Invisible Infections: A Partial Information Approach for Estimating the Transmission Dynamics of the Covid-19 Pandemic

In this paper, we develop a discrete time stochastic model under partial information to explain the evolution of Covid-19 pandemic. Our model is a modification of the well-known SIR model for epidemics, which accounts for some peculiar features of Covid-19. In particular, we work with a random transmission rate and we assume that the true number of infectious people at any observation time is random and not directly observable, to account for asymptomatic and non-tested people. We elaborate a nested particle filtering approach to estimate the reproduction rate and the model parameters. We apply our methodology to Austrian Covid-19 infection data in the period from May 2020 to June 2022. Finally, we discuss forecasts and model tests.