The COVID-19 pandemic has been characterised by multiple waves of transmission driven by interventions and emerging variants, challenging epidemic models that assume gradually evolving transmission dynamics. We propose a class of state-space models in which the transmission rate evolves through persistent regimes of random duration, governed by a semi-Markov process. This formulation yields an interpretable representation of sustained transmission phases and retains a parsimonious parameterisation. Particle-based Bayesian methods are well established for standard state-space models, but their use in semi-Markov settings has received comparatively limited attention. In epidemic applications, inference is further complicated by differential equation-driven latent dynamics and observation models defined through functionals of the latent process. We develop an inferential framework that accommodates these features, combining particle-based state updates with gradient-based parameter updates and enabling batch and sequential inference via particle and sequential Monte Carlo. We apply the proposed methodology to COVID-19 data from the United Kingdom and show that combining reported cases and deaths leads to more precise and stable inference compared to using deaths alone. These results illustrate the practical value of semi-Markov transmission models for epidemic analysis under complex observation schemes.

翻译：COVID-19疫情的特征在于干预措施和新兴变异株驱动的多波传播，这对假设传播动态缓慢演变的流行病模型提出了挑战。我们提出了一类状态空间模型，其中传播率通过半马尔可夫过程支配的持久随机时段进行演化。该公式生成了持续传播阶段的可解释表征，并保留了简约的参数化方法。基于粒子的贝叶斯方法在标准状态空间模型中已发展成熟，但在半马尔可夫设置中的应用相对较少。在流行病应用中，推断因微分方程驱动的潜在动态以及通过潜在过程泛函数定义的观测模型而进一步复杂化。我们开发了一个适应这些特征的推断框架，将基于粒子的状态更新与基于梯度的参数更新相结合，并通过粒子蒙特卡洛和序贯蒙特卡洛实现批量推断和序贯推断。我们将所提出的方法应用于英国COVID-19数据，结果表明，结合报告病例和死亡数据比仅使用死亡数据能获得更精确和稳定的推断。这些结果说明了半马尔可夫传播模型在复杂观测方案下进行流行病分析的实际价值。