicOde(state, param_list, transition=transition)
            if model == None:
                print('Error in make_model constructing DeterministicOde (in pygom)')
            model.modelname=mod_name+'_A'+str(age_structure)
            model.ei=slice(1*age_structure,3*age_structure)
            model.confirmed=slice(2*age_structure,6*age_structure)
            model.recovered=slice(3*age_structure,4*age_structure)
            model.deaths=slice(4*age_structure,5*age_structure)
            model.all_susceptibles=[slice(0,1*age_structure),slice(6*age_structure,7*age_structure)]   # CHECK that this works !!!!!!!!!!!!!!!!!!
            model.S_c=slice(6*age_structure,7*age_structure)

            first_infected_agegroup = int(age_structure//4)       # first approximation : would give 20-25 year olds for 16 group 0-80 in 5 year intervals
            model.I_1 = 1*age_structure + first_infected_agegroup
            #x0 = [1.0-I_0, I_0, 0.0, 0.0]
            x0_SC3EIR = initial_state_age(I_0,state0,'E',first_infected_agegroup,age_structure)
            model.initial_values = (x0_SC3EIR, 0) # 0 for t[0]

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn
        else:
            state = ['S', 'E', 'I', 'R', 'D', 'I_c', 'S_c', 'E_c']
            param_list = ['beta', 'alpha', 'gamma', 'mu', 'c_0', 'c_1', 'c_2', 'N']

            transition = [
                Transition(origin='S',   destination='E',   equation='beta*(I+c_0*I_c)*S',      transition_type=TransitionType.T),
                Transition(origin='S',   destination='S_c', equation=c_2s+'c_2*(I+I_c)*S',      transition_type=TransitionType.T),
                Transition(origin='S_c', destination='S',   equation='c_1*S_c',                 transition_type=TransitionType.T),
                Transition(origin='S_c', destination='E_c', equation='c_0*beta*(I+c_0*I_c)*S_c',transition_type=TransitionType.T),
                Transition(origin='E',   destination='I',   equation='alpha*E',                 transition_type=TransitionType.T),
                Transition(origin='E',   destination='E_c', equation=c_2s+'c_2*(I+I_c)*E',      transition_type=TransitionType.T),
                Transition(origin='E_c', destination='I_c', equation='alpha*E_c',               transition_type=TransitionType.T),
                Transition(origin='E_c', destination='E',   equation='c_1*E_c',                 transition_type=TransitionType.T),
                Transition(origin='I',   destination='R',   equation='gamma*I',                 transition_type=TransitionType.T),
                Transition(origin='I',   destination='I_c', equation=c_2s+'c_2*(I+I_c)*I',      transition_type=TransitionType.T),
                Transition(origin='I',   destination='D',   equation='mu*I',                    transition_type=TransitionType.T),
                Transition(origin='I_c', destination='R',   equation='gamma*I_c',               transition_type=TransitionType.T),
                Transition(origin='I_c', destination='I',   equation='c_1*I_c',                 transition_type=TransitionType.T),
                Transition(origin='I_c', destination='D',   equation='mu*I_c',                  transition_type=TransitionType.T)
                ]

            model = DeterministicOde(state, param_list, transition=transition)
            model.modelname='SC3EIR'
            model.ei=slice(1,3) # cases 1,2 i.e. E,I  # note E_c and I_c not included
            model.confirmed=slice(2,6)  # cases 2-5 i.e. I, R, D, and I_c, not E, E_c
            model.recovered=slice(3,4)
            model.deaths=slice(4,5)
            model.all_susceptibles=[0,6]
            model.S_c=6
            model.I_1 = 2
            x0_SC3EIR = [1.0-I_0, 0.0, I_0, 0.0, 0.0, 0.0, 0.0, 0.0]
            model.initial_values = (x0_SC3EIR, 0)

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn

    if mod_name == 'SC3FEIR':
        if age_structure:  # age_structure is integer number of age compartments
            state0 = ['S', 'E', 'I', 'R', 'D', 'I_c', 'S_c', 'E_c', 'S_f']
            sa,state = state_age(state0,age_structure)

            param_list0 = ['beta_1', 'beta','alpha', 'gamma','mu','c_0','c_1','c_2','c_3','c_4','N']
            param_list,contact = param_list_age(param_list0.copy(),age_structure)

            phi = phi_age(contact,sa,'I',age_structure)
            phi_c = phi_age(contact,sa,'I_c',age_structure)
            phi_1c = [p[0]+'+c_0*'+p[1] for p in zip(phi,phi_c)]   # '(I_1+c_0*I_c)' to corresponding phi combination
            sumI = state_sum_age('I',sa,age_structure)

            transition = []
            transition = transition_age(transition,'S','E','beta*','S',sa,TransitionType.T,age_structure,phi=phi_1c)
            transition = transition_age(transition,'S_f','E','beta*','S_f',sa,TransitionType.T,age_structure,phi=phi_1c)
            transition = transition_age(transition,'S','S_c',c_2s+'c_2*'+sumI_3+'*','S',sa,TransitionType.T,age_structure,
                                        yfactor=c_2s+'c_3*'+sumI_3+'*')  # c_2s+'c_2*I*S'
            transition = transition_age(transition,'S_c','S_f','c_1*','S_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'S_f','S','c_4*','S_f',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'S_c','E_c','c_0*beta*','S_c',sa,TransitionType.T,age_structure,phi=phi_1c) # 'c_0*beta*(I+c_0*I_c)*S_c'
            transition = transition_age(transition,'E','I','alpha*','E',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E','E_c',c_2s+'c_2*'+sumI_3+'*','E',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E_c','I_c','alpha*','E_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E_c','E','c_1*','E_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I','R','gamma*','I',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I','I_c',c_2s+'c_2*'+sumI+'*','I',sa,TransitionType.T,age_structure,
                                        yfactor=c_2s+'c_3*'+sumI+'*')  # c_2s+'c_2*I*I'
            transition = transition_age(transition,'I','D','mu*','I',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','R','gamma*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','I','c_1*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','D','mu*','I_c',sa,TransitionType.T,age_structure)

            model = DeterministicOde(state, param_list, transition=transition)
            if model == None:
                print('Error in make_model constructing DeterministicOde (in pygom)')
            model.modelname=mod_name+'_A'+str(age_structure)
            model.ei=slice(1*age_structure,3*age_structure)
            model.confirmed=slice(2*age_structure,6*age_structure)
            model.recovered=slice(3*age_structure,4*age_structure)
            model.deaths=slice(4*age_structure,5*age_structure)
            model.all_susceptibles=[slice(0,1*age_structure),slice(6*age_structure,7*age_structure),slice(8*age_structure,9*age_structure)]
            model.S_c=slice(6*age_structure,7*age_structure)

            first_infected_agegroup = int(age_structure//4)       # first approximation : would give 20-25 year olds for 16 group 0-80 in 5 year intervals
            model.I_1 = 1*age_structure + first_infected_agegroup
            #x0 = [1.0-I_0, I_0, 0.0, 0.0]
            x0_SC3EIR = initial_state_age(I_0,state0,'E',first_infected_agegroup,age_structure)
            model.initial_values = (x0_SC3EIR, 0) # 0 for t[0]

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn
        else:
            state = ['S', 'E', 'I', 'R', 'D', 'I_c', 'S_c', 'E_c','S_f']
            param_list = ['beta', 'alpha', 'gamma', 'mu', 'c_0', 'c_1', 'c_2', 'c_4', 'N']

            transition = [
                Transition(origin='S',   destination='E',   equation='beta*(I+c_0*I_c)*S',      transition_type=TransitionType.T),
                Transition(origin='S_f', destination='E',   equation='beta*(I+c_0*I_c)*S_f',    transition_type=TransitionType.T),
                Transition(origin='S',   destination='S_c', equation=c_2s+'c_2*(I+I_c)*S',      transition_type=TransitionType.T),
                Transition(origin='S_c', destination='S_f', equation='c_1*S_c',                 transition_type=TransitionType.T),
                Transition(origin='S_f', destination='S',   equation='c_4*S_f',                 transition_type=TransitionType.T),
                Transition(origin='S_c', destination='E_c', equation='c_0*beta*(I+c_0*I_c)*S_c',transition_type=TransitionType.T),
                Transition(origin='E',   destination='I',   equation='alpha*E',                 transition_type=TransitionType.T),
                Transition(origin='E',   destination='E_c', equation=c_2s+'c_2*(I+I_c)*E',      transition_type=TransitionType.T),
                Transition(origin='E_c', destination='I_c', equation='alpha*E_c',               transition_type=TransitionType.T),
                Transition(origin='E_c', destination='E',   equation='c_1*E_c',                 transition_type=TransitionType.T),
                Transition(origin='I',   destination='R',   equation='gamma*I',                 transition_type=TransitionType.T),
                Transition(origin='I',   destination='I_c', equation=c_2s+'c_2*(I+I_c)*I',      transition_type=TransitionType.T),
                Transition(origin='I',   destination='D',   equation='mu*I',                    transition_type=TransitionType.T),
                Transition(origin='I_c', destination='R',   equation='gamma*I_c',               transition_type=TransitionType.T),
                Transition(origin='I_c', destination='I',   equation='c_1*I_c',                 transition_type=TransitionType.T),
                Transition(origin='I_c', destination='D',   equation='mu*I_c',                  transition_type=TransitionType.T)
                ]

            model = DeterministicOde(state, param_list, transition=transition)
            model.modelname='SC3FEIR'
            model.ei=slice(1,3) # cases 1,2 i.e. E,I  # note E_c and I_c not included
            model.confirmed=slice(2,6)  # cases 2-5 i.e. I, R, D, and I_c, not E, E_c
            model.recovered=slice(3,4)
            model.deaths=slice(4,5)
            model.all_susceptibles=[0,6,8]
            model.S_c=6
            model.I_1 = 2
            x0_SC3FEIR = [1.0-I_0, 0.0, I_0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
            model.initial_values = (x0_SC3FEIR, 0)

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn

    if mod_name == 'SEI3R':
        if age_structure:                                         # age_structure is integer number of age compartments
            state0 = ['S', 'E', 'I_1', 'I_2', 'I_3', 'R', 'D']
            sa,state = state_age(state0,age_structure)

            param_list0 = ['beta_1', 'beta_2','beta_3','alpha', 'gamma_1', 'gamma_2', 'gamma_3',
                          'p_1','p_2','mu','N']
            param_list,contact = param_list_age(param_list0.copy(),age_structure)

            phi = phi_age(contact,sa,'I_1',age_structure)
            # note that beta_2 and beta_3 are set to zero in default installation, and with age-dept I3 models we enforce this
            transition = []
            transition = transition_age(transition,'S','E','beta_1 *','S',sa,TransitionType.T,age_structure,phi=phi)
            transition = transition_age(transition,'E','I_1','alpha * ','E',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_1','R','gamma_1 * ','I_1',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_2','R','gamma_2 * ','I_2',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_3','R','gamma_3 * ','I_3',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_1','I_2','p_1 * ','I_1',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_2','I_3','p_2 * ','I_2',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_3','D','mu * ','I_3',sa,TransitionType.T,age_structure)

            model = DeterministicOde(state, param_list, transition=transition)
            if model == None:
                print('Error in make_model constructing DeterministicOde (in pygom)')
            model.modelname='SEI3R'+'_A'+str(age_structure)
            model.ei=slice(1*age_structure,5*age_structure)
            model.confirmed=slice(2*age_structure,7*age_structure)
            model.recovered=slice(5*age_structure,6*age_structure)
            model.deaths=slice(6*age_structure,7*age_structure)

            first_infected_agegroup = int(age_structure//4)       # first approximation : would give 20-25 year olds for 16 group 0-80 in 5 year intervals
            model.I_1 = 1*age_structure + first_infected_agegroup
            #x0 = [1.0-I_0, I_0, 0.0, 0.0]
            x0_SEI3R = initial_state_age(I_0,state0,'E',first_infected_agegroup,age_structure)
            model.initial_values = (x0_SEI3R, 0) # 0 for t[0]

