Functional Central limit theorems for epidemic models with varying infectivity and waning immunity
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910919166001152 |
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| author | Zotsa-Ngoufack, Arsene-Brice |
| author_facet | Zotsa-Ngoufack, Arsene-Brice |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02260 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Functional Central limit theorems for epidemic models with varying infectivity and waning immunity Zotsa-Ngoufack, Arsene-Brice Probability Populations and Evolution 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. |
| title | Functional Central limit theorems for epidemic models with varying infectivity and waning immunity |
| topic | Probability Populations and Evolution |
| url | https://arxiv.org/abs/2311.02260 |