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.

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