论文标题
与社交聚会的模特先生
SIR model with social gatherings
论文作者
论文摘要
我们在流行病学中引入了Kermack和McKendrick经典的易感感染（SIR）模型的扩展，其感染的潜在机制由参加随机产生的社交聚会的人组成。这引起了一种ODES系统，其中感染项的力量非线性取决于感染个体的比例。一些特定的实例产生了文献中已经研究的模型，目前的工作为此提供了概率基础。基本的繁殖数被认为四处依赖于聚会的平均大小，这可能有助于了解对社交聚会的限制如何影响疾病的传播。我们通过表明ODES系统是与有限人群中该疾病进化的跳跃马尔可夫过程的平均场限制来严格地证明我们的模型的合理性。
We introduce an extension to Kermack and McKendrick's classic susceptible-infected-recovered (SIR) model in epidemiology, whose underlying mechanism of infection consists of individuals attending randomly generated social gatherings. This gives rise to a system of ODEs where the force of infection term depends non-linearly on the proportion of infected individuals. Some specific instances yield models already studied in the literature, to which the present work provides a probabilistic foundation. The basic reproduction number is seen to depend quadratically on the average size of the gatherings, which may be helpful to understand how restrictions on social gatherings affect the spread of the disease. We rigorously justify our model by showing that the system of ODEs is the mean-field limit of the jump Markov process corresponding to the evolution of the disease in a finite population.
