A filtering approach for statistical inference in a stochastic SIR model with an application to Covid-19 data

TL;DR

This paper introduces a nested particle filtering method for statistical inference in a stochastic SIR model, effectively capturing randomness in transmission and infections, and applies it to Austrian Covid-19 data for improved epidemic analysis.

Contribution

It presents a novel nested particle filtering approach for parameter estimation in stochastic SIR models with partial data, specifically applied to Covid-19 data.

Findings

Successful estimation of reproduction rate and parameters from Covid-19 data

Effective handling of unobservable infectious individuals and random fluctuations

Enhanced forecasting and model testing capabilities

Abstract

In this paper, we consider a discrete-time stochastic SIR model, where the transmission rate and the true number of infectious individuals are random and unobservable. An advantage of this model is that it permits us to account for random fluctuations in infectiousness and for non-detected infections. However, a difficulty arises because statistical inference has to be done in a partial information setting. We adopt a nested particle filtering approach to estimate the reproduction rate and the model parameters. As a case study, we apply our methodology to Austrian Covid-19 infection data. Moreover, we discuss forecasts and model tests.