Inference Classes

This section documents the classes used for the parameter inference of epidemiological models curated in this collection.

Overview:

Public Health England & Cambridge Model

class epimodels.inference.PheSEIRInfer(model)[source]

PheSEIRInfer Class: Controller class for the optimisation or inference of parameters of the PHE model in a PINTS framework.

Parameters:

model (PheSEIRModel) – The model for which we solve the optimisation or inference problem.

inference_problem_setup(times, num_iter, wd=1, wp=1)[source]

Runs the parameter inference routine for the PHE model.

Parameters:

  • times (list) – List of time points at which we have data for the log-likelihood computation.

  • num_iter (integer) – Number of iterations the MCMC sampler algorithm is run for.

  • wd (float or int) – Proportion of the contribution of the deaths data to the log-likelihood.

  • wp (float or int) – Proportion of the contribution of the serology data to the log-likelihood.

Returns:

3D-matrix of the proposed parameters for each iteration for each of the chains of the MCMC sampler.

Return type:

numpy.array

optimisation_problem_setup(times, wd=1, wp=1)[source]

Runs the initial conditions optimisation routine for the PHE model.

Parameters:

  • times (list) – List of time points at which we have data for the log-likelihood computation.

  • wd (float or int) – Proportion of the contribution of the deaths data to the log-likelihood.

  • wp (float or int) – Proportion of the contribution of the serology data to the log-likelihood.

Returns:

  • numpy.array – Matrix of the optimised parameters at the end of the optimisation procedure.

  • float – Value of the log-posterior at the optimised point in the free parameter space.

read_deaths_data(deaths_data, deaths_times, time_to_death, fatality_ratio)[source]

Sets the serology data used for the model’s parameters inference.

Parameters:

  • deaths_data (numpy.array) – List of region-specific age-structured number of deaths as a matrix. Each column represents an age group.

  • deaths_times (numpy.array) – Matrix of timepoints for which deaths data is available.

  • time_to_death (list) – List of probabilities of death of individual d days after infection.

  • fatality_ratio (list) – List of age-specific fatality ratios.

read_model_data(susceptibles_data, infectives_data)[source]

Sets the initial data used for the model’s parameters optimisation or inference.

Parameters:

  • susceptibles_data (list) – List of regional age-structured lists of the initial number of susceptibles.

  • infectives_data (list) – List of regional age-structured lists of the initial number of infectives in the first infectives compartment.

read_serology_data(tests_data, positives_data, serology_times, sens, spec)[source]

Sets the serology data used for the model’s parameters inference.

Parameters:

  • tests_data (list of numpy.array) – List of region-specific age-structured number of tests conducted as a matrix. Each column represents an age group.

  • positives_data (list of numpy.array) – List of region-specific age-structured number of positive test results as a matrix. Each column represents an age group.

  • serology_times (numpy.array) – Matrix of timepoints for which serology data is available.

  • sens (float or int) – Sensitivity of the test (or ratio of true positives).

  • spec (float or int) – Specificity of the test (or ratio of true negatives).

return_loglikelihood(times, x, wd=1, wp=1)[source]

Return the log-likelihood used for the optimisation or inference.

Parameters:

  • times (list) – List of time points at which we have data for the log-likelihood computation.

  • x (list) – List of free parameters used for computing the log-likelihood.

  • wd (float or int) – Proportion of the contribution of the deaths data to the log-likelihood.

  • wp (float or int) – Proportion of the contribution of the serology data to the log-likelihood.

Returns:

Value of the log-likelihood at the given point in the free parameter space.

Return type:

float

class epimodels.inference.PHELogLik(model, susceptibles_data, infectives_data, times, deaths, time_to_death, deaths_times, fatality_ratio, tests_data, positives_data, serology_times, sens, spec, wd=1, wp=1)[source]

PHELogLik Class: Controller class to construct the log-likelihood needed for optimisation or inference in a PINTS framework.

Parameters:

  • model (PheSEIRModel) – The model for which we solve the optimisation or inference problem.

  • susceptibles_data (list) – List of regional age-structured lists of the initial number of susceptibles.

  • infectives_data (list) – List of regional age-structured lists of the initial number of infectives in the first infectives compartment.

  • times (list) – List of time points at which we have data for the log-likelihood computation.

  • deaths_data (numpy.array) – List of region-specific age-structured number of deaths as a matrix. Each column represents an age group.

