Identifiability, Observability, Uncertainty and Bayesian System Identification of Epidemiological Models

TL;DR

This study analyzes the identifiability, observability, and uncertainty in deterministic and stochastic epidemiological models, revealing conditions under which parameters can be reliably estimated and the impact of overdispersion varies with population size.

Contribution

It provides a comprehensive evaluation of model properties and introduces an efficient C++ library for parameter estimation in epidemiological models.

Findings

Deterministic SIR and SEIR models are structurally identifiable and observable.

Overdispersion has minimal impact on large populations but affects small populations.

The C++ library efficiently estimates parameters, though SEIAR remains challenging to identify.

Abstract

In this project, identifiability, observability and uncertainty properties of the deterministic and Chain Binomial stochastic SIR, SEIR and SEIAR epidemiological models are studied. Techniques for modeling overdispersion are investigated and used to compare simulated trajectories for moderately sized, homogenous populations. With the chosen model parameters overdispersion was found to have small impact, but larger impact on smaller populations and simulations closer to the initial outbreak of an epidemic. Using a software tool for model identifiability and observability (DAISY[Bellu et al. 2007]), the deterministic SIR and SEIR models was found to be structurally identifiable and observable under mild conditions, while SEIAR in general remains structurally unidentifiable and unobservable. Sequential Monte Carlo and Markov Chain Monte Carlo methods were implemented in a custom C++ library and applied to stochastic SIR, SEIR and SEIAR models in order to generate parameter distributions. With the chosen model parameters overdispersion was found to have a small impact on parameter distributions for SIR and SEIR models. For SEIAR, the algorithm did not converge around the true parameters of the deterministic model. The custom C++ library was found to be computationally efficient, and is very likely to be used in future projects.