Model Parameters Classes

This page contains information about the different classes which contain parameters used for the forward simulation of the various models currently included in the epimodels library: PHE Model, Roche Model, and Warwick-Household Model.

Overview:

• Initial Conditions Classes:

  • PheICs

  • RocheICs

  • WarwickICs

• Regional and Time Dependent Parameters Classes:

  • PheRegParameters

  • WarwickRegParameters

• Disease Specific Parameters Classes:

  • PheDiseaseParameters

  • RocheCompartmentTimes

  • RocheProportions

  • RocheTransmission

  • WarwickDiseaseParameters

  • WarwickTransmission

• Simulation Method Parameters Classes:

  • PheSimParameters

  • RocheSimParameters

  • WarwickSimParameters

• Social Distancing Parameters Classes:

  • WarwickSocDistParameters

• Parameters Controller Classes:

  • PheParametersController

  • RocheParametersController

  • WarwickParametersController

Parameter Classes for the PHE Model

Below we list the methods for all the parameter classes associated with the forward simulation of the PHE model.

Initial Conditions Parameters

class epimodels.PheICs(model, susceptibles_IC, exposed1_IC, exposed2_IC, infectives1_IC, infectives2_IC, recovered_IC)

PheICs: Base class for the ICs of the PHE model: a deterministic SEIR used by the Public Health England to model the Covid-19 epidemic in UK based on region.

Parameters:

• susceptibles_IC (list of lists) – Initial number of susceptibles classified by age (column name) and region (row name).

• exposed1_IC (list of lists) – Initial number of exposed of the first type classified by age (column name) and region (row name).

• exposed2_IC (list of lists) – Initial number of exposed of the second type classified by age (column name) and region (row name).

• infectives1_IC (list of lists) – Initial number of infectives of the first type classified by age (column name) and region (row name).

• infectives2_IC (list of lists) – Initial number of infectives of the second type classified by age (column name) and region (row name).

• recovered_IC (list of lists) – Initial number of recovered classified by age (column name) and region (row name).

Regional and Time Dependent Parameters

class epimodels.PheRegParameters(model, initial_r, region_index, betas, times)

PheRegParameters: Base class for the regional and time dependent parameters of the PHE model: a deterministic SEIR used by the Public Health England to model the Covid-19 epidemic in UK based on region.

Parameters:

• initial_r (list) – Initial values of the reproduction number by region.

• region_index (int) – Index of region for which we wish to simulate.

• betas (list of lists) – Temporal and regional fluctuation matrix.

• times (list) – List of time points at which we wish to evaluate the ODEs system.

Disease Specific Parameters

class epimodels.PheDiseaseParameters(model, dL, dI)

PheDiseaseParameters: Base class for the disease-specific parameters of the PHE model: a deterministic SEIR used by the Public Health England to model the Covid-19 epidemic in UK based on region.

Parameters:

• dL (int or float) – Mean latent period.

• dI (int or float) – Mean infection period.

Simulation Method Parameters

class epimodels.PheSimParameters(model, delta_t, method)

PheSimParameters: Base class for the simulation method’s parameters of the PHE model: a deterministic SEIR used by the Public Health England to model the Covid-19 epidemic in UK based on region.

Parameters:

• delta_t (float) – Time step for the ‘homemade’ solver.

• method (str) – The type of solver implemented by the simulator.

Parameters Controller

class epimodels.PheParametersController(model, regional_parameters, ICs, disease_parameters, simulation_parameters)

PheParametersController Class: Base class for the parameters of the PHE model: a deterministic SEIR used by the Public Health England to model the Covid-19 epidemic in UK based on region.

In order to simulate using the PHE model, the following parameters are required, which are stored as part of this class.

Parameters:

• model (PheSEIRModel) – The model whose parameters are stored.

• regional_parameters (PheRegParameters) – Class of the regional and time dependent parameters used in the simulation of the model.

• ICs (PheICs) – Class of the ICs used in the simulation of the model.

• disease_parameters (PheDiseaseParameters) – Class of the disease-specific parameters used in the simulation of the model.

• simulation_parameters (PheSimParameters) – Class of the simulation method’s parameters used in the simulation of the model.

Parameter Classes for the Roche SEIRD Model

Below we list the methods for all the parameter classes associated with the forward simulation of the Roche model.

Initial Conditions Parameters

class epimodels.RocheICs(model, susceptibles_IC, exposed_IC, infectives_pre_IC, infectives_asym_IC, infectives_sym_IC, infectives_pre_ss_IC, infectives_asym_ss_IC, infectives_sym_ss_IC, infectives_q_IC, recovered_IC, recovered_asym_IC, dead_IC)

RocheICs: Base class for the ICs of the Roche model: deterministic SEIRD used by the F. Hoffmann-La Roche Ltd to model the Covid-19 epidemic and the effects of non-pharmaceutical interventions (NPIs) on the epidemic dynamic in different countries.

