The epidemic inference allows us to make predictions on the evolution of an epidemic to develop containment measures or infer the infection channels and the origin of the epidemic. In this thesis work, we discuss a metapopulation structure approach to stochastic inference, where the total population is partitioned in many subpopulations which interact with each other. We assume to receive daily information about the aggregate number of infected individuals at the single population level. The information from such time-scattered observations together with some prior information can be used to develop a Bayesian framework to address different epidemic inference problems such as to predict the future evolution of the outbreak (epidemic forecast), to infer the current state of the epidemics in unobserved populations (risk assessment), or to infer the past state of the epidemics (causal paths, patient zero).