Abstract
This paper presents a Markovian analysis of the spatio-temporal dynamics of an epidemic. We develop an explicit semi-Markovian model that accounts for spatial dependence, operating in discrete time over a finite state space. The model allowed us to have a propagation model conditioned by neighboring states and quantifies two key characteristics : spatial propagation timescales and propagation law in an region dependent on neighbor states. The model is inferred from data collected on the spread of Covid'19 in Madagascar's 22 regions, using a bayesian approach to take into account the knowledge of disease specialists. The result has demonstrated the effect of neighborhoods on the propagation dynamics of the deseases. We conclude with a discussion of potential future theoretical developments.