The Bayesian analysis of infectious disease surveillance data from multiple locations typically involves building and fitting a spatio-temporal model of how the disease spreads in the structured population. Here we present new generally applicable methodology to perform this task. We introduce a parsimonious representation of seasonality and a biologically informed specification of the outbreak component to avoid parameter identifiability issues. We develop a computationally efficient Bayesian inference methodology for the proposed models, including techniques to detect outbreaks by computing marginal posterior probabilities at each spatial location and time point. We show that it is possible to efficiently integrate out the discrete parameters associated with outbreak states, enabling the use of dynamic Hamiltonian Monte Carlo (HMC) as a complementary alternative to a hybrid Markov chain Monte Carlo (MCMC) algorithm. Furthermore, we introduce a robust Bayesian model comparison framework based on importance sampling to approximate model evidence in high-dimensional space. The performance of our methodology is validated through systematic simulation studies, where simulated outbreaks were successfully detected, and our model comparison strategy demonstrates strong reliability. We also apply our new methodology to monthly incidence data on invasive meningococcal disease from 28 European countries. The results highlight outbreaks across multiple countries and months, with model comparison analysis showing that the new specification outperforms previous approaches. The accompanying software is freely available as a R package at https://github.com/Matthewadeoye/DetectOutbreaks.

翻译：对来自多个地点的传染病监测数据进行贝叶斯分析，通常需要构建并拟合描述疾病在结构化人群中传播的时空模型。本文提出了一种适用于此任务的通用新方法。我们引入了季节性的简约表示方法，并采用基于生物学原理的暴发成分设定，以避免参数可识别性问题。针对所提出的模型，我们开发了计算高效的贝叶斯推断方法，包括通过计算每个空间位置和时间点的边际后验概率来检测暴发的技术。研究表明，可以高效地整合与暴发状态相关的离散参数，从而能够使用动态哈密顿蒙特卡洛（HMC）作为混合马尔可夫链蒙特卡洛（MCMC）算法的补充替代方案。此外，我们引入了一个基于重要性采样的稳健贝叶斯模型比较框架，用于近似高维空间中的模型证据。通过系统模拟研究验证了我们方法的性能，其中成功检测到模拟的暴发事件，且我们的模型比较策略展现出高度可靠性。我们还将新方法应用于来自28个欧洲国家的侵袭性脑膜炎球菌病月发病率数据。结果凸显了多个国家和月份的暴发情况，模型比较分析表明新设定优于以往方法。相关软件已作为R包在https://github.com/Matthewadeoye/DetectOutbreaks 免费发布。