The spatial Markov matrix of Rey [21].

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.

本文提出了一种疾病动力学随机分析方法。我们构建了一个显式半马尔可夫（semi-Markovian）模型，该模型考虑了空间相关性，在有限状态空间上以离散时间运行。该模型支持构建以邻域状态为条件的传播模型，并量化了两项核心特征：空间传播时间尺度，以及依赖于邻域状态的区域内传播规律。我们基于马达加斯加22个地区的新冠（Covid-19）疫情传播收集的数据，结合贝叶斯（Bayesian）方法推断模型参数，以更精准地确定模型参数取值。研究结果证实了邻域效应对疾病传播动力学的影响。最后，本文对未来潜在的理论研究方向展开了讨论。