Gordillo Luis F, Greenwood Priscilla E, Strong Dana
Department of Mathematics and Statistics, Utah State University, Logan, UT, USA.
Department of Mathematics, University of British Columbia, Vancouver, BC, Canada.
J Biol Dyn. 2023 Dec;17(1):2189001. doi: 10.1080/17513758.2023.2189001.
We derive a stochastic epidemic model for the evolving density of infective individuals in a large population. Data shows main features of a typical epidemic consist of low periods interspersed with outbreaks of various intensities and duration. In our stochastic differential model, a novel reproductive term combines a factor expressing the recent notion of 'attenuated Allee effect' and a capacity factor is controlling the size of the process. Simulation of this model produces sample paths of the stochastic density of infectives, which behave much like long-time Covid-19 case data of recent years. Writing the process as a stochastic diffusion allows us to derive its stationary distribution, showing the relative time spent in low levels and in outbursts. Much of the behaviour of the density of infectives can be understood in terms of the interacting drift and diffusion coefficient processes, or, alternatively, in terms of the balance between noise level and the attenuation parameter of the Allee effect. Unexpected results involve the effect of increasing overall noise variance on the density of infectives, in particular on its level-crossing function.
我们为大量人群中感染个体的不断变化的密度推导了一个随机流行病模型。数据显示，典型流行病的主要特征包括穿插着不同强度和持续时间爆发的低发期。在我们的随机微分模型中，一个新颖的繁殖项结合了一个表达近期 “减弱的阿利效应” 概念的因子和一个控制过程规模的容量因子。对该模型的模拟产生了感染个体随机密度的样本路径，其行为与近年来长期的新冠疫情病例数据非常相似。将该过程写成随机扩散形式使我们能够推导出其平稳分布，显示出在低水平和爆发期所花费的相对时间。感染个体密度的许多行为可以通过相互作用的漂移和扩散系数过程来理解，或者，也可以通过噪声水平与阿利效应的衰减参数之间的平衡来理解。意外的结果涉及增加总体噪声方差对感染个体密度的影响，特别是对其水平穿越函数的影响。