Parameters:

• susceptibles_IC (list of lists) – Initial number of susceptibles classified by age (column name) and region (row name).

• exposed_IC (list of lists) – Initial number of exposed classified by age (column name) and region (row name).

• infectives_pre_IC (list of lists) – Initial number of presymptomatic infectives classified by age (column name) and region (row name).

• infectives_asym_IC (list of lists) – Initial number of asymptomatic infectives classified by age (column name) and region (row name).

• infectives_sym_IC (list of lists) – Initial number of symptomatic infectives classified by age (column name) and region (row name).

• infectives_pre_ss_IC (list of lists) – Initial number of presymptomatic superspreader infectives classified by age (column name) and region (row name).

• infectives_asym_ss_IC (list of lists) – Initial number of asymptomatic superspreader infectives classified by age (column name) and region (row name).

• infectives_sym_ss_IC (list of lists) – Initial number of symptomatic superspreader infectives classified by age (column name) and region (row name).

• infectives_q_IC (list of lists) – Initial number of symptomatic infectives quarantined classified by age (column name) and region (row name).

• recovered_IC (list of lists) – Initial number of symptomatic recovered classified by age (column name) and region (row name).

• recovered_asym_IC (list of lists) – Initial number of asymptomatic recovered classified by age (column name) and region (row name).

• dead_IC (list of lists) – Initial number of dead classified by age (column name) and region (row name).

Average Times in Compartments Parameters

class epimodels.RocheCompartmentTimes(model, k, kS, kQ, kR, kRI)

RocheCompartmentTimes: Base class for the average-time-in-compartment parameters of the Roche model: deterministic SEIRD used by the F. Hoffmann-La Roche Ltd to model the Covid-19 epidemic and the effects of non-pharmaceutical interventions (NPIs) on the epidemic dynamic in different countries.

Parameters:

• k (float or int) – The average time it takes for an individual to become infectious once exposed. Non age-dependent.

• kS (float or int) – The average time it takes for an individual to develop symptoms (or remain asymptomatic) once they becomes infectious. Non age-dependent.

• kQ (float or int) – The average time it takes for an individual to enter quarantine once they develop symptoms. Non age-dependent.

• kR (float or int or list) – The average time it takes for a quarantined individual to recover or die. Age-dependent.

• kRI (float or int or list) – The average time it takes for an asymptomatic individual to recover. Age-dependent.

Proportions of Asymptomatic, Super-spreader and Dead Parameters

class epimodels.RocheProportions(model, Pa, Pss, Pd)

RocheProportions: Base class for the proportions of asymptomatic, super-spreader and dead cases parameters of the Roche model: deterministic SEIRD used by the F. Hoffmann-La Roche Ltd to model the Covid-19 epidemic and the effects of non-pharmaceutical interventions (NPIs) on the epidemic dynamic in different countries.

Parameters:

• Pa (int or float or list) – Proportion of asymptomatic cases.

• Pss (int or float) – Proportion of super-spreader cases.

• Pd (int or float or list) – Proportion of dead cases.

Transmission Specific Parameters

class epimodels.RocheTransmission(model, beta_min, beta_max, bss, gamma, s50)

RocheTransmission: Base class for the transmission-specific parameters of the Roche model: deterministic SEIRD used by the F. Hoffmann-La Roche Ltd to model the Covid-19 epidemic and the effects of non-pharmaceutical interventions (NPIs) on the epidemic dynamic in different countries.

Parameters:

• beta_min (int or float) – The minimum possible transmission rate of the virus.

• beta_max (int or float) – The maximum possible transmission rate of the virus.

• bss (int or float) – The relative increase in transmission of a super-spreader case.

• gamma (: int or float) – The sharpness of the intervention wave used for function continuity purposes.

• s50 (int or float) – The stringency index needed to reach 50% of the maximum effect on the infection rate.

Simulation Method Parameters

class epimodels.RocheSimParameters(model, region_index, method, times)

RocheSimParameters: Base class for the simulation method’s parameters of the Roche model: deterministic SEIRD used by the F. Hoffmann-La Roche Ltd to model the Covid-19 epidemic and the effects of non-pharmaceutical interventions (NPIs) on the epidemic dynamic in different countries.

Parameters:

• region_index (int) – Index of region for which we wish to simulate.

• method (str) – The type of solver implemented by the simulator.

• times (list) – List of time points at which we wish to evaluate the ODEs system.