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn
        else:
            state = ['S', 'E', 'I_1', 'I_2','I_3','R','D']
            param_list = ['beta_1', 'beta_2','beta_3','alpha', 'gamma_1', 'gamma_2', 'gamma_3',
                          'p_1','p_2','mu','N']

            transition = [
                Transition(origin='S', destination='E', equation='(beta_1*I_1+beta_2*I_2+beta_3*I_3)*S',
                           transition_type=TransitionType.T),
                Transition(origin='E', destination='I_1', equation='alpha*E',
                           transition_type=TransitionType.T),
                Transition(origin='I_1', destination='R', equation='gamma_1*I_1',
                           transition_type=TransitionType.T),
                Transition(origin='I_2', destination='R', equation='gamma_2*I_2',
                           transition_type=TransitionType.T),
                Transition(origin='I_3', destination='R', equation='gamma_3*I_3',
                           transition_type=TransitionType.T),
                Transition(origin='I_1', destination='I_2', equation='p_1*I_1',
                           transition_type=TransitionType.T),
                Transition(origin='I_2', destination='I_3', equation='p_2*I_2',
                           transition_type=TransitionType.T),
                Transition(origin='I_3', destination='D', equation='mu*I_3',
                           transition_type=TransitionType.T)
                ]

            model = DeterministicOde(state, param_list, transition=transition)
            model.modelname='SEI3R'
            model.ei=slice(1,5)
            model.confirmed=slice(2,7)  # cases 2-6 i.e. I1, I2, I3, R and D
            model.recovered=slice(5,6)
            model.deaths=slice(6,7)
            model.I_1 = 2
            x0_SEI3R = [1.0-I_0, 0.0, I_0, 0.0, 0.0, 0.0, 0.0]
            model.initial_values = (x0_SEI3R, 0)

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn

    if mod_name == 'SCEI3R':
        if age_structure:  # age_structure is integer number of age compartments
            print('Error: Age structure NYI for model',mod_name)
        else:
            state = ['S', 'E', 'I_1', 'I_2','I_3','R','D','S_c']
            param_list = ['beta_1', 'beta_2','beta_3','alpha', 'gamma_1', 'gamma_2', 'gamma_3',
                          'p_1','p_2','mu','c_0','c_1','c_2','N']

            transition = [
                Transition(origin='S', destination='E', equation='(beta_1*I_1+beta_2*I_2+beta_3*I_3)*S',
                           transition_type=TransitionType.T),
                Transition(origin='S', destination='S_c', equation=c_2s+'c_2*I_3*S',
                           transition_type=TransitionType.T),
                Transition(origin='S_c', destination='S', equation='c_1*S_c',
                           transition_type=TransitionType.T),
                Transition(origin='S_c', destination='E', equation='c_0*(beta_1*I_1+beta_2*I_2+beta_3*I_3)*S_c',
                           transition_type=TransitionType.T),
                Transition(origin='E', destination='I_1', equation='alpha*E',
                           transition_type=TransitionType.T),
                Transition(origin='I_1', destination='R', equation='gamma_1*I_1',
                           transition_type=TransitionType.T),
                Transition(origin='I_2', destination='R', equation='gamma_2*I_2',
                           transition_type=TransitionType.T),
                Transition(origin='I_3', destination='R', equation='gamma_3*I_3',
                           transition_type=TransitionType.T),
                Transition(origin='I_1', destination='I_2', equation='p_1*I_1',
                           transition_type=TransitionType.T),
                Transition(origin='I_2', destination='I_3', equation='p_2*I_2',
                           transition_type=TransitionType.T),
                Transition(origin='I_3', destination='D', equation='mu*I_3',
                           transition_type=TransitionType.T)
                ]

            model = DeterministicOde(state, param_list, transition=transition)
            model.modelname='SCEI3R'
            model.ei=slice(1,5)
            model.confirmed=slice(2,7)  # cases 2-6 i.e. I1, I2, I3, R and D
            model.recovered=slice(5,6)
            model.deaths=slice(6,7)
            model.all_susceptibles=[0,7]
            model.S_c=7
            model.I_1 = 2
            x0_SCEI3R = [1.0-I_0, 0.0, I_0, 0.0, 0.0, 0.0, 0.0, 0.0]
            model.initial_values = (x0_SCEI3R, 0)

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn

    if mod_name == 'SC3EI3R':
        if age_structure:  # age_structure is integer number of age compartments
            state0 = ['S', 'E', 'I_1', 'I_2','I_3', 'R', 'D', 'I_c', 'S_c', 'E_c']
            sa,state = state_age(state0,age_structure)

            param_list0 = ['beta_1', 'beta_2','beta_3','alpha', 'gamma_1', 'gamma_2', 'gamma_3',
                          'p_1','p_2','mu','c_0','c_1','c_2','c_3','N']
            param_list,contact = param_list_age(param_list0.copy(),age_structure)

            phi = phi_age(contact,sa,'I_1',age_structure)
            phi_c = phi_age(contact,sa,'I_c',age_structure)
            phi_1c = [p[0]+'+c_0*'+p[1] for p in zip(phi,phi_c)]   # '(I_1+c_0*I_c)' to corresponding phi combination
            sumI_3 = state_sum_age('I_3',sa,age_structure)

            # note that beta_2 and beta_3 are set to zero in default installation, and with age-dept I3 models we enforce this
            transition = []
            transition = transition_age(transition,'S','E','beta_1*','S',sa,TransitionType.T,age_structure,phi=phi_1c)
            transition = transition_age(transition,'S_c','E_c','c_0*beta_1*','S_c',sa,TransitionType.T,age_structure,phi=phi_1c) # 'c_0*beta_1*(I_1+c_0*I_c)*S_c'
            transition = transition_age(transition,'S','S_c',c_2s+'c_2*'+sumI_3+'*','S',sa,TransitionType.T,age_structure,
                                        yfactor=c_2s+'c_3*'+sumI_3+'*')  # c_2s+'c_2*I_3*S'
            transition = transition_age(transition,'S_c','S','c_1*','S_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E','I_1','alpha*','E',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E','E_c',c_2s+'c_2*'+sumI_3+'*','E',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E_c','I_c','alpha*','E_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E_c','E','c_1*','E_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_1','R','gamma_1*','I_1',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_1','I_c',c_2s+'c_2*'+sumI_3+'*','I_1',sa,TransitionType.T,age_structure,
                                        yfactor=c_2s+'c_3*'+sumI_3+'*')  # c_2s+'c_2*I_3*I_1'
            transition = transition_age(transition,'I_c','R','gamma_1*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','I_1','c_1*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_2','R','gamma_2*','I_2',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_3','R','gamma_3*','I_3',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_1','I_2','p_1*','I_1',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','I_2','p_1*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_2','I_3','p_2*','I_2',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_3','D','mu*','I_3',sa,TransitionType.T,age_structure)

            model = DeterministicOde(state, param_list, transition=transition)
            if model == None:
                print('Error in make_model constructing DeterministicOde (in pygom)')
            model.modelname='SC3EI3R'+'_A'+str(age_structure)
            model.ei=slice(1*age_structure,5*age_structure)
            model.confirmed=slice(2*age_structure,8*age_structure)
            model.recovered=slice(5*age_structure,6*age_structure)
            model.deaths=slice(6*age_structure,7*age_structure)
            model.all_susceptibles=[slice(0,1*age_structure),slice(8*age_structure,9*age_structure)]   # CHECK that this works !!!!!!!!!!!!!!!!!!
            model.S_c=slice(8*age_structure,9*age_structure)

            first_infected_agegroup = int(age_structure//4)       # first approximation : would give 20-25 year olds for 16 group 0-80 in 5 year intervals
            model.I_1 = 2*age_structure + first_infected_agegroup

            #x0 = [1.0-I_0, I_0, 0.0, 0.0]
            x0_SC3EI3R = initial_state_age(I_0,state0,'E',first_infected_agegroup,age_structure)
            model.initial_values = (x0_SC3EI3R, 0) # 0 for t[0]

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn
        else:
            state = ['S', 'E', 'I_1', 'I_2','I_3', 'R', 'D', 'I_c', 'S_c', 'E_c']
            param_list = ['beta_1', 'beta_2','beta_3','alpha', 'gamma_1', 'gamma_2', 'gamma_3',
                          'p_1','p_2','mu','c_0','c_1','c_2','N']

            transition = [
                Transition(origin='S', destination='E', equation='(beta_1*I_1+beta_2*I_2+beta_3*I_3+c_0*beta_1*I_c)*S',
                           transition_type=TransitionType.T),
                Transition(origin='S_c', destination='E_c', equation='c_0*(beta_1*I_1+beta_2*I_2+beta_3*I_3+c_0*beta_1*I_c)*S_c',
                           transition_type=TransitionType.T),
                Transition(origin='S', destination='S_c', equation=c_2s+'c_2*I_3*S',
                           transition_type=TransitionType.T),
                Transition(origin='S_c', destination='S', equation='c_1*S_c',
                           transition_type=TransitionType.T),
                Transition(origin='E', destination='I_1', equation='alpha*E',
                           transition_type=TransitionType.T),
                Transition(origin='E', destination='E_c', equation=c_2s+'c_2*I_3*E',
                           transition_type=TransitionType.T),
                Transition(origin='E_c', destination='I_c', equation='alpha*E_c',
                           transition_type=TransitionType.T),
                Transition(origin='E_c', destination='E', equation='c_1*E_c',
                           transition_type=TransitionType.T),
                Transition(origin='I_1', destination='R', equation='gamma_1*I_1',
                           transition_type=TransitionType.T),
                Transition(origin='I_1', destination='I_c', equation=c_2s+'c_2*I_3*I_1',
                           transition_type=TransitionType.T),
                Transition(origin='I_c', destination='R', equation='gamma_1*I_c',
                           transition_type=TransitionType.T),
                Transition(origin='I_c', destination='I_1', equation='c_1*I_c',
                           transition_type=TransitionType.T),
                Transition(origin='I_2', destination='R', equation='gamma_2*I_2',
                           transition_type=TransitionType.T),
                Transition(origin='I_3', destination='R', equation='gamma_3*I_3',
                           transition_type=TransitionType.T),
                Transition(origin='I_1', destination='I_2', equation='p_1*I_1',
                           transition_type=TransitionType.T),
                Transition(origin='I_c', destination='I_2', equation='p_1*I_c',
                           transition_type=TransitionType.T),
                Transition(origin='I_2', destination='I_3', equation='p_2*I_2',
                           transition_type=TransitionType.T),
                Transition(origin='I_3', destination='D', equation='mu*I_3',
                           transition_type=TransitionType.T)
                ]

            model = DeterministicOde(state, param_list, transition=transition)
            model.modelname='SC3EI3R'
            model.ei=slice(1,5) # 1,2,3,4 i.e. E,I_1,I_2,I_3 – not E_c and I_c
            model.confirmed=slice(2,8)  # cases 2-7 i.e. I1, I2, I3, R, D and I_c
            model.recovered=slice(5,6)
            model.deaths=slice(6,7)
            model.all_susceptibles=[0,8]
            model.S_c=8
            model.I_1 = 2
            x0_SC3EI3R = [1.0-I_0, 0.0, I_0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
            model.initial_values = (x0_SC3EI3R, 0)

