We propose a Bayesian Heterogeneity Learning approach for Susceptible-Infected-Removal-Susceptible (SIRS) model that allows underlying clustering patterns for transmission rate, recovery rate, and loss of immunity rate for the latest coronavirus (COVID-19) among different regions. Our proposed method provides simultaneously inference on parameter estimation and clustering information which contains both number of clusters and cluster configurations. Specifically, our key idea is to formulates the SIRS model into a hierarchical form and assign the Mixture of Finite mixtures priors for heterogeneity learning. The properties of the proposed models are examined and a Markov chain Monte Carlo sampling algorithm is used to sample from the posterior distribution. Extensive simulation studies are carried out to examine empirical performance of the proposed methods. We further apply the proposed methodology to analyze the state level COVID-19 data in U.S.

中文翻译：

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SIRS 模型的异质性学习：对 COVID-19 的应用

我们提出了一种用于易感-感染-去除-易感 (SIRS) 模型的贝叶斯异质性学习方法，该方法允许不同区域之间最新冠状病毒 (COVID-19) 的传播率、恢复率和免疫力丧失率的潜在聚类模式。我们提出的方法同时提供了对包含集群数量和集群配置的参数估计和集群信息的推断。具体来说，我们的关键思想是将 SIRS 模型制定为分层形式，并为异质性学习分配有限混合先验的混合。检查了所提出模型的特性，并使用马尔可夫链蒙特卡罗采样算法从后验分布中进行采样。进行了广泛的模拟研究以检查所提出方法的经验性能。我们进一步应用所提出的方法来分析美国的州级 COVID-19 数据