Spatial Markov matrices for measuring the spatial dependencies of an epidemiological spread : case Covid’19 Madagascar

This article applies a variant of the Markov chain that explicitly incorporates spatial effects. It is an extension of the Markov class allowing a more complete analysis of the spatial dimensions of transition dynamics. The aim is to provide a methodology for applying the explicit model to spatial dependency analysis.

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. This article used published data on confirmed cases of Covid’19 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 Covid’19 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 Covid’19 in Madagascar.

After analysis, we can say that there is spatial dependency according to these spatial transition matrices.