一种新型随机流行病模型及其在COVID-19中的应用
A Novel Stochastic Epidemic Model with Application to COVID-19
AI总结：
提出一种新型SEIR随机流行病模型，基于排队系统占用率推导疫情收缩条件，并设计稳定缓解策略，验证其在COVID-19中的有效性。
摘要：
本文提出了一种新型的SEIR随机流行病模型。该新模型的一个显著特征是，它允许我们在一般潜伏期和传染期分布的设定下进行研究。在某种程度上，具有无穷多个服务器的排队系统和具有时变转移率的Markov链是本文的核心技术基础。尽管更具一般性，该Markov链与针对指数分布潜伏期和传染期的以往模型一样易于处理。它也比具有类似一般性水平的半Markov模型显著更简单且更易于处理。基于随机稳定性的概念，我们推导出了以驱动动态的排队系统占用率表示的疫情收缩充分条件。基于此条件，我们提出了一类特定的稳定缓解策略，旨在在规定的无缓解期后保持平衡的占用率。我们结合最近的COVID-19疫情数据验证了该方法，并评估了不同稳定策略的效果。结果表明，只要缓解措施不被过度拖延，就有可能通过各种占用率水平来控制疫情。
英文摘要：
In this paper we propose a novel SEIR stochastic epidemic model. A distinguishing feature of this new model is that it allows us to consider a set up under general latency and infectious period distributions. To some extent, queuing systems with infinitely many servers and a Markov chain with time-varying transition rate are the very technical underpinning of the paper. Although more general, the Markov chain is as tractable as previous models for exponentially distributed latency and infection periods. It is also significantly simpler and more tractable than semi-Markov models with a similar level of generality. Based on the notion of stochastic stability, we derive a sufficient condition for a shrinking epidemic in terms of the queuing system's occupation rate that drives the dynamics. Relying on this condition, we propose a class of ad-hoc stabilising mitigation strategies that seek to keep a balanced occupation rate after a prescribed mitigation-free period. We validate the approach in the light of recent data on the COVID-19 epidemic and assess the effect of different stabilising strategies. The results suggest that it is possible to curb the epidemic with various occupation rate levels, as long as the mitigation is not excessively procrastinated.
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