Parameters Controller

class epimodels.RocheParametersController(model, ICs, compartment_times, proportion_parameters, transmission_parameters, simulation_parameters)

RocheParametersController Class: Base class for the parameters of the Roche model: deterministic SEIRD used by the F. Hoffmann-La Roche Ltd to model the Covid-19 epidemic and the effects of non-pharmaceutical interventions (NPIs) on the epidemic dynamic in different countries.

In order to simulate using the Roche model, the following parameters are required, which are stored as part of this class.

Parameters:

• model (RocheSEIRModel) – The model whose parameters are stored.

• ICs (RocheICs) – Class of the ICs used in the simulation of the model.

• compartment_times (RocheCompartmentTimes) – Class of the average-time-in-compartment parameters used in the simulation of the model.

• proportion_parameters (RocheProportions) – Class of the proportions of asymptomatic, super-spreader and dead cases parameters used in the simulation of the model.

• transmission_parameters (RocheTransmission) – Class of the parameters used to compute transmission of virus used in the simulation of the model.

• simulation_parameters (RocheSimParameters) – Class of the simulation method’s parameters used in the simulation of the model.

Parameter Classes for the Warwick-Household Model

Below we list the methods for all the parameter classes associated with the forward simulation of the Warwick-Household model.

Initial Conditions Parameters

class epimodels.WarwickICs(model, susceptibles_IC, exposed_1_f_IC, exposed_1_sd_IC, exposed_1_su_IC, exposed_1_q_IC, exposed_2_f_IC, exposed_2_sd_IC, exposed_2_su_IC, exposed_2_q_IC, exposed_3_f_IC, exposed_3_sd_IC, exposed_3_su_IC, exposed_3_q_IC, detected_f_IC, detected_qf_IC, detected_sd_IC, detected_su_IC, detected_qs_IC, undetected_f_IC, undetected_s_IC, undetected_q_IC, recovered_IC)

WarwickICs: Base class for the ICs of the Warwick model: a deterministic SEIR developed by University of Warwick to model the Covid-19 epidemic and the effects of within-household dynamics on the epidemic trajectory in different countries.

Parameters:

• susceptibles_IC (list of lists) – Initial number of susceptibles classified by age (column name) and region (row name).

• exposed_1_f_IC (list of lists) – Initial number of exposed by a first household case classified by age (column name) and region (row name) in compartment 1.

• exposed_1_sd_IC (list of lists) – Initial number of exposed by a subsequent detected household case classified by age (column name) and region (row name) in compartment 1.

• exposed_1_su_IC (list of lists) – Initial number of exposed by a subsequent undetected household case classified by age (column name) and region (row name) in compartment 1.

• exposed_1_q_IC (list of lists) – Initial number of exposed by a quarantined household case classified by age (column name) and region (row name) in compartment 1.

• exposed_2_f_IC (list of lists) – Initial number of exposed by a first household case classified by age (column name) and region (row name) in compartment 2.

• exposed_2_sd_IC (list of lists) – Initial number of exposed by a subsequent detected household case classified by age (column name) and region (row name) in compartment 2.

• exposed_2_su_IC (list of lists) – Initial number of exposed by a subsequent undetected household case classified by age (column name) and region (row name) in compartment 2.

• exposed_2_q_IC (list of lists) – Initial number of exposed by a quarantined household case classified by age (column name) and region (row name) in compartment 2.

• exposed_3_f_IC (list of lists) – Initial number of exposed by a first household case classified by age (column name) and region (row name) in compartment 3.

• exposed_3_sd_IC (list of lists) – Initial number of exposed by a subsequent detected household case classified by age (column name) and region (row name) in compartment 3.

• exposed_3_su_IC (list of lists) – Initial number of exposed by a subsequent undetected household case classified by age (column name) and region (row name) in compartment 3.

• exposed_3_q_IC (list of lists) – Initial number of exposed by a quarantined household case classified by age (column name) and region (row name) in compartment 3.

• detected_f_IC (list of lists) – Initial number of detected infectives by a first household case classified by age (column name) and region (row name).

• detected_qf_IC (list of lists) – Initial number of detected infectives by a quarantined first household case classified by age (column name) and region (row name).

• detected_sd_IC (list of lists) – Initial number of detected infectives by a subsequent detected household case classified by age (column name) and region (row name).

• detected_su_IC (list of lists) – Initial number of detected infectives by a subsequent undetected household case classified by age (column name) and region (row name).

• detected_qs_IC (list of lists) – Initial number of detected infectives by a quarantined subsequent household case classified by age (column name) and region (row name).

