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

## TL;DR

This paper introduces a statistical method to estimate the spread of infectious diseases like Covid-19 using a model that accounts for hidden infections and random changes in transmission.

## Contribution

The novelty is using nested particle filtering in a Bayesian framework for inference in a partially observed stochastic SIR model.

## Key findings

- The method successfully estimates unobserved states and parameters in the SIR model.
- The approach was applied to Austrian Covid-19 data, showing its practical utility.
- Posterior predictive checks were used to validate the model and improve forecasts.

## Abstract

In this paper, we consider a discrete-time stochastic SIR model, where the transmission rate and the number of infectious individuals are random and unobservable. This model accounts for random fluctuations in infectiousness and for non-detected infections. Thus, statistical inference has to be performed in a partial information setting. We adopt a Bayesian approach and use nested particle filtering to estimate the state of the system and the parameters. Moreover, we discuss forecasts and model tests based on the posterior predictive distribution. As a case study, we apply our methodology to Austrian Covid-19 infection data.