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn

    if mod_name == 'SC3FEI3R':
        if age_structure:  # age_structure is integer number of age compartments
            state0 = ['S', 'E', 'I_1', 'I_2','I_3', 'R', 'D', 'I_c', 'S_c', 'S_f', 'E_c']
            sa,state = state_age(state0,age_structure)

            param_list0 = ['beta_1', 'beta_2','beta_3','alpha', 'gamma_1', 'gamma_2', 'gamma_3',
                          'p_1','p_2','mu','c_0','c_1','c_2','c_3','c_4','N']
            param_list,contact = param_list_age(param_list0.copy(),age_structure)

            phi = phi_age(contact,sa,'I_1',age_structure)
            phi_c = phi_age(contact,sa,'I_c',age_structure)
            phi_1c = [p[0]+'+c_0*'+p[1] for p in zip(phi,phi_c)]   # '(I_1+c_0*I_c)' to corresponding phi combination
            sumI_3 = state_sum_age('I_3',sa,age_structure)

            # note that beta_2 and beta_3 are set to zero in default installation, and with age-dept I3 models we enforce this
            transition = []
            transition = transition_age(transition,'S','E','beta_1*','S',sa,TransitionType.T,age_structure,phi=phi_1c)
            transition = transition_age(transition,'S_f','E','beta_1*','S_f',sa,TransitionType.T,age_structure,phi=phi_1c)
            transition = transition_age(transition,'S_c','E_c','c_0*beta_1*','S_c',sa,TransitionType.T,age_structure,phi=phi_1c) # 'c_0*beta_1*(I_1+c_0*I_c)*S_c'
            transition = transition_age(transition,'S','S_c',c_2s+'c_2*'+sumI_3+'*','S',sa,TransitionType.T,age_structure,
                                        yfactor=c_2s+'c_3*'+sumI_3+'*')  # c_2s+'c_2*I_3*S'
            transition = transition_age(transition,'S_c','S_f','c_1*','S_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'S_f','S','c_4*','S_f',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E','I_1','alpha*','E',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E','E_c',c_2s+'c_2*'+sumI_3+'*','E',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E_c','I_c','alpha*','E_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E_c','E','c_1*','E_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_1','R','gamma_1*','I_1',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_1','I_c',c_2s+'c_2*'+sumI_3+'*','I_1',sa,TransitionType.T,age_structure,
                                        yfactor=c_2s+'c_3*'+sumI_3+'*')  # c_2s+'c_2*I_3*I_1'
            transition = transition_age(transition,'I_c','R','gamma_1*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','I_1','c_1*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_2','R','gamma_2*','I_2',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_3','R','gamma_3*','I_3',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_1','I_2','p_1*','I_1',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','I_2','p_1*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_2','I_3','p_2*','I_2',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_3','D','mu*','I_3',sa,TransitionType.T,age_structure)

            model = DeterministicOde(state, param_list, transition=transition)
            if model == None:
                print('Error in make_model constructing DeterministicOde (in pygom)')
            model.modelname='SC3FEI3R'+'_A'+str(age_structure)
            model.ei=slice(1*age_structure,5*age_structure)
            model.confirmed=slice(2*age_structure,8*age_structure)
            model.recovered=slice(5*age_structure,6*age_structure)
            model.deaths=slice(6*age_structure,7*age_structure)
            model.all_susceptibles=[slice(0,1*age_structure),slice(8*age_structure,10*age_structure)]
            model.S_c=slice(8*age_structure,9*age_structure)

            first_infected_agegroup = int(age_structure//4)       # first approximation : would give 20-25 year olds for 16 group 0-80 in 5 year intervals
            model.I_1 = 1*age_structure + first_infected_agegroup
            #x0 = [1.0-I_0, I_0, 0.0, 0.0]
            x0_SC3FEI3R = initial_state_age(I_0,state0,'E',first_infected_agegroup,age_structure)
            model.initial_values = (x0_SC3FEI3R, 0) # 0 for t[0]

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn
        else:
            state = ['S', 'E', 'I_1', 'I_2','I_3', 'R', 'D', 'I_c', 'S_c', 'S_f', 'E_c']
            param_list = ['beta_1', 'beta_2','beta_3','alpha', 'gamma_1', 'gamma_2', 'gamma_3',
                          'p_1','p_2','mu','c_0','c_1','c_2','c_4','N']

            transition = [
                Transition(origin='S',   destination='E',   equation='(beta_1*I_1+beta_2*I_2+beta_3*I_3+c_0*beta_1*I_c)*S',
                                                                                transition_type=TransitionType.T),
                Transition(origin='S_f', destination='E',   equation='(beta_1*I_1+beta_2*I_2+beta_3*I_3+c_0*beta_1*I_c)*S_f',
                                                                                transition_type=TransitionType.T),
                Transition(origin='S_c', destination='E_c', equation='c_0*(beta_1*I_1+beta_2*I_2+beta_3*I_3+c_0*beta_1*I_c)*S_c',
                                                                                transition_type=TransitionType.T),
                Transition(origin='S',   destination='S_c', equation=c_2s+'c_2*I_3*S',transition_type=TransitionType.T),
                Transition(origin='S_c', destination='S_f', equation='c_1*S_c',transition_type=TransitionType.T),
                Transition(origin='S_f', destination='S',   equation='c_4*S_f',transition_type=TransitionType.T),
                Transition(origin='E',   destination='I_1', equation='alpha*E',transition_type=TransitionType.T),
                Transition(origin='E',   destination='E_c', equation=c_2s+'c_2*I_3*E',transition_type=TransitionType.T),
                Transition(origin='E_c', destination='I_c', equation='alpha*E_c',transition_type=TransitionType.T),
                Transition(origin='E_c', destination='E',   equation='c_1*E_c',transition_type=TransitionType.T),
                Transition(origin='I_1', destination='R',   equation='gamma_1*I_1',transition_type=TransitionType.T),
                Transition(origin='I_1', destination='I_c', equation=c_2s+'c_2*I_3*I_1',transition_type=TransitionType.T),
                Transition(origin='I_c', destination='R',   equation='gamma_1*I_c',transition_type=TransitionType.T),
                Transition(origin='I_c', destination='I_1', equation='c_1*I_c',transition_type=TransitionType.T),
                Transition(origin='I_2', destination='R',   equation='gamma_2*I_2',transition_type=TransitionType.T),
                Transition(origin='I_3', destination='R',   equation='gamma_3*I_3',transition_type=TransitionType.T),
                Transition(origin='I_1', destination='I_2', equation='p_1*I_1',transition_type=TransitionType.T),
                Transition(origin='I_c', destination='I_2', equation='p_1*I_c',transition_type=TransitionType.T),
                Transition(origin='I_2', destination='I_3', equation='p_2*I_2',transition_type=TransitionType.T),
                Transition(origin='I_3', destination='D',   equation='mu*I_3',transition_type=TransitionType.T)
                ]

            model = DeterministicOde(state, param_list, transition=transition)
            model.modelname='SC3FEI3R'
            model.ei=slice(1,5) # 1,2,3,4 i.e. E,I_1,I_2,I_3 – not E_c and I_c
            model.confirmed=slice(2,8)  # cases 2-7 i.e. I1, I2, I3, R, D and I_c
            model.recovered=slice(5,6)
            model.deaths=slice(6,7)
            model.all_susceptibles=[0,8,9]
            model.S_c=8
            model.I_1 = 2
            x0_SC3FEI3R = [1.0-I_0, 0.0, I_0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
            model.initial_values = (x0_SC3FEI3R, 0)

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn

    # this is the equation based (not transition based) version. The transition based version belows needs a birth and death section
    if mod_name == 'SC2UIR':
        if age_structure:  # age_structure is integer number of age compartments
            print('Error: Age structure NYI for model',mod_name)
        else:
            state = ['S', 'I', 'R', 'D', 'I_c', 'S_c', 'S_u', 'W']
            param_list = ['beta', 'gamma', 'mu', 'c_0', 'c_1', 'c_2', 'k_u', 'k_1', 'k_w','kappa', 'N']

            transition = [
                Transition(origin='S', equation='-beta*(I+c_0*I_c)*S+c_1*S_c-%f*c_2*(I+I_c)*S-k_u*(1-W)*S+k_1*S_u' % C_2s),
                Transition(origin='S_c', equation='-c_0*beta*(I+c_0*I_c)*S_c-c_1*S_c+%f*c_2*(I+I_c)*S-k_u*(1-W)*S_c' % C_2s),
                Transition(origin='S_u', equation='-beta*(I+c_0*I_c)*S_u+k_u*(1-W)*(S+S_c)-k_1*S_u'),
                Transition(origin='I', equation='beta*(I+c_0*I_c)*S-gamma*I-mu*I+c_1*I_c-%f*c_2*(I+I_c)*I' % C_2s),
                Transition(origin='I_c', equation='c_0*beta*(I+c_0*I_c)*S_c-gamma*I_c-mu*I_c-c_1*I_c+%f*c_2*(I+I_c)*I' % C_2s),
                Transition(origin='R', equation='gamma*(I+I_c)'),
                Transition(origin='D', equation='mu*(I+I_c)'),
                #Transition(origin='W', equation='0.')
                Transition(origin='W', equation='k_w*W*(1-kappa*S_c-W)')
                ]

            model = DeterministicOde(state, param_list, ode=transition)
            model.modelname='SC2UIR'
            model.ei=1                  # case 1 i.e. I  # note I_c not included
            model.confirmed=slice(1,5)  # cases 1-4 i.e. I, R, D, and I_c
            model.recovered=slice(2,3)
            model.deaths=slice(3,4)
            model.all_susceptibles=[0,5,6]
            model.S_c=5
            model.I_1=1
            model.W=7
            x0_SC2UIR = [1.0-I_0, I_0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]
            model.initial_values = (x0_SC2UIR, 0)

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn
    """
    if mod_name == 'SC2UIR':
        if age_structure:  # age_structure is integer number of age compartments
            print('Error: Age structure NYI for model',mod_name)
        else:
            state = ['S', 'I', 'R', 'D', 'I_c', 'S_c', 'S_u', 'W']
            param_list = ['beta', 'gamma', 'mu', 'c_0', 'c_1', 'c_2', 'k_u', 'k_1', 'k_w','kappa', 'N']

            transition = [
                Transition(origin='S', destination='I', equation='beta*(I+c_0*I_c)*S', transition_type=TransitionType.T),
                Transition(origin='S', destination='S_c', equation=c_2s+'c_2*(I+I_c)*S', transition_type=TransitionType.T),
                Transition(origin='S', destination='S_u', equation='k_u*(1-W)*S', transition_type=TransitionType.T),
                Transition(origin='S_c', destination='S', equation='c_1*S_c', transition_type=TransitionType.T),
                Transition(origin='S_c', destination='I_c', equation='c_0*beta*(I+c_0*I_c)*S_c', transition_type=TransitionType.T),
                Transition(origin='S_c', destination='S_u', equation='k_u*(1-W)*S_c', transition_type=TransitionType.T),
                Transition(origin='S_u', destination='S', equation='k_1*S_u', transition_type=TransitionType.T),
                Transition(origin='S_u', destination='I', equation='beta*(I+c_0*I_c)*S_u', transition_type=TransitionType.T),
                Transition(origin='I', destination='I_c', equation=c_2s+'c_2*(I+I_c)*I', transition_type=TransitionType.T),
                Transition(origin='I', destination='R', equation='gamma*I', transition_type=TransitionType.T),
                Transition(origin='I', destination='D', equation='mu*I', transition_type=TransitionType.T),
                Transition(origin='I_c', destination='I', equation='c_1*I_c', transition_type=TransitionType.T),
                Transition(origin='I_c', destination='R', equation='gamma*I_c', transition_type=TransitionType.T),
                Transition(origin='I_c', destination='D', equation='mu*I_c', transition_type=TransitionType.T),
                Transition(origin='W', destination='D', equation='0*W', transition_type=TransitionType.T)
                ]
            bdlist =     [Transition(origin='W',equation='k_w*W*(1-kappa*S_c-W)', transition_type=TransitionType.B)
                ]
            model = DeterministicOde(state, param_list, transition=transition)
            model.birth_death_list = bdlist
            model.modelname='SC2UIR'
            model.ei=1                  # case 1 i.e. I  # note I_c not included
            model.confirmed=slice(1,5)  # cases 1-4 i.e. I, R, D, and I_c
            model.recovered=slice(2,3)
            model.deaths=slice(3,4)
            model.all_susceptibles=[0,5,6]
            model.S_c=5
            model.I_1=1
            model.W=7
            x0_SC2UIR = [1.0-I_0, 0.0, I_0, 0.0, 0.0, 0.0, 0.0, 1.0]
            model.initial_values = (x0_SC2UIR, 0)

