The recent COVID-19 pandemic has shown that when the reproduction number is high and there are no proper measurements in place, the number of infected people can increase dramatically in a short time, producing a phenomenon that many stochastic SIR-like models cannot describe: overdispersion of the number of infected people (i.e., the variance of the number of infected people during any interval is very high compared to the average). To address this issue, in this paper we explore the possibility of modeling the total number of infections as a state-dependent self-exciting point process. In this way, infections are not independent among themselves, but any infection will increase the likelihood of a new infection while also the number of currently infected and recovered individuals are included into determining the likelihood of new infections, Since long term simulation is extremely computationally intensive, exact expressions for the moments of the processes determining the number of infected and recovered individuals are computed, while also simulation algorithms for these state-dependent processes are provided.

中文翻译：

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使用状态相关点过程的高传染性流行病早期阶段的随机模型


最近的 COVID-19 大流行表明，当传染数很高且没有适当的测量时，感染人数可能会在短时间内急剧增加，从而产生许多类似 SIR 的随机模型无法描述的现象：感染人数过度分散（即任何时间间隔内感染人数的方差与平均值相比非常高）。为了解决这个问题，在本文中，我们探讨了将感染总数建模为状态相关的自激点过程的可能性。这样，感染之间并不是独立的，但任何感染都会增加新感染的可能性，同时当前感染和康复的个体的数量也被包括在确定新感染的可能性中，因为长期模拟的计算量极大，计算确定感染和康复个体数量的过程时刻的精确表达式，同时还提供这些状态相关过程的模拟算法。