  • time_to_death (list) – List of probabilities of death of individual d days after infection.

  • deaths_times (numpy.array) – Matrix of timepoints for which deaths data is available.

  • fatality_ratio (list) – List of age-specific fatality ratios.

  • tests_data (list of numpy.array) – List of region-specific age-structured number of tests conducted as a matrix. Each column represents an age group.

  • positives_data (list of numpy.array) – List of region-specific age-structured number of positive test results as a matrix. Each column represents an age group.

  • serology_times (numpy.array) – Matrix of timepoints for which serology data is available.

  • sens (float or int) – Sensitivity of the test (or ratio of true positives).

  • spec (float or int) – Specificity of the test (or ratio of true negatives).

  • wd (float or int) – Proportion of the contribution of the deaths data to the log-likelihood.

  • wp (float or int) – Proportion of the contribution of the serology data to the log-likelihood.

n_parameters()[source]

Returns number of parameters for log-likelihood object.

Returns:

Number of parameters for log-likelihood object.

Return type:

int

set_fixed_parameters()[source]

Sets the non-changing parameters of the model in the class structure to save time in the evaluation of the log-likelihood.

class epimodels.inference.PHELogPrior(model, times)[source]

PHELogPrior Class: Controller class to construct the log-prior needed for optimisation or inference in a PINTS framework.

Parameters:

  • model (PheSEIRModel) – The model for which we solve the optimisation or inference problem.

  • times (list) – List of time points at which we have data for the log-likelihood computation.

n_parameters()[source]

Returns number of parameters for log-prior object.

Returns:

Number of parameters for log-prior object.

Return type:

int

Roche SEIRD Model

class epimodels.inference.RocheSEIRInfer(model)[source]

RocheSEIRInfer Class: Controller class for the optimisation or inference of parameters of the Roche model in a PINTS framework.

Parameters:

model (RocheSEIRModel) – The model for which we solve the optimisation or inference problem.

inference_problem_setup(times, num_iter, wd=1, wp=1)[source]

Runs the parameter inference routine for the Roche model.

Parameters:

  • times (list) – List of time points at which we have data for the log-likelihood computation.

  • num_iter (integer) – Number of iterations the MCMC sampler algorithm is run for.

  • wd (float or int) – Proportion of the contribution of the deaths data to the log-likelihood.

  • wp (float or int) – Proportion of the contribution of the serology data to the log-likelihood.

Returns:

3D-matrix of the proposed parameters for each iteration for each of the chains of the MCMC sampler.

Return type:

numpy.array

optimisation_problem_setup(times, wd=1, wp=1)[source]

Runs the initial conditions optimisation routine for the Roche model.

Parameters:

  • times (list) – List of time points at which we have data for the log-likelihood computation.

  • wd (float or int) – Proportion of the contribution of the deaths data to the log-likelihood.

  • wp (float or int) – Proportion of the contribution of the serology data to the log-likelihood.

Returns:

  • numpy.array – Matrix of the optimised parameters at the end of the optimisation procedure.

  • float – Value of the log-posterior at the optimised point in the free parameter space.

read_deaths_data(deaths_data, deaths_times)[source]

Sets the serology data used for the model’s parameters inference.

Parameters:

  • deaths_data (numpy.array) – List of region-specific age-structured number of deaths as a matrix. Each column represents an age group.

  • deaths_times (numpy.array) – Matrix of timepoints for which deaths data is available.

read_model_data(susceptibles_data, infectives_data)[source]

Sets the initial data used for the model’s parameters optimisation or inference.

Parameters:

  • susceptibles_data (list) – List of regional age-structured lists of the initial number of susceptibles.

  • infectives_data (list) – List of regional age-structured lists of the initial number of infectives in the presymptomatic infectives compartment.

read_npis_data(max_levels_npi, targeted_npi, general_npi, reg_levels_npi, time_changes_npi, time_changes_flag)[source]

Sets the non-pharmaceutical interventions data used for the model’s parameters inference.

Parameters:

  • max_levels_npi (list of int) – List of maximum levels the non-pharmaceutical interventions can reach.

  • targeted_npi (list of bool) – List of the targeted non-pharmaceutical interventions.

  • general_npi (list of list of int) – List of the general values of the targeted non-pharmaceutical interventions. In chronological order.

  • reg_levels_npi (list of list of int) – List of region-specific levels the non-pharmaceutical interventions changes. In chronological order.