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn
    """
    if mod_name == 'SC2FUIR':
        if age_structure:  # age_structure is integer number of age compartments
            print('Error: Age structure NYI for model',mod_name)
        else:
            state = ['S', 'I', 'R', 'D', 'I_c', 'S_c', 'S_f', 'S_u', 'W']
            param_list = ['beta', 'gamma', 'mu', 'c_0', 'c_1', 'c_2', 'c_4', 'k_u', 'k_1', 'k_w','kappa', 'N']

            transition = [
                Transition(origin='S', destination='I', equation='beta*(I+c_0*I_c)*S', transition_type=TransitionType.T),
                Transition(origin='S_f', destination='I', equation='beta*(I+c_0*I_c)*S_f', transition_type=TransitionType.T),
                Transition(origin='S', destination='S_c', equation=c_2s+'c_2*(I+I_c)*S', transition_type=TransitionType.T),
                Transition(origin='S', destination='S_u', equation='k_u*(1-W)*S', transition_type=TransitionType.T),
                Transition(origin='S_f', destination='S_u', equation='k_u*(1-W)*S_f', transition_type=TransitionType.T),
                Transition(origin='S_c', destination='S_f', equation='c_1*S_c', transition_type=TransitionType.T),
                Transition(origin='S_f', destination='S', equation='c_4*S_f', transition_type=TransitionType.T),
                Transition(origin='S_c', destination='I_c', equation='c_0*beta*(I+c_0*I_c)*S_c', transition_type=TransitionType.T),
                Transition(origin='S_c', destination='S_u', equation='k_u*(1-W)*S_c', transition_type=TransitionType.T),
                Transition(origin='S_u', destination='S_f', equation='k_1*S_u', transition_type=TransitionType.T),
                Transition(origin='S_u', destination='I', equation='beta*(I+c_0*I_c)*S_u', transition_type=TransitionType.T),
                Transition(origin='I', destination='I_c', equation=c_2s+'c_2*(I+I_c)*I', transition_type=TransitionType.T),
                Transition(origin='I', destination='R', equation='gamma*I', transition_type=TransitionType.T),
                Transition(origin='I', destination='D', equation='mu*I', transition_type=TransitionType.T),
                Transition(origin='I_c', destination='I', equation='c_1*I_c', transition_type=TransitionType.T),
                Transition(origin='I_c', destination='R', equation='gamma*I_c', transition_type=TransitionType.T),
                Transition(origin='I_c', destination='D', equation='mu*I_c', transition_type=TransitionType.T),
                Transition(origin='W', destination='D', equation='0*W', transition_type=TransitionType.T)
                ]
            bdlist =     [Transition(origin='W',equation='k_w*W*(1-kappa*S_c-W)', transition_type=TransitionType.B)
                ]
            model = DeterministicOde(state, param_list, transition=transition)
            model.birth_death_list = bdlist
            model.modelname='SC2FUIR'
            model.ei=1                  # case 1 i.e. I  # note I_c not included
            model.confirmed=slice(1,5)  # cases 1-4 i.e. I, R, D, and I_c
            model.recovered=slice(2,3)
            model.deaths=slice(3,4)
            model.all_susceptibles=[0,5,6,7]
            model.S_c=5
            model.I_1=1
            model.W=8
            x0_SC2FUIR = [1.0-I_0, 0.0, I_0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]
            model.initial_values = (x0_SC2FUIR, 0)

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn

    if mod_name == 'SC3UEIR':
        if age_structure:  # age_structure is integer number of age compartments
            print('Error: Age structure NYI for model',mod_name)
        else:
            state = ['S', 'E', 'I', 'R', 'D', 'I_c', 'S_c', 'E_c', 'S_u', 'W']
            param_list = ['beta', 'alpha', 'gamma', 'mu', 'c_0', 'c_1', 'c_2', 'k_u', 'k_1', 'k_w','kappa', 'N']

            transition = [
                Transition(origin='S', equation='-beta*(I+c_0*I_c)*S+c_1*S_c-%f*c_2*(I+I_c)*S-k_u*(1-W)*S+k_1*S_u' % C_2s),
                Transition(origin='S_c', equation='-c_0*beta*(I+c_0*I_c)*S_c-c_1*S_c+%f*c_2*(I+I_c)*S-k_u*(1-W)*S_c' % C_2s),
                Transition(origin='S_u', equation='-beta*(I+c_0*I_c)*S_u+k_u*(1-W)*(S+S_c)-k_1*S_u'),
                Transition(origin='E', equation='beta*(I+c_0*I_c)*(S+S_u)-alpha*E+c_1*E_c-%f*c_2*(I+I_c)*E' % C_2s),
                Transition(origin='E_c', equation='c_0*beta*(I+c_0*I_c)*S_c-alpha*E_c-c_1*E_c+%f*c_2*(I+I_c)*E' % C_2s),
                Transition(origin='I', equation='alpha*E-gamma*I-mu*I+c_1*I_c-%f*c_2*(I+I_c)*I' % C_2s),
                Transition(origin='I_c', equation='alpha*E_c-gamma*I_c-mu*I_c-c_1*I_c+%f*c_2*(I+I_c)*I' % C_2s),
                Transition(origin='R', equation='gamma*(I+I_c)'),
                Transition(origin='D', equation='mu*(I+I_c)'),
                Transition(origin='W', equation='k_w*W*(1-kappa*S_c-W)')
                ]

            model = DeterministicOde(state, param_list, ode=transition)
            model.modelname='SC3UEIR'
            model.ei=slice(1,3) # cases 1,2 i.e. E,I  # note E_c and I_c not included
            model.confirmed=slice(2,6)  # cases 2-5 i.e. I, R, D, and I_c, not E, E_c
            model.recovered=slice(3,4)
            model.deaths=slice(4,5)
            model.all_susceptibles=[0,6,8]
            model.S_c=6
            model.I_1=2
            model.W=9
            x0_SC3UEIR = [1.0-I_0, 0.0, I_0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]
            model.initial_values = (x0_SC3UEIR, 0)

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn

    if mod_name == 'SC3UEI3R':
        if age_structure:  # age_structure is integer number of age compartments
            state0 = ['S', 'E', 'I_1', 'I_2','I_3', 'R', 'D', 'I_c', 'S_c', 'E_c', 'S_u', 'W']
            sa,state = state_age(state0,age_structure)

            param_list0 = ['beta_1', 'beta_2', 'beta_3', 'p_1', 'p_2', 'alpha',
                          'gamma_1', 'gamma_2', 'gamma_3','mu', 'c_0', 'c_1', 'c_2', 'c_3', 'k_u', 'k_1', 'k_w', 'kappa', 'N'] # order also important
            param_list,contact = param_list_age(param_list0.copy(),age_structure)

            phi = phi_age(contact,sa,'I_1',age_structure)
            phi_c = phi_age(contact,sa,'I_c',age_structure)
            phi_1c = [p[0]+'+c_0*'+p[1] for p in zip(phi,phi_c)]   # '(I_1+c_0*I_c)' to corresponding phi combination
            sumI_3 = state_sum_age('I_3',sa,age_structure)
            sumS_c = state_sum_age('S_c',sa,age_structure)

            # note that beta_2 and beta_3 are set to zero in default installation, and with age-dept I3 models we enforce this
            transition = []
            transition = transition_age(transition,'S','E','beta_1*','S',sa,TransitionType.T,age_structure,phi=phi_1c)
            transition = transition_age(transition,'S','S_c',c_2s+'c_2*'+sumI_3+'*','S',sa,TransitionType.T,age_structure,
                                        yfactor=c_2s+'c_3*'+sumI_3+'*')  # c_2s+'c_2*I_3*S'
            transition = transition_age(transition,'S','S_u','k_u*(1-W)*','S', sa,TransitionType.T,age_structure)       # new
            transition = transition_age(transition,'S_c','E_c','c_0*beta_1*','S_c',sa,TransitionType.T,age_structure,phi=phi_1c) # 'c_0*beta_1*(I_1+c_0*I_c)*S_c'
            transition = transition_age(transition,'S_c','S','c_1*','S_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'S_c','S_u','k_u*(1-W)*','S_c',sa,TransitionType.T,age_structure) #new
            transition = transition_age(transition,'S_u','S','k_1*','S_u',sa,TransitionType.T,age_structure)   #new
            transition = transition_age(transition,'S_u','E','beta_1*','S_u',sa,TransitionType.T,age_structure,phi=phi_1c)   #new
            transition = transition_age(transition,'E','I_1','alpha*','E',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E','E_c',c_2s+'c_2*'+sumI_3+'*','E',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E_c','I_c','alpha*','E_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E_c','E','c_1*','E_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_1','R','gamma_1*','I_1',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_1','I_c',c_2s+'c_2*'+sumI_3+'*','I_1',sa,TransitionType.T,age_structure,
                                        yfactor=c_2s+'c_3*'+sumI_3+'*')  # c_2s+'c_2*I_3*I_1'
            transition = transition_age(transition,'I_c','R','gamma_1*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','I_1','c_1*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_2','R','gamma_2*','I_2',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_3','R','gamma_3*','I_3',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_1','I_2','p_1*','I_1',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','I_2','p_1*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_2','I_3','p_2*','I_2',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_3','D','mu*','I_3',sa,TransitionType.T,age_structure)
            transition.append(Transition(origin='W', destination='D', equation='0*W', transition_type=TransitionType.T))      # new
            bdlist = [Transition(origin='W',equation='k_w*W*(1-kappa*('+sumS_c+')-W)', transition_type=TransitionType.B)]     # new
            model = DeterministicOde(state, param_list, transition=transition)
            model.birth_death_list = bdlist                                                                                # new
            if model == None:
                print('Error in make_model constructing DeterministicOde (in pygom)')
            model.modelname='SC3UEI3R'+'_A'+str(age_structure)
            model.ei=slice(1*age_structure,5*age_structure)
            model.confirmed=slice(2*age_structure,8*age_structure)
            model.recovered=slice(5*age_structure,6*age_structure)
            model.deaths=slice(6*age_structure,7*age_structure)
            model.all_susceptibles=[slice(0,1*age_structure),slice(8*age_structure,9*age_structure),slice(10*age_structure,11*age_structure)]   # CHECK that this works !!!!!!!!!!!!!!!!!!
            model.S_c=slice(8*age_structure,9*age_structure)

            first_infected_agegroup = int(age_structure//4)       # first approximation : would give 20-25 year olds for 16 group 0-80 in 5 year intervals
            model.I_1 = 1*age_structure + first_infected_agegroup
            model.W = slice(11*age_structure,11*age_structure+1)
            #x0 = [1.0-I_0, I_0, 0.0, 0.0]

            x0_SC3UEI3R = initial_state_age(I_0,state0,'E',first_infected_agegroup,age_structure)
            model.initial_values = (x0_SC3UEI3R, 0) # 0 for t[0]

