STOCHASTIC EPIDEMIC MODELS WITH VARYING INFECTIVITY AND WANING IMMUNITY

• 成果类型: Article
• 署名作者: Forien, Raphael; Pang, Guodong; Pardoux, Etienne; Zotsa-Ngoufack, Arsene-Brice
• 署名单位: INRAE; Rice University; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/25-AAP2170
• 发表日期: 2025
• 页码: 2175-2216
• 关键词: general branching-processes; LIMIT-THEOREMS; mathematical-theory; kermack

摘要

We study an individual-based stochastic epidemic model in which infected individuals become susceptible again, after each infection. In contrast to classical compartment models, after each infection, the infectivity is a random function of the time elapsed since infection. Similarly, recovered individuals become gradually susceptible after some time according to a random susceptibility function. We study the large population asymptotic behaviour of the model: we prove a functional law of large numbers (FLLN) and investigate the endemic equilibria of the limiting deterministic model. The limit depends on the law of the susceptibility random functions but only on the mean infectivity functions. The FLLN is proved by constructing a sequence of i.i.d. auxiliary processes and adapting the approach from the theory of propagation of chaos. The limit is a generalisation of a PDE model introduced by Kermack and McKendrick, and we show how this PDE model can be obtained as a special case of our FLLN limit. If R0 is less than (or equal to) some threshold, the epidemic does not last forever and eventually disappears from the population, while if R0 is larger than this threshold, the epidemic will not go extinct and there exists an endemic equilibrium. The value of this threshold turns out to be the harmonic mean of the susceptibility a long time after an infection.