  • time_changes_npi (list) – List of times at which the next instances of region-specific non-pharmaceutical interventions start to be used. In increasing order.

  • time_changes_flag (list) – List of times at which the next instances of region-specific non-pharmaceutical interventions start to be used. In increasing order.

read_serology_data(tests_data, positives_data, serology_times, sens, spec)[source]

Sets the serology data used for the model’s parameters inference.

Parameters:

  • tests_data (list of numpy.array) – List of region-specific age-structured number of tests conducted as a matrix. Each column represents an age group.

  • positives_data (list of numpy.array) – List of region-specific age-structured number of positive test results as a matrix. Each column represents an age group.

  • serology_times (numpy.array) – Matrix of timepoints for which serology data is available.

  • sens (float or int) – Sensitivity of the test (or ratio of true positives).

  • spec (float or int) – Specificity of the test (or ratio of true negatives).

return_loglikelihood(times, x, wd=1, wp=1)[source]

Return the log-likelihood used for the optimisation or inference.

Parameters:

  • times (list) – List of time points at which we have data for the log-likelihood computation.

  • x (list) – List of free parameters used for computing the log-likelihood.

  • wd (float or int) – Proportion of the contribution of the deaths data to the log-likelihood.

  • wp (float or int) – Proportion of the contribution of the serology data to the log-likelihood.

Returns:

Value of the log-likelihood at the given point in the free parameter space.

Return type:

float

class epimodels.inference.RocheLogLik(model, susceptibles_data, infectives_data, times, deaths, deaths_times, tests_data, positives_data, serology_times, sens, spec, max_levels_npi, targeted_npi, general_npi, reg_levels_npi, time_changes_npi, time_changes_flag, wd=1, wp=1)[source]

RocheLogLik Class: Controller class to construct the log-likelihood needed for optimisation or inference in a PINTS framework.

Parameters:

  • model (RocheSEIRModel) – The model for which we solve the optimisation or inference problem.

  • susceptibles_data (list) – List of regional age-structured lists of the initial number of susceptibles.

  • infectives_data (list) – List of regional age-structured lists of the initial number of infectives in the presymptomatic infectives compartments.

  • times (list) – List of time points at which we have data for the log-likelihood computation.

  • deaths_data (numpy.array) – List of region-specific age-structured number of deaths as a matrix. Each column represents an age group.

  • deaths_times (numpy.array) – Matrix of timepoints for which deaths data is available.

  • tests_data (list of numpy.array) – List of region-specific age-structured number of tests conducted as a matrix. Each column represents an age group.

  • positives_data (list of numpy.array) – List of region-specific age-structured number of positive test results as a matrix. Each column represents an age group.

  • serology_times (numpy.array) – Matrix of timepoints for which serology data is available.

  • sens (float or int) – Sensitivity of the test (or ratio of true positives).

  • spec (float or int) – Specificity of the test (or ratio of true negatives).

  • max_levels_npi (list of int) – List of maximum levels the non-pharmaceutical interventions can reach.

  • targeted_npi (list of bool) – List of the targeted non-pharmaceutical interventions.

  • general_npi (list of list of int) – List of the general values of the targeted non-pharmaceutical interventions. In chronological order.

  • reg_levels_npi (list of list of int) – List of region-specific levels the non-pharmaceutical interventions changes. In chronological order.

  • time_changes_npi (list) – List of times at which the next instances of region-specific non-pharmaceutical interventions start to be used. In increasing order.

  • time_changes_flag (list) – List of times at which the next instances of region-specific non-pharmaceutical interventions start to be used. In increasing order.

  • wd (float or int) – Proportion of the contribution of the deaths data to the log-likelihood.

  • wp (float or int) – Proportion of the contribution of the serology data to the log-likelihood.

n_parameters()[source]

Returns number of parameters for log-likelihood object.

Returns:

Number of parameters for log-likelihood object.

Return type:

int

set_fixed_parameters()[source]

Sets the non-changing parameters of the model in the class structure to save time in the evaluation of the log-likelihood.

class epimodels.inference.RocheLogPrior(model, times)[source]

RocheLogPrior Class: Controller class to construct the log-prior needed for optimisation or inference in a PINTS framework.

Parameters:

  • model (RocheSEIRModel) – The model for which we solve the optimisation or inference problem.

  • times (list) – List of time points at which we have data for the log-likelihood computation.

n_parameters()[source]

Returns number of parameters for log-prior object.