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn
        else:
            state = ['S', 'E', 'I_1', 'I_2', 'I_3', 'R', 'D',  'I_c', 'S_c', 'E_c', 'S_u', 'W'] # order important to allow correct plot groupings
            param_list = ['beta_1', 'beta_2', 'beta_3', 'p_1', 'p_2', 'alpha',
                          'gamma_1', 'gamma_2', 'gamma_3','mu', 'c_0', 'c_1', 'c_2', 'k_u', 'k_1', 'k_w', 'kappa', 'N'] # order also important

            transition = [
                Transition(origin='S', equation='-(beta_1*(I_1+c_0*I_c)+beta_2*I_2+beta_3*I_3)*S+c_1*S_c-%f*c_2*(I_3)*S-k_u*(1-W)*S+k_1*S_u' % C_2s),
                Transition(origin='S_c', equation='-c_0*(beta_1*(I_1+c_0*I_c)+beta_2*I_2+beta_3*I_3)*S_c-c_1*S_c+%f*c_2*(I_3)*S-k_u*(1-W)*S_c' % C_2s),
                Transition(origin='S_u', equation='-(beta_1*(I_1+c_0*I_c)+beta_2*I_2+beta_3*I_3)*S_u+k_u*(1-W)*(S+S_c)-k_1*S_u'),
                Transition(origin='W', equation='k_w*W*(1-kappa*S_c-W)'),
                Transition(origin='E', equation='beta_1*(I_1+c_0*I_c)*(S+S_u)-alpha*E-%f*c_2*(I_3)*E+c_1*E_c' % C_2s),   # note: really need separate class E_u
                Transition(origin='E_c', equation='c_0*beta_1*(I_1+c_0*I_c)*S_c-alpha*E_c+%f*c_2*(I_3)*E-c_1*E_c' % C_2s),
                Transition(origin='I_1', equation='alpha*E-gamma_1*I_1-p_1*I_1-%f*c_2*(I_3)*I_1+c_1*I_c' % C_2s),
                Transition(origin='I_c', equation='alpha*E_c-gamma_1*I_c-p_1*I_c+%f*c_2*(I_3)*I_1-c_1*I_c' % C_2s), # changed to I_c, prints better
                Transition(origin='I_2', equation='p_1*(I_1+I_c)-gamma_2*I_2-p_2*I_2'),
                Transition(origin='I_3', equation='p_2*I_2-gamma_3*I_3-mu*I_3'),     # error corrected, this is equation for I_3 not I_2
                Transition(origin='R', equation='gamma_1*(I_1+I_c)+gamma_2*I_2+gamma_3*I_3'),
                Transition(origin='D', equation='mu*I_3')
                ]

            model = DeterministicOde(state, param_list, ode=transition)
            model.modelname='SC3UEI3R'  # following needs to be adjusted for new models, NB add new species at end to preserve slice subsets
            model.ei=slice(1,5)         # 1,2,3,4 i.e. E,I_1,I_2,I_3 – not E_c and I_c
            model.confirmed=slice(2,8)  # cases 2-7 i.e. I1, I2, I3, R, D and I_c
            model.recovered=slice(5,6)  # case 5 R
            model.deaths=slice(6,7)     # case 6 D
            model.all_susceptibles=[0,8,10]
            model.S_c=8
            model.I_1 = 2
            model.W = 11
            x0_SC3UEI3R = [1.0-I_0, 0.0, I_0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]
            model.initial_values = (x0_SC3UEI3R, 0)

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn
    if mod_name == 'SC3FUEI3R':
        if age_structure:  # age_structure is integer number of age compartments
            state0 = ['S', 'E', 'I_1', 'I_2','I_3', 'R', 'D', 'I_c', 'S_c', 'E_c', 'S_f', 'S_u', 'W']
            sa,state = state_age(state0,age_structure)

            param_list0 = ['beta_1', 'beta_2', 'beta_3', 'p_1', 'p_2', 'alpha',
                          'gamma_1', 'gamma_2', 'gamma_3','mu', 'c_0', 'c_1', 'c_2', 'c_3', 'c_4', 'k_u', 'k_1', 'k_w', 'kappa', 'N'] # order also important
            param_list,contact = param_list_age(param_list0.copy(),age_structure)

            phi = phi_age(contact,sa,'I_1',age_structure)
            phi_c = phi_age(contact,sa,'I_c',age_structure)
            phi_1c = [p[0]+'+c_0*'+p[1] for p in zip(phi,phi_c)]   # '(I_1+c_0*I_c)' to corresponding phi combination
            sumI_3 = state_sum_age('I_3',sa,age_structure)
            sumS_c = state_sum_age('S_c',sa,age_structure)

            # note that beta_2 and beta_3 are set to zero in default installation, and with age-dept I3 models we enforce this
            transition = []
            transition = transition_age(transition,'S','E','beta_1*','S',sa,TransitionType.T,age_structure,phi=phi_1c)
            transition = transition_age(transition,'S_f','E','beta_1*','S_f',sa,TransitionType.T,age_structure,phi=phi_1c)
            transition = transition_age(transition,'S','S_c',c_2s+'c_2*'+sumI_3+'*','S',sa,TransitionType.T,age_structure,
                                        yfactor=c_2s+'c_3*'+sumI_3+'*')  # c_2s+'c_2*I_3*S'
            transition = transition_age(transition,'S','S_u','k_u*(1-W)*','S', sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'S_f','S_u','k_u*(1-W)*','S_f', sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'S_c','S_u','k_u*(1-W)*','S_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'S_c','E_c','c_0*beta_1*','S_c',sa,TransitionType.T,age_structure,phi=phi_1c) # 'c_0*beta_1*(I_1+c_0*I_c)*S_c'
            transition = transition_age(transition,'S_c','S_f','c_1*','S_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'S_f','S','c_4*','S_f',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'S_u','S_f','k_1*','S_u',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'S_u','E','beta_1*','S_u',sa,TransitionType.T,age_structure,phi=phi_1c)
            transition = transition_age(transition,'E','I_1','alpha*','E',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E','E_c',c_2s+'c_2*'+sumI_3+'*','E',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E_c','I_c','alpha*','E_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'E_c','E','c_1*','E_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_1','R','gamma_1*','I_1',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_1','I_c',c_2s+'c_2*'+sumI_3+'*','I_1',sa,TransitionType.T,age_structure,
                                        yfactor=c_2s+'c_3*'+sumI_3+'*')  # c_2s+'c_2*I_3*I_1'
            transition = transition_age(transition,'I_c','R','gamma_1*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','I_1','c_1*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_2','R','gamma_2*','I_2',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_3','R','gamma_3*','I_3',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_1','I_2','p_1*','I_1',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_c','I_2','p_1*','I_c',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_2','I_3','p_2*','I_2',sa,TransitionType.T,age_structure)
            transition = transition_age(transition,'I_3','D','mu*','I_3',sa,TransitionType.T,age_structure)
            transition.append(Transition(origin='W', destination='D', equation='0*W', transition_type=TransitionType.T))
            bdlist = [Transition(origin='W',equation='k_w*W*(1-kappa*('+sumS_c+')-W)', transition_type=TransitionType.B)]
            model = DeterministicOde(state, param_list, transition=transition)
            model.birth_death_list = bdlist
            if model == None:
                print('Error in make_model constructing DeterministicOde (in pygom)')
            model.modelname='SC3UEI3R'+'_A'+str(age_structure)

            model.ei=slice(1*age_structure,5*age_structure)
            model.confirmed=slice(2*age_structure,8*age_structure)
            model.recovered=slice(5*age_structure,6*age_structure)
            model.deaths=slice(6*age_structure,7*age_structure)
            model.all_susceptibles=[slice(0,1*age_structure),slice(8*age_structure,9*age_structure),slice(10*age_structure,12*age_structure)]   # CHECK that this works !!!!!!!!!!!!!!!!!!
            model.S_c=slice(8*age_structure,9*age_structure)
            model.W = slice(12*age_structure,12*age_structure+1)

            first_infected_agegroup = int(age_structure//4)       # first approximation : would give 20-25 year olds for 16 group 0-80 in 5 year intervals
            model.I_1 = 1*age_structure + first_infected_agegroup
            #x0 = [1.0-I_0, I_0, 0.0, 0.0]

            x0_SC3UEI3R = initial_state_age(I_0,state0,'E',first_infected_agegroup,age_structure)
            model.initial_values = (x0_SC3UEI3R, 0) # 0 for t[0]

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn
        else:
            state = ['S', 'E', 'I_1', 'I_2','I_3', 'R', 'D', 'I_c', 'S_c', 'E_c', 'S_f', 'S_u', 'W'] # order important to allow correct plot groupings
            param_list = ['beta_1', 'beta_2', 'beta_3', 'p_1', 'p_2', 'alpha',
                          'gamma_1', 'gamma_2', 'gamma_3','mu', 'c_0', 'c_1', 'c_2', 'c_4', 'k_u', 'k_1', 'k_w', 'kappa', 'N'] # order also important

            transition = [
                Transition(origin='S',   equation='-(beta_1*(I_1+c_0*I_c)+beta_2*I_2+beta_3*I_3)*S+c_4*S_f-%f*c_2*(I_3)*S-k_u*(1-W)*S' % C_2s),
                Transition(origin='S_c', equation='-c_0*(beta_1*(I_1+c_0*I_c)+beta_2*I_2+beta_3*I_3)*S_c-c_1*S_c+%f*c_2*(I_3)*S-k_u*(1-W)*S_c' % C_2s),
                Transition(origin='S_f', equation='-(beta_1*(I_1+c_0*I_c)+beta_2*I_2+beta_3*I_3)*S_c+c_1*S_c-c_4*S_f-k_u*(1-W)*S_f+k_1*S_u'),
                Transition(origin='S_u', equation='-(beta_1*(I_1+c_0*I_c)+beta_2*I_2+beta_3*I_3)*S_f+k_u*(1-W)*(S+S_c+S_f)-k_1*S_u'),
                Transition(origin='W',   equation='k_w*W*(1-kappa*S_c-W)'),
                Transition(origin='E',   equation='beta_1*(I_1+c_0*I_c)*(S+S_f+S_u)-alpha*E-%f*c_2*(I_3)*E+c_1*E_c' % C_2s),   # note: really need separate class E_u
                Transition(origin='E_c', equation='c_0*beta_1*(I_1+c_0*I_c)*S_c-alpha*E_c+%f*c_2*(I_3)*E-c_1*E_c' % C_2s),
                Transition(origin='I_1', equation='alpha*E-gamma_1*I_1-p_1*I_1-%f*c_2*(I_3)*I_1+c_1*I_c' % C_2s),
                Transition(origin='I_c', equation='alpha*E_c-gamma_1*I_c-p_1*I_c+%f*c_2*(I_3)*I_1-c_1*I_c' % C_2s), # changed to I_c, prints better
                Transition(origin='I_2', equation='p_1*(I_1+I_c)-gamma_2*I_2-p_2*I_2'),
                Transition(origin='I_3', equation='p_2*I_2-gamma_3*I_3-mu*I_3'),     # error corrected, this is equation for I_3 not I_2
                Transition(origin='R',   equation='gamma_1*(I_1+I_c)+gamma_2*I_2+gamma_3*I_3'),
                Transition(origin='D',   equation='mu*I_3')
                ]

            model = DeterministicOde(state, param_list, ode=transition)
            model.modelname='SC3FUEI3R'  # following needs to be adjusted for new models, NB add new species at end to preserve slice subsets
            model.ei=slice(1,5)         # 1,2,3,4 i.e. E,I_1,I_2,I_3 – not E_c and I_c
            model.confirmed=slice(2,8)  # cases 2-7 i.e. I1, I2, I3, R, D and I_c
            model.recovered=slice(5,6)  # case 5 R
            model.deaths=slice(6,7)     # case 6 D
            model.all_susceptibles=[0,8,10,11]
            model.S_c=8
            model.I_1=2
            model.W=12
            x0_SC3FUEI3R = [1.0-I_0, 0.0, I_0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]
            model.initial_values = (x0_SC3FUEI3R, 0)

            rtn['state'] = state
            rtn['param_list'] = param_list
            rtn['model'] = model
            return rtn
    print('make-model:  ERROR:  could not make model',mod_name);
    return None

def param_copy(model):
    params = model.parameters
    newparams = {}
    pkeys1 = list(model.params.keys())
    pkeys2 = list(model.parameters.keys())
    for i in range(len(pkeys1)):
        newparams[pkeys1[i]] = params[pkeys2[i]]
    print(newparams)
    model.parameters=newparams

def param_modify(model,param,value):
    params = model.parameters
    newparams = {}
    pkeys1 = list(model.params.keys())
    pkeys2 = list(model.parameters.keys())
    for i in range(len(pkeys1)):
        newparams[pkeys1[i]] = params[pkeys2[i]]
    newparams[param]=value
    print(newparams)
    model.parameters=newparams