• undetected_f_IC (list of lists) – Initial number of undetected infectives by a first household case classified by age (column name) and region (row name).

• undetected_s_IC (list of lists) – Initial number of undetected infectives by a subsequent household case classified by age (column name) and region (row name).

• undetected_q_IC (list of lists) – Initial number of undetected infectives by a quarantined household case classified by age (column name) and region (row name).

• recovered_IC (list of lists) – Initial number of recovered classified by age (column name) and region (row name).

Regional and Time Dependent Parameters

class epimodels.WarwickRegParameters(model, region_index, H)

WarwickRegParameters: Base class for the regional and time dependent parameters of the Warwick model: a deterministic SEIR developed by University of Warwick to model the Covid-19 epidemic and the effects of within-household dynamics on the epidemic trajectory in different countries.

Parameters:

• region_index (int) – Index of region for which we wish to simulate.

• H (list) – List of region dependent quarantine proportions.

Disease Specific Parameters

class epimodels.WarwickDiseaseParameters(model, tau, d)

WarwickDiseaseParameters: Base class for the disease-specific parameters of the Warwick model: a deterministic SEIR developed by University of Warwick to model the Covid-19 epidemic and the effects of within-household dynamics on the epidemic trajectory in different countries.

Parameters:

• tau (int or float) – Reduction in transmission for an asymptomatic infectious compared to the symptomatic case.

• d (int or float or list) – Age-dependent probabilities of displaying symptoms.

Transmission Specific Parameters

class epimodels.WarwickTransmission(model, epsilon, gamma, sigma)

RocheTransmission: Base class for the transmission-specific parameters of the Warwick model: a deterministic SEIR developed by University of Warwick to model the Covid-19 epidemic and the effects of within-household dynamics on the epidemic trajectory in different countries.

Parameters:

• epsilon (int or float) – Rate of progression to infection from exposed.

• gamma (int or float) – Rate of recovery.

• sigma (int or float or list) – Age-dependent susceptibility to infection.

Simulation Method Parameters

class epimodels.WarwickSimParameters(model, method, times)

WarwickSimParameters: Base class for the simulation method’s parameters of the Warwick model: a deterministic SEIR developed by University of Warwick to model the Covid-19 epidemic and the effects of within-household dynamics on the epidemic trajectory in different countries.

Parameters:

• method (str) – The type of solver implemented by the simulator.

• times (list) – List of time points at which we wish to evaluate the ODEs system.

Social Distancing Parameters

class epimodels.WarwickSocDistParameters(model, theta=[0.3], phi=[0], q_H=[1.25], q_S=[0.05], q_W=[0.2], q_O=[0.05], times_npis=[1])

WarwickSocDistParameters: Base class for the social distancing parameters of the Warwick model: a deterministic SEIR developed by University of Warwick to model the Covid-19 epidemic and the effects of within-household dynamics on the epidemic trajectory in different countries.

Parameters:

• theta (list of int or float) – List of proportions of work interactions in public-facing industries.

• phi (list of int or float) – List of scaling factors between pre- and full-lockdown contact matrices.

• q_H (list of int or float) – List of increases in the amount of household interactions during lockdown.

• q_S (list of int or float) – List of reductions in attendance at school during lockdown.

• q_W (list of int or float) – List of reductions in attendance at workplaces during lockdown.

• q_O (list of int or float) – List of reductions in engagement with shopping and leisure activities during lockdown.

• times_npis (list of int) – List of times of points at which the social distancing parameters changes.

Parameters Controller

class epimodels.WarwickParametersController(model, regional_parameters, ICs, disease_parameters, transmission_parameters, simulation_parameters, soc_dist_parameters=None)

WarwickParametersController Class: Base class for the parameters of the Warwick model: a deterministic SEIR developed by University of Warwick to model the Covid-19 epidemic and the effects of within-household dynamics on the epidemic trajectory in different countries.

In order to simulate using the Warwick model, the following parameters are required, which are stored as part of this class.

Parameters:

• model (WarwickSEIRModel) – The model whose parameters are stored.

• regional_parameters (WarwickRegParameters) – Class of the regional and time dependent parameters used in the simulation of the model.

• ICs (WarwickICs) – Class of the ICs used in the simulation of the model.

• disease_parameters (WarwickDiseaseParameters) – Class of the disease-specific parameters used in the simulation of the model.

• transmission_parameters (WarwickTransmission) – Class of the rates of progression parameters used in the simulation of the model.

• simulation_parameters (WarwickSimParameters) – Class of the simulation method’s parameters used in the simulation of the model.

• soc_dist_parameters (WarwickSocDistParameters) – Class of the social distancing parameters used in the simulation of the model.