  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.