# param_modify(SCIR_model,'beta',0.721)  # requires .params to be set (see below)

def vector2params(b,a,g,p,u,c,k,N,modelname):
    """allows the construction of model specific parameters for different models from a single set
    based on SEI3R model with vector b,g,p as well as vector caution c and economics k"""
    if 'I3' in modelname:  # models with hospitalization
        params = {
            'beta_1' : b[1],
            'beta_2' : b[2],
            'beta_3' : b[3],
            'alpha' : a,
            'gamma_1': g[1],
            'gamma_2': g[2],
            'gamma_3': g[3],
            'p_1'    : p[1],
            'p_2'    : p[2],
            'mu'    : u}
    elif 'E' in modelname:
        irat = 1 + p[1]/(g[2]+p[2]) + p[2]/(g[3]+u)
        #irat = 1
        params = {
            'beta' : b[1],  # see above for explanations
            'alpha' : a,
            'gamma': (g[1]+g[2]*(p[1]/(g[2]+p[2]))+g[3]*(p[1]/(g[2]+p[2]))*(p[2]/(g[3]+u)))/irat,
            'mu'    : u*(p[1]/(g[2]+p[2])*(p[2]/(g[3]+u))/irat)}
    else:
        irat = 1 + p[1]/(g[2]+p[2]) + p[2]/(g[3]+u)
        #irat = 1
        params = {
            #'beta' : np.sqrt(b[1]*a),  # see above for explanations
            'beta' : b[1],  # see above for explanations
            'gamma': (g[1]+g[2]*(p[1]/(g[2]+p[2]))+g[3]*(p[1]/(g[2]+p[2]))*(p[2]/(g[3]+u)))/irat,
            'mu'    : u*(p[1]/(g[2]+p[2])*(p[2]/(g[3]+u))/irat)}

    if 'C' in modelname: # models with caution
        params['c_0'] = c[0]
        params['c_1'] = c[1]
        if 'I3' in modelname: # models with hospitalization
            params['c_2'] = c[2]
            if '_A' in modelname:
                params['c_3'] = c[3]
            if 'F' in modelname:
                params['c_4'] = c[4]
        else:
            # params['c_2'] = c[2]*FracCritical  # this can be calculated explicitly in next line
            params['c_2'] = c[2]*(p[1]/(g[1]+p[1]))*(p[2]/(g[2]+p[2]))
            if '_A' in modelname:
                params['c_3'] = c[3]*(p[1]/(g[1]+p[1]))*(p[2]/(g[2]+p[2]))
            if 'F' in modelname:
                params['c_4'] = c[4]*(p[1]/(g[1]+p[1]))*(p[2]/(g[2]+p[2]))

    if 'U' in modelname: # models with economic correction to caution
        params['k_u'] = k[0]
        params['k_1'] = k[1]
        params['k_w'] = k[2]
        params['kappa'] = k[3]

    params['N'] = N
    return params

def gamma_div_mu(gp3,p21,p32,g13,g23):
    """ calculates gamma/mu : included here for reference and to enable check of algebra
    """
    return gp3*p21*(1.+g23*p32*(1+gp3)+g13*p32*p21*(1.+gp3)(1.+g23*p32*gp3))

def f3cubic(x,gamma,mu,p12,p23,g13,g23):
    """ calculates cubic equation for solving for gp3
        in the form ax^3+bx^2+cx+d = 0
        normalized with constant term d = -p12*gamma/mu
        note that p12 and p23 are inverses of p21 and p32 in gamma_div_mu
    """
    if p12==0 or p23==0:
        print("Error: zero value of p[1] or p[2]")
        return 1.
    d = -p12*gamma/mu
    c = 1.+(g23+g13/p12)/p23
    b = (g23+g13/p12+g13*g23/(p12*p23))/p23
    a = g13*g23/(p12*p23*p23)

    return a*x*x*x+b*x*x+c*x+d

def f3inv(f3cubic,gamma,mu,p12,p23,g13,g23):
    """
    return real root of f3cubic in range [0,100] using Brent's method (scipy.optimize.brentq)
    https://en.wikipedia.org/wiki/Root-finding_algorithms#Brent's_method
    """
    return brentq(f3cubic,0.,100.,args=(gamma,mu,p12,p23,g13,g23))

def f4(gp3,p12,p23,g23):
    """ calculates u/mu = p3/mu in terms of
        gp3 = g3/p3, p23 = p2/p3, g23 = g2/g3
    """
    if p12==0 or p23==0:
        print("Error: zero value of p[1] or p[2]")
        return 1.
    fac1 = p12/(1.+g23*gp3/p23)
    fac2 = p23/(1.+gp3)
    return (1.+fac1+fac2)/(fac1*fac2)

def params2vector(self,params,modelname='SC3UEI3R'):
    b = [None,None,None,None]
    g = [None,None,None,None]
    p = [None,None,None]
    c = [None,None,None,None,None]
    k = [None,None,None,None]

    if 'E' in modelname:
        a=params['alpha']
    else:
        a = 1./self.sbparams['IncubPeriod']  # derive parameter from base parameters if model does not use E (exposed individuals)
    if 'I3' not in modelname:
        b_0,a_0,g_0,p_0,u_0,c_0,k_0,N_0,I0_0 = base2vectors(self.sbparams,self.cbparams,self.fbparams)  # only use ratios of g and p to u from base parameters

        #irat = 1 + p[1]/(g[2]+p[2]) + p[2]/(g[3]+u)
        #gamma = (g[1]+g[2]*(p[1]/(g[2]+p[2]))+g[3]*(p[1]/(g[2]+p[2]))*(p[2]/(g[3]+u)))/irat
        #mu = u*(p[1]/(g[2]+p[2])*(p[2]/(g[3]+u))/irat)

        b[0]=0.0
        b[1]=params['beta']
        b[2]=0.
        b[3]=0.

        p12=p_0[1]/p_0[2]
        p23=p_0[2]/u_0
        g13=g_0[1]/g_0[3]
        g23=g_0[2]/g_0[3]
        gp3 = f3inv(f3cubic,params['gamma'],params['beta'],p12,p23,g13,g23) # finds gp3=g[3]/p[3]=g[3]/u
        u = params['mu']*f4(gp3,p12,p23,g23)

        g[3]=u*gp3
        g[2]=g[3]*g23
        g[1]=g[3]*g13
        g[0]=0.0

        p[2]=u*p_0[2]/u_0
        p[1]=u*p_0[1]/u_0
        p[0]=0.0
    else:
        b[0]=0.0
        b[1]=params['beta_1']
        b[2]=params['beta_2']
        b[3]=params['beta_3']

        g[0]=0.0
        g[1]=params['gamma_1']
        g[2]=params['gamma_2']
        g[3]=params['gamma_3']

        p[0]=0.0
        p[1]=params['p_1']
        p[2]=params['p_2']
        u=params['mu']       # equivalent to p[3]

    N=params['N']

    if 'C' in modelname: # models with caution
        c[0]=params['c_0']
        c[1]=params['c_1']
        c[2]=params['c_2']
        if 'F' in modelname: # models with fatigue of caution
            c[4]=params['c_4']
        else:
            c[4]=0.
    if '_A' in modelname: # models with age structure
        if 'c_3' in params:
            c[3]=params['c_3']
        else:
            print('Error: c_3 not in params',params)
    else:
        c[3] = 0.

    if 'U' in modelname: # models with economic correction to caution
        k[0] = params['k_u']
        k[1] = params['k_1']
        k[2] = params['k_w']
        k[3] = params['kappa']
    return (b,a,g,p,u,c,k,N)

def base2vectors(sbparams,cbparams,fbparams):
    """ converts dictionary of base parameters to vector of parameters and then to pygom simulation parameters"""
    global C_2s # scaling factor for c_2 (1000) to allow c_2 parameter to be same order of magnitude as other parameters
    Exposure =sbparams['Exposure']
    IncubPeriod = sbparams['IncubPeriod']
    DurMildInf = sbparams['DurMildInf']
    FracMild = sbparams['FracMild']
    FracCritical = sbparams['FracCritical']
    FracSevere=1-FracMild-FracCritical
    CFR = sbparams['CFR']
    TimeICUDeath = sbparams['TimeICUDeath']
    DurHosp = sbparams['DurHosp']
    ICUFrac = sbparams['ICUFrac']
    I0 = 10**sbparams['logI_0']

    CautionFactor = cbparams['CautionFactor']
    CautionRetention = cbparams['CautionRetention']
    CautionExposure = cbparams['CautionExposure']
    CautionExposureYoung = cbparams['CautionExposureYoung'] # optional additional parameter, by default CautionExposure
    CautionFatigueRet = cbparams['CautionFatigueRet']

    EconomicStriction =  cbparams['EconomicStriction']
    EconomicRetention =  cbparams['EconomicRetention']
    EconomyRelaxation =  cbparams['EconomyRelaxation']
    EconomicCostOfCaution = cbparams['EconomicCostOfCaution']

    FracConfirmedDet = fbparams['FracConfirmedDet']
    FracRecoveredDet = FracConfirmedDet
    FracDeathsDet = fbparams['FracDeathsDet']

    N=1
    b=np.zeros(4)     # beta
    g=np.zeros(4)     # gamma
    p=np.zeros(3)     # progression
    c=np.zeros(5)     # caution
    k=np.zeros(4)     # economic caution

    a=1/IncubPeriod                       # transition rate from exposed to infected
    b=Exposure*np.array([0,1,0,0])/N      # hospitalized cases don't transmit
    u=(1/TimeICUDeath)*(CFR/FracCritical) # death rate from ICU
    g[3]=(1/TimeICUDeath)-u               # recovery rate

    p[2]=(1/DurHosp)*(FracCritical/(1-FracMild))
    g[2]=(1/DurHosp)-p[2]

    g[1]=(1/DurMildInf)*FracMild
    p[1]=(1/DurMildInf)-g[1]

    c[0]=CautionFactor
    if CautionRetention:
        c[1]=1/(30.*CautionRetention)
    else:
        c[1]=0.
    if CautionExposure:
        c[2]=1/(N*(ICUFrac*C_2s)*CautionExposure)     # this is the rate coefficient giving 1/day at I3 = denominator
    else:
        c[2]=0.
    if CautionExposureYoung:
        c[3]=1/(N*(ICUFrac*C_2s)*CautionExposureYoung)
    else:
        c[3]=0.
    if CautionFatigueRet:
        c[4]=1/(30.*CautionFatigueRet)
    else:
        c[4]=0.
    if EconomicStriction:
        k[0]=1/(30.*EconomicStriction)
    else:
        k[0]=0.
    if EconomicRetention:
        k[1]=1/(30.*EconomicRetention)
    else:
        k[1]=0.
    if EconomyRelaxation:
        k[2]=1/(30.*EconomyRelaxation)
    else:
        k[2]=0.
    k[3]=EconomicCostOfCaution

    return(b,a,g,p,u,c,k,N,I0)

def base2params(sbparams,cbparams,fbparams,smodel):
    b,a,g,p,u,c,k,N,I0 = base2vectors(sbparams,cbparams,fbparams)
    return(vector2params(b,a,g,p,u,c,k,N,smodel))

def vectors2base(b,a,g,p,u,c,k,N,I0,ICUFrac):
    """ converts vector of parameters back to dictionaries of base parameters
        assumes only one parameter for bvector in the form b*[0,1,0,0]"""
    global C_2s
    Exposure          = b[1]*N # assuming b vector has structure b*[0,1,0,0]
    IncubPeriod       = 1.0/a

