Analysis of Virus Propagation: A Transition Model Representation of Stochastic Epidemiological Models

TL;DR

This paper introduces a unified discrete-time transition model for SIR-type stochastic epidemiological models, enhancing transparency, comparability, and estimation capabilities over traditional deterministic models.

Contribution

It provides a common, flexible representation for SIR models, addressing limitations of deterministic approaches and enabling easier estimation from data.

Findings

Unified transition model classifies SIR-type models.

Eliminates limitations of deterministic models.

Enables estimation via extended Kalman filter.

Abstract

The growing literature on the propagation of COVID-19 relies on various dynamic SIR-type models (Susceptible-Infected-Recovered) which yield model-dependent results. For transparency and ease of comparing the results, we introduce a common representation of the SIR-type stochastic epidemiological models. This representation is a discrete time transition model, which allows us to classify the epidemiological models with respect to the number of states (compartments) and their interpretation. Additionally, the transition model eliminates several limitations of the deterministic continuous time epidemiological models which are pointed out in the paper. We also show that all SIR-type models have a nonlinear (pseudo) state space representation and are easily estimable from an extended Kalman filter.