Returns:

Number of parameters for log-prior object.

Return type:

int

Warwick-Household Model

class epimodels.inference.WarwickSEIRInfer(model)[source]

WarwickSEIRInfer Class: Controller class for the optimisation or inference of parameters of the Warwick model in a PINTS framework.

Parameters:

model (WarwickSEIRModel) – The model for which we solve the optimisation or inference problem.

inference_problem_setup(times, num_iter, wd=1, wp=1)[source]

Runs the parameter inference routine for the Warwick model.

Parameters:

  • times (list) – List of time points at which we have data for the log-likelihood computation.

  • num_iter (integer) – Number of iterations the MCMC sampler algorithm is run for.

  • wd (float or int) – Proportion of the contribution of the deaths data to the log-likelihood.

  • wp (float or int) – Proportion of the contribution of the serology data to the log-likelihood.

Returns:

3D-matrix of the proposed parameters for each iteration for each of the chains of the MCMC sampler.

Return type:

numpy.array

optimisation_problem_setup(times, wd=1, wp=1)[source]

Runs the initial conditions optimisation routine for the Warwick model.

Parameters:

  • times (list) – List of time points at which we have data for the log-likelihood computation.

  • wd (float or int) – Proportion of the contribution of the deaths data to the log-likelihood.

  • wp (float or int) – Proportion of the contribution of the serology data to the log-likelihood.

Returns:

  • numpy.array – Matrix of the optimised parameters at the end of the optimisation procedure.

  • float – Value of the log-posterior at the optimised point in the free parameter space.

read_deaths_data(deaths_data, deaths_times)[source]

Sets the serology data used for the model’s parameters inference.

Parameters:

  • deaths_data (numpy.array) – List of region-specific age-structured number of deaths as a matrix. Each column represents an age group.

  • deaths_times (numpy.array) – Matrix of timepoints for which deaths data is available.

read_delay_data(pDtoH, dDtoH, pHtoDeath, dHtoDeath)[source]

Sets the hospitalisation and death delays data used for the model’s parameters inference.

Parameters:

  • pDtoH (list) – Age-dependent fractions of the number of symptomatic cases that end up hospitalised.

  • dDtoH (list) – Distribution of the delay between onset of symptoms and hospitalisation. Must be normalised.

  • pHtoDeath (list) – Age-dependent fractions of the number of hospitalised cases that die.

  • dHtoDeath (list) – Distribution of the delay between onset of hospitalisation and death. Must be normalised.

read_extended_contact_matrices(extended_house_cont_mat, extended_school_cont_mat, extended_work_cont_mat, extended_other_cont_mat)[source]

Sets the initial contact matrix with more age groups used for the model’s parameters optimisation or inference.

Parameters:

  • extended_house_cont_mat (ContactMatrix) – Initial contact matrix with more age groups used for the modelling, underlying household interactions.

  • extended_school_cont_mat (ContactMatrix) – Initial contact matrix with more age groups used for the modelling, underlying school interactions.

  • extended_work_cont_mat (ContactMatrix) – Initial contact matrix with more age groups used for the modelling, underlying workplace interactions.

  • extended_other_cont_mat (ContactMatrix) – Initial contact matrix with more age groups used for the modelling, underlying other non-household interactions.

read_extended_population_structure(extended_susceptibles, extended_infectives_prop)[source]

Sets the initial data with more age groups used for the model’s parameters optimisation or inference.

Parameters:

  • extended_susceptibles (list) – List country-level initial number of susceptibles organised in an extended age classification.

  • extended_infectives_prop (list) – List country-level initial proportions of infective individuals in each age group when the population is organised in an extended age classification.

read_model_data(susceptibles_data, infectives_data)[source]

Sets the initial data used for the model’s parameters optimisation or inference.

Parameters:

  • susceptibles_data (list) – List of regional age-structured lists of the initial number of susceptibles.

  • infectives_data (list) – List of regional age-structured lists of the initial number of infectives in the presymptomatic infectives compartment.

read_serology_data(tests_data, positives_data, serology_times, sens, spec)[source]

Sets the serology data used for the model’s parameters inference.

Parameters:

  • tests_data (list of numpy.array) – List of region-specific age-structured number of tests conducted as a matrix. Each column represents an age group.

  • positives_data (list of numpy.array) – List of region-specific age-structured number of positive test results as a matrix. Each column represents an age group.

  • serology_times (numpy.array) – Matrix of timepoints for which serology data is available.

