# Bayesian inference of a spatially dependent semi-Markovian model with application to Madagascar Covid’19 data

## TL;DR

The paper introduces a spatially dependent model to study how diseases like Covid-19 spread, using Bayesian methods on Madagascar's data.

## Contribution

A novel semi-Markovian model with spatial dependence is proposed and applied to real-world disease data.

## Key findings

- The model captures spatial propagation timescales and regional disease spread influenced by neighboring states.
- Bayesian inference applied to Madagascar's data reveals the impact of neighboring regions on disease dynamics.
- The study highlights the importance of spatial dependencies in understanding and modeling disease propagation.

## Abstract

This article presents an approach to stochastic analysis of disease dynamics. 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 a region dependent on neighboring states. The model is inferred from data collected on the spread of Covid’19 in Madagascar’s 22 regions, using the Bayesian approach to get a better idea of model parameter values. The result has demonstrated the effect of neighborhoods on the propagation dynamics of diseases. We conclude with a discussion of potential future theoretical developments.