Functional Central limit theorems for epidemic models with varying infectivity and waning immunity
Abstract
We study an individual-based stochastic epidemic model in which infected individuals become susceptible again following each infection (generalized SIS model). Specifically, after each infection, the infectivity is a random function of the time elapsed since the infection, and each recovered individual loses immunity gradually (equivalently, becomes gradually susceptible) after some time according to a random susceptibility function. The epidemic dynamics is described by the average infectivity and susceptibility processes in the population together with the numbers of infected and susceptible/uninfected individuals. In \cite{forien-Zotsa2022stochastic}, a functional law of large numbers (FLLN) is proved as the population size goes to infinity, and asymptotic endemic behaviors are also studied. In this paper, we prove a functional central limit theorem (FCLT) for the stochastic fluctuations of the epidemic dynamics around the FLLN limit. The FCLT limit for the aggregate infectivity and susceptibility processes is given by a system of stochastic non-linear integral equation driven by a two-dimensional Gaussian process.
Keywords
Cite
@article{arxiv.2311.02260,
title = {Functional Central limit theorems for epidemic models with varying infectivity and waning immunity},
author = {Arsene-Brice Zotsa-Ngoufack},
journal= {arXiv preprint arXiv:2311.02260},
year = {2025}
}
Comments
epidemic model, varying infectivity, waning immunity, Gaussian-driven stochastic Volterra integral equations, Poisson random measure, stochastic integral with respect to Poisson random measure, Covariance for Hawkes Process, Stochastic integral with respect to Poisson random measure, quarantine model