AI 中文总结
该研究通过状态依赖马尔可夫切换模型评估疫情防控影响，开发有限种群随机框架，利用易感群体单调性推导递归，得出相关分布和矩，用卢森堡猴痘数据校准模型并比较不同控制方案，显示切换机制对感染数和灭绝时间的影响。
AI 中文摘要
我们为在干预方案之间进行马尔可夫切换下演变的SIR疫情开发了一个精确的有限种群随机框架。疫情状态通过一个有限阶段成分增强，使传播、恢复和直接免疫获取率取决于活跃方案。相变强度可能取决于当前疫情状态，以便政策升级能对感染个体数量做出反应。利用易感群体的单调性，我们推导了灭绝时间和灭绝前产生的感染数量的联合拉普拉斯 - 斯蒂尔杰斯变换和概率生成函数的分层递归。这些递归得出感染计数分布、条件灭绝时间变换以及连接疫情持续时间和感染负担的混合矩，同时用小阶段级求解取代大型全局线性系统。用卢森堡的每周猴痘发病率数据说明了该框架。在泊松观测模型下通过最大似然校准基线单阶段SIR模型。然后使用校准后的基线对固定控制方案、早期与延迟严格干预、疫苗接种支持的控制以及状态依赖升级进行条件比较。结果显示了切换机制如何影响感染个体总数和灭绝时间，包括它们的离散程度。由于切换机制是指定的而非从干预历史中估计，结果是基于条件模型的比较而非卢森堡干预历史效果的估计。
英文摘要
We develop an exact finite-population stochastic framework for SIR epidemics evolving under Markovian switching between intervention regimes. The epidemic state is augmented by a finite phase component, allowing transmission, recovery, and direct immunity-acquisition rates to depend on the active regime. Phase-transition intensities may depend on the current epidemic state, so that policy escalation can react to the number of infectious individuals. Exploiting the monotonicity of the susceptible compartment, we derive level-wise recursions for the joint Laplace--Stieltjes transform and probability generating function of the extinction time and the number of infections generated before extinction. These recursions yield the infection-count distribution, conditional extinction-time transforms, and mixed moments linking epidemic duration and infection burden, while replacing a large global linear system with small phase-level solves. The framework is illustrated using weekly mpox incidence data from Luxembourg. A baseline one-phase SIR model is calibrated by maximum likelihood under a Poisson observation model. The calibrated baseline is then used for conditional comparisons of fixed control regimes, early versus delayed strict intervention, vaccination-supported control, and state-dependent escalation. The results show how switching mechanisms affect both the total number of infected individuals and the extinction time, including their dispersion. Since the switching mechanisms are specified rather than estimated from the intervention history, the results are conditional model-based comparisons rather than estimates of the historical effects of interventions in Luxembourg.
