Arsene-Brice Zotsa-Ngoufack

arXiv2023

Functional Central limit theorems for epidemic models with varying infectivity and waning immunity

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.

math.PR↗

arXiv2023

Weighted norm inequalities in the variableLlebesgue spaces for the Bergman projector on the unit ball of $\mathbb{c}^n$

In this work, we extend the theory of Békollè-Bonami $B_p$ weights. Here we replace the constant $p$ by a non-negative measurable function $p(\cdot),$ which is log-Hölder continuous function with lower bound $1$. We show that the Bergman projector on the unit ball of $\mathbb C^n$ is continuous on the weighted variable Lebesgue spaces $L^{p(\cdot)}(w)$ if and only if $w$ belongs to the generalised Békollè-Bonami class $B_{p(\cdot)}$. To achieve this, we define a maximal function and show that it is bounded on $L^{p(\cdot)}(w)$ if $w\in B_{p(\cdot)}$. We next state and prove a weighted extrapolation theorem that allows us to conclude.

math.CV↗