Issue |
ESAIM: PS
Volume 29, 2025
|
|
---|---|---|
Page(s) | 45 - 112 | |
DOI | https://doi.org/10.1051/ps/2024015 | |
Published online | 15 January 2025 |
Functional Central Limit Theorems for epidemic models with varying infectivity and waning immunity
Aix Marseille Univ, CNRS, I2M, Marseille, France
* Corresponding author: arsene-brice.zotsa-ngoufack@univ-amu.fr
Received:
12
January
2024
Accepted:
15
December
2024
We study an individual-based stochastic epidemic model in which infected individuals gradually become susceptible again following each infection (generalized SIS model). 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 R. Forien et al., Stochastic epidemic models with varying infectivity and susceptibility. arXiv preprint arXiv:2210.04667 (2022), 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.
Mathematics Subject Classification: 60F05 / 60F17 / 60G55 / 60H05 / 60k35
Key words: Epidemic model / varying infectivity / waning immunity / Gaussian-driven stochastic Volterra integral equations / Poisson random measure / stochastic integral with respect to Poisson random measure / quarantine model
© The authors. Published by EDP Sciences, SMAI 2025
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