Related papers: Functional Limit Theorems for Non-Markovian Epidem…
In this paper, we prove functional central limit theorems (FCLTs) for a stochastic epidemic model with varying infectivity and general infectious periods recently introduced in Forien, Pang and Pardoux (2020).The infectivity process (total…
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…
In this survey paper, we review the recent advances in individual based non--Markovian epidemic models. They include epidemic models with a constant infectivity rate, varying infectivity rate or infection-age dependent infectivity,…
We study the fluctuations of a stochastic epidemic model with memory of the last infections, varying infectivity, and waning immunity, as introduced in Guerin and Zotsa-Ngoufack:arXiv preprint arXiv:2505.00601. The dynamics of the epidemic…
We study epidemic models where the infectivity of each individual is a random function of the infection age (the elapsed time of infection). To describe the epidemic evolution dynamics, we use a stochastic process that tracks the number of…
We study the stochastic SIR epidemic model with infection-age dependent infectivity for which a measure-valued process is used to describe the ages of infection for each individual. We establish a functional law of large numbers (FLLN) and…
We study multi-patch epidemic models where individuals may migrate from one patch to another in either of the susceptible, exposed/latent, infectious and recovered states. We assume that infections occur both locally with a rate that…
We introduce an epidemic model with varying infectivity and general exposed and infectious periods, where the infectivity of each individual is a random function of the elapsed time since infection, those function being i.i.d. for the…
We study a stochastic compartmental susceptible-infected (SI) epidemic process on a configuration model random graph with a given degree distribution over a finite time interval $[0,T],$ for some $ T>0$. In this setting, we split the…
We study an individual-based stochastic epidemic model in which infected individuals become susceptible again following each infection. In contrast to classical compartment models, after each infection, the infectivity is a random function…
The impact of spatial structure on the spread of an epidemic is an important issue in the propagation of infectious diseases. Recent studies, both deterministic and stochastic, have made it possible to understand the importance of the…
In this article, we study an interacting particle system in the context of epidemiology where the individuals (particles) are characterized by their position and infection state. We begin with a description at the microscopic level where…
Using the regenerative scheme of Comets, Fern\'andez and Ferrari (2002), we establish a functional central limit theorem (FCLT) for discrete time stochastic processes (chains) with summable memory decay. Furthermore, under stronger…
We consider an individual-based SIR stochastic epidemic model in continuous space. The evolution of the epidemic involves the rates of infection and cure of individuals. We assume that individuals move randomly on the two-dimensional torus…
A stochastic SIR epidemic model taking into account the heterogeneity of the spatial environment is constructed. The deterministic model is given by a partial differential equation and the stochastic one by a space-time jump Markov process.…
The purpose of this note is to show that it is possible to establish a many-server functional strong law of large numbers (FSLLN) for the fraction of occupied servers (i.e., the scaled number-in-system) without explicitly tracking either…
This is an expository review paper elaborating on the proof of the martingale functional central limit theorem (FCLT). This paper also reviews tightness and stochastic boundedness, highlighting one-dimensional criteria for tightness used in…
In this paper we study the functional central limit theorem for stationary Markov chains with self-adjoint operator and general state space. We investigate the case when the variance of the partial sum is not asymptotically linear in n; and…
In this paper, we are concerned with the stochastic susceptible-infectious-susceptible (SIS) epidemic model on the complete graph with $n$ vertices. This model has two parameters, which are the infection rate and the recovery rate. By…
A functional limit theorem is established for the partial-sum process of a class of stationary sequences which exhibit both heavy tails and long-range dependence. The stationary sequence is constructed using multiple stochastic integrals…