Functional central limit theorems for epidemic models with varying infectivity

In this paper, we prove a functional central limit theorem (FCLT) for stochastic epidemic model with varying infectivity and general infectious periods recently introduced in R. Forien et al. [Epidemic models infectivity, SIAM J. Appl. Math. 81 (2021), pp. 1893–1930]. The process (total force of infection at each time) is composed the independent random functions individual, which starts time infection. These induce (as well as exposed, recovered or immune full generality), whose probability distributions can be very general. includes generalized non–Markovian SIR, SEIR, SIS, SIRS infection-age dependent infectivity. FCLTs SIR SEIR models, limits diffusion-scaled fluctuations susceptible processes are unique solution to two-dimensional Gaussian-driven Volterra integral equations, then given these solutions, infected (exposed/infectious) Gaussian expressed terms solutions those equations. We also present SIS models.