  • sens (float or int) – Sensitivity of the test (or ratio of true positives).

  • spec (float or int) – Specificity of the test (or ratio of true negatives).

return_loglikelihood(times, x, wd=1, wp=1)[source]

Return the log-likelihood used for the optimisation or inference.

Parameters:

  • times (list) – List of time points at which we have data for the log-likelihood computation.

  • x (list) – List of free parameters used for computing the log-likelihood.

  • wd (float or int) – Proportion of the contribution of the deaths data to the log-likelihood.

  • wp (float or int) – Proportion of the contribution of the serology data to the log-likelihood.

Returns:

Value of the log-likelihood at the given point in the free parameter space.

Return type:

float

class epimodels.inference.WarwickLogLik(model, extended_susceptibles, extended_infectives_prop, extended_house_cont_mat, extended_school_cont_mat, extended_work_cont_mat, extended_other_cont_mat, pDtoH, dDtoH, pHtoDeath, dHtoDeath, susceptibles_data, infectives_data, times, deaths, deaths_times, tests_data, positives_data, serology_times, sens, spec, wd=1, wp=1)[source]

WarwickLogLik Class: Controller class to construct the log-likelihood needed for optimisation or inference in a PINTS framework.

Parameters:

  • model (WarwickSEIRModel) – The model for which we solve the optimisation or inference problem.

  • extended_susceptibles (list) – List country-level initial number of susceptibles organised in an extended age classification.

  • extended_infectives_prop (list) – List country-level initial proportions of infective individuals in each age group when the population is organised in an extended age classification.

  • extended_house_cont_mat (ContactMatrix) – Initial contact matrix with more age groups used for the modelling, underlying household interactions.

  • extended_school_cont_mat (ContactMatrix) – Initial contact matrix with more age groups used for the modelling, underlying school interactions.

  • extended_work_cont_mat (ContactMatrix) – Initial contact matrix with more age groups used for the modelling, underlying workplace interactions.

  • extended_other_cont_mat (ContactMatrix) – Initial contact matrix with more age groups used for the modelling, underlying other non-household interactions.

  • pDtoH (list) – Age-dependent fractions of the number of symptomatic cases that end up hospitalised.

  • dDtoH (list) – Distribution of the delay between onset of symptoms and hospitalisation. Must be normalised.

  • pHtoDeath (list) – Age-dependent fractions of the number of hospitalised cases that die.

  • dHtoDeath (list) – Distribution of the delay between onset of hospitalisation and death. Must be normalised.

  • susceptibles_data (list) – List of regional age-structured lists of the initial number of susceptibles.

  • infectives_data (list) – List of regional age-structured lists of the initial number of infectives in the presymptomatic infectives compartments.

  • times (list) – List of time points at which we have data for the log-likelihood computation.

  • deaths_data (numpy.array) – List of region-specific age-structured number of deaths as a matrix. Each column represents an age group.

  • deaths_times (numpy.array) – Matrix of timepoints for which deaths data is available.

  • tests_data (list of numpy.array) – List of region-specific age-structured number of tests conducted as a matrix. Each column represents an age group.

  • positives_data (list of numpy.array) – List of region-specific age-structured number of positive test results as a matrix. Each column represents an age group.

  • serology_times (numpy.array) – Matrix of timepoints for which serology data is available.

  • sens (float or int) – Sensitivity of the test (or ratio of true positives).

  • spec (float or int) – Specificity of the test (or ratio of true negatives).

  • wd (float or int) – Proportion of the contribution of the deaths data to the log-likelihood.

  • wp (float or int) – Proportion of the contribution of the serology data to the log-likelihood.

n_parameters()[source]

Returns number of parameters for log-likelihood object.

Returns:

Number of parameters for log-likelihood object.

Return type:

int

set_fixed_parameters()[source]

Sets the non-changing parameters of the model in the class structure to save time in the evaluation of the log-likelihood.

class epimodels.inference.WarwickLogPrior(model, times)[source]

WarwickLogPrior Class: Controller class to construct the log-prior needed for optimisation or inference in a PINTS framework.

Parameters:

  • model (WarwickSEIRModel) – The model for which we solve the optimisation or inference problem.

  • times (list) – List of time points at which we have data for the log-likelihood computation.

n_parameters()[source]

Returns number of parameters for log-prior object.

Returns:

Number of parameters for log-prior object.

Return type:

int