This paper refines statistical inference of computer virus propagation with maximum likelihood (ML) estimation. In particular, in order to utilize actual infection data that are opened in Web sites, we reformulate classical stochastic models by Markovian arrival processes (MAPs). The reformulated models lead to plausible parameter estimation based on the ML estimation. We propose efficient algorithms to compute the ML estimates of epidemic models using the EM (expectation-maximization) algorithm. Experiments illustrate the estimation of virus propagation with real infection data by our methods. Finally we refer to characterization of virus propagation from the view point of stochastic modeling.