Spatial markov for measuring the spatial dependencies of an epidemiological spread : case covid'19 Madagascar

International audience This article presents a Markov chain variant that explicitly incorporates spatial effects. It is an extension of the Markovian class allowing a more complete analysis of the spatial dimensions of transitional dynamics. The aim is to have an explicit model that allows analysis of spatial dimensions. Here, the question is to study and quantify whether neighborhood context affects transitional dynamics. Rather than estimating a homogeneous law, the model requires the estimation of k transition laws, each dependent on spatial neighbor state. Consequently, this article used published data on confirmed cases of COVID19 in the 22 regions of Madagascar. These data were discretized to obtain a discrete state of propagation intensity. The analysis gave us the transition probabilities between Covid19 intensity states knowing the context of neighboring regions, and the propagation time laws knowing the spatial contexts. The results showed that neighboring regions had an effect on the propagation of Covid19 in Madagascar. After analysis, we can say that there is spatial dependency according to these spatial transition matrices.