    FracMild          = g[1]/(g[1]+p[1])
    FracCritical       = (g[1]/(g[1]+p[1]))*(p[2]/(g[2]+p[2]))
    #FracSevere        = (p[1]/(g[1]+p[1]))*(g[2]/(g[2]+p[2]))
    FracSevere        = 1 - FracMild -FracCritical
    CFR               = (u/(g[3]+u))*(p[2]/(g[2]+p[2]))*(p[1]/(g[1]+p[1]))
    DurMildInf        = 1/(g[1]+p[1])
    DurHosp           = 1/(g[2]+p[2])
    TimeICUDeath      = 1/(g[3]+u)

    CautionFactor     = c[0]
    if c[1]:
        CautionRetention  = 1/(30.*c[1])
    else:
        CautionRetention  = None
    if c[2]:
        CautionExposure    = 1/(N*c[2]*(C_2s*ICUFrac))
    else:
        CautionExposure    = None
    if c[3]:
        CautionExposureYoung    = 1/(N*c[3]*(C_2s*ICUFrac))
    else:
        CautionExposureYoung    = CautionExposure
    if c[4]:
        CautionFatigueRet    = 1/(30.*c[4])
    else:
        CautionFatigueRet    = None

    if k[0]:
        EconomicStriction     =  1.0/(30.*k[0])
    else:
        EconomicStriction     =  None
    if k[1]:
        EconomicRetention     =  1.0/(30.*k[1])
    else:
        EconomicRetention     = None
    if k[2]:
        EconomyRelaxation     =  1.0/(30.*k[2])
    else:
        EconomyRelaxation     = None
    EconomicCostOfCaution =  k[3]

    sbparams = {'Exposure':Exposure,'IncubPeriod':IncubPeriod,'DurMildInf':DurMildInf,
                'FracMild':FracMild,'FracCritical':FracCritical,'CFR':CFR,
                'TimeICUDeath':TimeICUDeath,'DurHosp':DurHosp,'ICUFrac':ICUFrac,'logI_0':np.log10(I0)}
    cbparams = {'CautionFactor':CautionFactor,'CautionRetention':CautionRetention,
                'CautionExposure':CautionExposure,'CautionExposureYoung':CautionExposureYoung,
                'CautionFatigueRet':CautionFatigueRet,
                'EconomicStriction':EconomicStriction,'EconomicRetention':EconomicRetention,
                'EconomyRelaxation':EconomyRelaxation,'EconomicCostOfCaution':EconomicCostOfCaution}

    return (sbparams,cbparams)

def base2ICs(I0,N,smodel,model,age_structure=None):

    (x0old,t0) = model.initial_values
    nstates = len(x0old)
    x0 = [0.]*nstates
    if age_structure:
        first_infected_agegroup = int(age_structure//4)
    else:
        first_infected_agegroup = 0
    x0[first_infected_agegroup] = N*(1-I0)   # assumes susceptibles (first in state list)
    if model.I_1 < nstates: # age structure dealt with in model specific model.I_1
        x0[model.I_1] = N*I0
    else:
        print('error, initial infectives location out of bounds',model.I_1,'not <',nstates)
    if 'U' in smodel:
        x0[model.W]=1.0
    return (x0,t0)

def default_params(sbparams=None,cbparams=None,fbparams=None,dbparams=None):
    """ supply default parameters for those not already defined as arguments
        does not check if non None arguments are correctly defined """

    if not sbparams:      # standard params set 2 from Germany fit
        Exposure=0.4     # Rate coefficient for exposure per individual in contact per day
        IncubPeriod=5     #Incubation period, days
        DurMildInf=10     #Duration of mild infections, days
        FracMild=0.7      #Fraction of infections that are mild
        FracCritical=0.10   #Fraction of infections that are critical
        CFR=0.05          #Case fatality rate (fraction of infections resulting in death)
        TimeICUDeath=5    #Time from ICU admission to death, days
        DurHosp=4         #Duration of hospitalization, days
        ICUFrac= 0.001    # Fraction of ICUs relative to population size N
        logI_0 = np.log10(0.0000003)  # Fraction of population initially infected

        sbparams = {'Exposure':Exposure,'IncubPeriod':IncubPeriod,'DurMildInf':DurMildInf,
                   'FracMild':FracMild,'FracCritical':FracCritical,'CFR':CFR,
                   'TimeICUDeath':TimeICUDeath,'DurHosp':DurHosp,'ICUFrac':ICUFrac,'logI_0':logI_0}

    if not cbparams:          # Model extension by John McCaskill to include caution                     # set 2 based on Germany fit
        CautionFactor= 0.1    # Fractional reduction of exposure rate for cautioned individuals
        CautionRetention= 2.  # Duration of cautionary state of susceptibles (2 months)
        CautionExposure= 0.1  # Duration of transition to caution per (individual per ICU) days
        CautionExposureYoung= 0.1  # Duration of transition to caution per (individual per ICU) days, for young people
        CautionFatigueRet=2.  # Duration of fatigue state of individuals (for models with F) (2 months)
        EconomicStriction = 1. # Duration of transition to economic stringency (months)
        EconomicRetention = 2. # Duration of economic dominant state of susceptibles (here same as caution in months, typically longer)
        EconomyRelaxation = 2. # Relaxation time for economy (in months)
        EconomicCostOfCaution = 0.5 # Cost to economy of individual exercising caution

        cbparams = {'CautionFactor':CautionFactor,'CautionRetention':CautionRetention,
                'CautionExposure':CautionExposure,'CautionExposureYoung':CautionExposureYoung,
                'CautionFatigueRet':CautionFatigueRet,
                'EconomicStriction':EconomicStriction,'EconomicRetention':EconomicRetention,
                'EconomyRelaxation':EconomyRelaxation,'EconomicCostOfCaution':EconomicCostOfCaution}

    if not fbparams:          # Model fitting extension to allow for incomplete detection
        FracConfirmedDet=1.0 # Fraction of recovered individuals measured : plots made with this parameter
        FracRecoveredDet=FracConfirmedDet # Fraction of recovered individuals measured
        FracDeathsDet=1.0

        fbparams = {'FracConfirmedDet':FracConfirmedDet,'FracDeathsDet':FracDeathsDet}

    if not dbparams:     # extra data-related params for defining a run, including possible fitting with sliders:
        dbparams = {'country':'Germany','data_src':'owid'}

    return [sbparams,cbparams,fbparams,dbparams]

def default_base_params(modelname=None):
    """ supply default fit parameters for base parameters """
    logI0 = np.log10(0.0000003)
    fp = {}
    fp['Exposure']=               (0.4, 0.2, 0.7, 0.001)         # Rate coefficient for exposure per individual in contact per day
    fp['IncubPeriod']=            (5., 3., 7., 0.01)             # Incubation period, days
    fp['DurMildInf']=             (10., 5., 15., 0.01)           # Duration of mild infections, days
    fp['FracMild']=               (0.7, 0.5, 0.9, 0.01)          # Fraction of infections that are mild
    fp['FracCritical']=           (0.10, 0.05, 0.15, 0.01)       # Fraction of infections that are critical   # NB upper limit of 1- FracMild NYI
    fp['CFR']=                    (0.05,0.025,0.1,0.001)         # Case fatality rate (fraction of infections resulting in death)
    fp['TimeICUDeath']=           (5., 3., 10., 0.01)            # Time from ICU admission to death, days
    fp['DurHosp']=                (4., 2., 14., 0.01)            # Duration of hospitalization, days
    fp['ICUFrac']=                (0.001, 0.0001, 0.01, 0.00001) # Fraction of ICUs relative to population size N
    fp['logI_0'] =                (logI0,-10.,-6.,0.01)         # Fraction of population initially infected
    if modelname is None or 'C' in modelname:
        fp['CautionFactor']=          (0.1,0.05,0.5,0.01)            # Fractional reduction of exposure rate for cautioned individuals
        fp['CautionRetention']=       (2.,1./3.,6.,0.01)             # Duration of cautionary state of susceptibles (8 weeks)
        fp['CautionExposure']=        (0.1,0.01,1.,0.01)             # Rate of transition to caution per (individual per ICU) per day
        if '_A' in modelname:
            fp['CautionExposureYoung']=   (0.05,0.01,1.,0.01)            # Rate of transition to caution per (individual per ICU) per day for young people
        if 'F' in modelname:
            fp['CautionFatigueRet']=      (2.,1./3.,6.,0.01)             # Duration of fatigued state of susceptibles (8 weeks)
    if modelname is None or 'U' in modelname:
        fp['EconomicStriction'] =     (1.,1./3.,3.,0.01)             # Duration of transition to economically motivated non-cautionable state (in months)
        fp['EconomicRetention'] =     (2.,1./3.,4.,0.01)             # Duration of economic dominant state of susceptibles (in months)
        fp['EconomyRelaxation'] =     (2.,1./3.,4.,0.01)             # Relaxation time for economy (in months)
        fp['EconomicCostOfCaution'] = (0.5,0.2,0.8,0.001)            # Cost to economy of individual exercising caution

    fp['FracConfirmedDet']=       (1.0,0.1,1.0,0.01)             # Fraction of recovered individuals measured : plots made with this parameter
    # FracRecoveredDet=FracConfirmedDet                          # Fraction of recovered individuals measured
    fp['FracDeathsDet']=          (1.0,0.5,1.0,0.01)             # Fraction of deceased individuals from the disease that are identified
    return fp

default_fit_params = default_base_params # for backward compatibility

# Set up multimodel consistent sets of parameters, based on standard set defined by Dr. Alison Hill for SEI3RD
def parametrize_model(rootmodel,modelname,sbparams=None,cbparams=None,fbparams=None,dbparams=None,age_structure=None):
    """ smodel is root model name
    """
    if sbparams == None or cbparams==None or fbparams==None or dbparams==None:
        [sbparams,cbparams,fbparams,dbparams] = default_params(sbparams,cbparams,fbparams,dbparams)
        dbparams['run_name'] = modelname # default value when no country yet

    b,a,g,p,u,c,k,N,I0 = base2vectors(sbparams,cbparams,fbparams)
    fullmodel = make_model(rootmodel,age_structure=age_structure)
    model = fullmodel['model']
    params_in=vector2params(b,a,g,p,u,c,k,N,modelname)
    # print('In parametrize_model with rootmodel',rootmodel,'modelname',modelname,'and params',params_in)
    if age_structure:
        model.initial_values = base2ICs(I0,N,rootmodel,model,age_structure=age_structure)
    else:
        model.initial_values = base2ICs(I0,N,rootmodel,model)
    # model.baseparams = list(sbparams)+list(cbparams)+list(fbparams)  # was list
    # model.baseparams = {**sbparams,**cbparams,**fbparams}  # now a merged dictionary
    model.parameters = params_in # sets symbolic name parameters
    fullmodel['params'] = params_in    # sets string params
    fullmodel['sbparams'] = sbparams
    fullmodel['cbparams'] = cbparams
    fullmodel['fbparams'] = fbparams
    fullmodel['dbparams'] = dbparams
    fullmodel['age_structure'] = age_structure
    fullmodel['initial_values'] = model.initial_values  # this line probably not required, since already initialized in make_model
    return fullmodel

