  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.
