论文标题
通过使用状态依赖性点过程的高度传染性流行病早期阶段的随机模型
A Stochastic Model for the Early Stages of Highly Contagious Epidemics by using a State-Dependent Point Process
论文作者
论文摘要
最近的Covid-19大流行表明，当繁殖数量很高且没有适当的测量值时，受感染者的数量可以在短时间内急剧增加，产生一种现象，许多随机的sir模型无法描述：感染者数量过度的过度（即，在任何感染者的数量中，都非常高的人数比较。为了解决这个问题，在本文中，我们探讨了将感染总数作为州依赖的自我激发点过程进行建模的可能性。这样，感染并非彼此独立，但是任何感染都会增加新感染的可能性，而当前感染和恢复的个体的数量也包括在确定新感染的可能性中，因为长期模拟是非常计算的密集型，在确切的表达式上，对于所提供的流程的精确表达式，确定了被指定的流程数量，同时恢复了仿真的人数。
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.
