This paper develops an individual-based stochastic network SIR model for the empirical analysis of the Covid-19 pandemic. It derives moment conditions for the number of infected and active cases for single as well as multigroup epidemic models. These moment conditions are used to investigate the identification and estimation of the transmission rates. The paper then proposes a method that jointly estimates the transmission rate and the magnitude of under-reporting of infected cases. Empirical evidence on six European countries matches the simulated outcomes once the under-reporting of infected cases is addressed. It is estimated that the number of actual cases could be between 4 to 10 times higher than the reported numbers in October 2020 and declined to 2 to 3 times in April 2021. The calibrated models are used in the counterfactual analyses of the impact of social distancing and vaccination on the epidemic evolution and the timing of early interventions in the United Kingdom and Germany.