# smodels = ['SIR','SCIR','SC2IR','SEIR','SCEIR','SC3EIR','SEI3R','SCEI3R','SC3EI3R','SC2UIR','SC3UEIR','SC3UEI3R'] # full set
sim_param_inits = {
    'SIR':{
        "beta": (0.4, 0.3, 0.8,0.001),
        "mu": (.05,0.0,0.5,0.001),
        "logI_0": (-6.,-9.,-3.,0.001)},
    'SCIR':{
        "beta": (0.4, 0.0, 1.2,0.001),
        "mu": (.05,0.0,0.5,0.001),
        "c_0": (0.1, 0.0, 1.0,0.001),
        "c_1": (0.07, 0.0, 0.1,0.001),
        "c_2": (5., 1., 200., 0.01),
        "logI_0": (-6.,-12.,-3.,0.001)},
    'SC2IR':{
        "beta": (0.4, 0.0, 1.2,0.001),
        "mu": (.05,0.0,0.5,0.001),
        "c_0": (0.1, 0.0, 1.0,0.001),
        "c_1": (0.07, 0.0, 0.1,0.001),
        "c_2": (5., 1., 200., 0.01),
        "logI_0": (-6.,-12.,-3.,0.001)},
    'SC2FIR':{
        "beta": (0.4, 0.0, 1.2,0.001),
        "mu": (.05,0.0,0.5,0.001),
        "c_0": (0.1, 0.0, 1.0,0.001),
        "c_1": (0.07, 0.0, 0.1,0.001),
        "c_2": (5., 1., 200., 0.01),
        "c_4": (0.07, 0.0, 0.1,0.001),
        "logI_0": (-6.,-12.,-3.,0.001)},
    'SEIR':{
        "beta": (0.4, 0.3, 0.8,0.001),
        "alpha": (0.2, 0., 1.,0.001),
        "mu": (.05,0.0,0.5,0.001),
        "logI_0": (-6.,-9.,-3.,0.001)},
    'SCEIR':{
        "beta": (0.4, 0.0, 1.2,0.001),
        "alpha": (0.2, 0., 1.,0.001),
        "mu": (.05,0.0,0.5,0.001),
        "c_0": (0.1, 0.0, 1.0,0.001),
        "c_1": (0.07, 0.0, 0.1,0.001),
        "c_2": (5., 1., 200., 0.01),
        "logI_0": (-6.,-12.,-3.,0.001)},
    'SCFEIR':{
        "beta": (0.4, 0.0, 1.2,0.001),
        "alpha": (0.2, 0., 1.,0.001),
        "mu": (.05,0.0,0.5,0.001),
        "c_0": (0.1, 0.0, 1.0,0.001),
        "c_1": (0.07, 0.0, 0.1,0.001),
        "c_2": (5., 1., 200., 0.01),
        "c_4": (0.07, 0.0, 0.1,0.001),
        "logI_0": (-6.,-12.,-3.,0.001)},
    'SC3EIR':{
        "beta": (0.4, 0.0, 1.2,0.001),
        "alpha": (0.2, 0., 1.,0.001),
        "mu": (.05,0.0,0.5,0.001),
        "c_0": (0.1, 0.0, 1.0,0.001),
        "c_1": (0.07, 0.0, 0.1,0.001),
        "c_2": (5., 1., 200., 0.01),
        "logI_0": (-6.,-12.,-3.,0.001)},
    'SC3FEIR':{
        "beta": (0.4, 0.0, 1.2,0.001),
        "alpha": (0.2, 0., 1.,0.001),
        "mu": (.05,0.0,0.5,0.001),
        "c_0": (0.1, 0.0, 1.0,0.001),
        "c_1": (0.07, 0.0, 0.1,0.001),
        "c_2": (5., 1., 200., 0.01),
        "c_4": (0.07, 0.0, 0.1,0.001),
        "logI_0": (-6.,-12.,-3.,0.001)},
    'SEI3R':{
        "beta_1": (0.4, 0.3, 0.8,0.001),
        "alpha": (0.2, 0., 1.,0.001),
        "mu": (.05,0.0,0.15,0.001),
        "logI_0": (-6.,-9.,-3.,0.001)},
    'SCEI3R':{
        "beta_1": (0.4, 0.0, 1.2,0.001),
        "alpha": (0.2, 0., 1.,0.001),
        "mu": (.05,0.0,0.15,0.001),
        "c_0": (0.1, 0.0, 1.0,0.001),
        "c_1": (0.07, 0.0, 0.1,0.001),
        "c_2": (5., 1., 200., 0.01),
        "logI_0": (-6.,-12.,-3.,0.001)},
    'SC3EI3R':{
        "beta_1": (0.4, 0.0, 1.2,0.001),
        "alpha": (0.2, 0., 1.,0.001),
        "mu": (.05,0.0,0.5,0.001),
        "c_0": (0.1, 0.0, 1.0,0.001),
        "c_1": (0.07, 0.0, 0.1,0.001),
        "c_2": (5., 1., 200., 0.01),
        "logI_0": (-6.,-12.,-3.,0.001)},
    'SC3FEI3R':{
        "beta_1": (0.4, 0.0, 1.2,0.001),
        "alpha": (0.2, 0., 1.,0.001),
        "mu": (.05,0.0,0.5,0.001),
        "c_0": (0.1, 0.0, 1.0,0.001),
        "c_1": (0.07, 0.0, 0.1,0.001),
        "c_2": (5., 1., 200., 0.01),
        "c_4": (0.07, 0.0, 0.1,0.001),
        "logI_0": (-6.,-12.,-3.,0.001)},
    'SC2UIR':{
        "beta": (0.37526113317338305, 0., 2.,0.001),
        "mu": (0.11549404287611789,0.,.5,0.001),
        "c_0": (0.2583441976053431, 0., 1.0,0.001),
        "c_1": (0.03763741590817468, 0.0, 0.5,0.001),
        "c_2": (3.620445327728954, 2.,200.,0.01),
        "k_u": (1.0/(30.0*5.0),0.0,1.0,0.001),
        "k_1": (1.0/(30.0*3.0),0.0,1.0,0.001),
        "k_w": (1.0/(30.0*3.0),0.0,1.0,0.01),
        "kappa": (0.5,0.0,1.0,0.01),
        "logI_0": (-6.,-10.,0.0,0.01)},
    'SC2FUIR':{
        "beta": (0.37526113317338305, 0., 2.,0.001),
        "mu": (0.11549404287611789,0.,.5,0.001),
        "c_0": (0.2583441976053431, 0., 1.0,0.001),
        "c_1": (0.03763741590817468, 0.0, 0.5,0.001),
        "c_2": (3.620445327728954, 2.,200.,0.01),
        "c_4": (0.03763741590817468, 0.0, 0.5,0.001),
        "k_u": (1.0/(30.0*5.0),0.0,1.0,0.001),
        "k_1": (1.0/(30.0*3.0),0.0,1.0,0.001),
        "k_w": (1.0/(30.0*3.0),0.0,1.0,0.01),
        "kappa": (0.5,0.0,1.0,0.01),
        "logI_0": (-6.,-10.,0.0,0.01)},
    'SC3UEIR':{
        "beta": (0.37526113317338305, 0., 2.,0.001),
        "alpha": (0.2, 0., 1.,0.001),
        "mu": (0.11549404287611789,0.,.5,0.001),
        "c_0": (0.2583441976053431, 0., 1.0,0.001),
        "c_1": (0.03763741590817468, 0.0, 0.5,0.001),
        "c_2": (3.620445327728954, 2.,200.,0.01),
        "k_u": (1.0/(30.0*5.0),0.0,1.0,0.001),
        "k_1": (1.0/(30.0*3.0),0.0,1.0,0.001),
        "k_w": (1.0/(30.0*3.0),0.0,1.0,0.01),
        "kappa": (0.5,0.0,1.0,0.01),
        "logI_0": (-6.,-10.,0.0,0.01)},
    'SC3UEI3R':{
        "beta_1": (0.37526113317338305, 0., 3.,0.001),
        "alpha": (0.2, 0., 1.,0.001),
        "mu": (0.11549404287611789,0.,.5,0.001),
        "c_0": (0.2583441976053431, 0., 1.0,0.001),
        "c_1": (0.03763741590817468, 0.0, 0.5,0.001),
        "c_2": (10.0, 2.,200.,0.01),
        "k_u": (1.0/(30.0*5.0),0.0,1.0,0.001),
        "k_1": (1.0/(30.0*3.0),0.0,1.0,0.001),
        "k_w": (1.0/(30.0*3.0),0.0,1.0,0.01),
        "kappa": (0.,0.0,1.0,0.01),
        "logI_0": (-6.,-10.,0.0,0.01)},
    'SC3FUEI3R':{
        "beta_1": (0.37526113317338305, 0., 3.,0.001),
        "alpha": (0.2, 0., 1.,0.001),
        "mu": (0.11549404287611789,0.,.5,0.001),
        "c_0": (0.2583441976053431, 0., 1.0,0.001),
        "c_1": (0.03763741590817468, 0.0, 0.5,0.001),
        "c_2": (10.0, 2.,200.,0.01),
        "c_4": (0.03763741590817468, 0.0, 0.5,0.001),
        "k_u": (1.0/(30.0*5.0),0.0,1.0,0.001),
        "k_1": (1.0/(30.0*3.0),0.0,1.0,0.001),
        "k_w": (1.0/(30.0*3.0),0.0,1.0,0.01),
        "kappa": (0.5,0.0,1.0,0.01),
        "logI_0": (-6.,-10.,0.0,0.01)}
    }

# smodels = possmodels # full set
# smodels = ['SEIR','SC3EIR','SC3UEIR','SEI3R','SC3EI3R','SC3UEI3R'] # partial set with comparison
smodels = ['SC2UIR','SC2FIR','SC3FEIR','SEI3R','SC3FEI3R','SC2FUIR','SC3FUEI3R'] # short list, others can be added if required from notebook
# samodels = ['SIR_A4','SC2IR_A4','SEI3R_A4','SC3EI3R_A4','SC3UEI3R_A4']
# samodels = ['SEIR_A4',SEI3R_A4','SC3EI3R_A4','SC3UEI3R_A4']
# samodels = [x+'_A4' for x in agemodels]
samodels = []

# Initialize all models
cmodels = {}
fullmodels = {}
print('making the models...')
for smodel in smodels+samodels:
    if '_A' in smodel:
        [smodel_root,age_str] = smodel.split("_A")
        try:
            age_structure = int(age_str)
        except:
            print("Error in parameterize_model, age suffix is not an integer.")
    else:
        smodel_root = smodel
        age_structure = None

    if smodel_root not in possmodels:
        print('root model name',smodel_root,'not yet supported')
    else:
        fullmodel = parametrize_model(smodel_root,smodel,age_structure=age_structure)
        fullmodels[smodel] = fullmodel
        # take fullmodel['model'] so that modelnm is same model as before for backward compatibility
        cmodels[smodel] = fullmodel['model']
        modelnm = smodel+'_model'
        exec(modelnm+" = fullmodel['model']")
        print(smodel)

print('done with the models.')

max_stars_repo_name: ProtoLife/covid-recovery

max_issues_repo_name: ProtoLife/covid-recovery

max_forks_repo_name: ProtoLife/covid-recovery

reason: import numpy,import scipy,from scipy,import sympy,from sympy