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

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.