TY - JOUR
T1 - Functional central limit theorems for epidemic models with varying infectivity
AU - Pang, Guodong
AU - Pardoux, Étienne
N1 - Publisher Copyright:
© 2022 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2023
Y1 - 2023
N2 - In this paper, we prove a functional central limit theorem (FCLT) for a stochastic epidemic model with varying infectivity and general infectious periods recently introduced in R. Forien et al. [Epidemic models with varying infectivity, SIAM J. Appl. Math. 81 (2021), pp. 1893–1930]. The infectivity process (total force of infection at each time) is composed of the independent infectivity random functions of each infectious individual, which starts at the time of infection. These infectivity random functions induce the infectious periods (as well as exposed, recovered or immune periods in full generality), whose probability distributions can be very general. The epidemic model includes the generalized non–Markovian SIR, SEIR, SIS, SIRS models with infection-age dependent infectivity. In the FCLTs for the generalized SIR and SEIR models, the limits of the diffusion-scaled fluctuations of the infectivity and susceptible processes are a unique solution to a two-dimensional Gaussian-driven stochastic Volterra integral equations, and then given these solutions, the limits for the infected (exposed/infectious) and recovered processes are Gaussian processes expressed in terms of the solutions to those stochastic Volterra integral equations. We also present the FCLTs for the generalized SIS and SIRS models.
AB - In this paper, we prove a functional central limit theorem (FCLT) for a stochastic epidemic model with varying infectivity and general infectious periods recently introduced in R. Forien et al. [Epidemic models with varying infectivity, SIAM J. Appl. Math. 81 (2021), pp. 1893–1930]. The infectivity process (total force of infection at each time) is composed of the independent infectivity random functions of each infectious individual, which starts at the time of infection. These infectivity random functions induce the infectious periods (as well as exposed, recovered or immune periods in full generality), whose probability distributions can be very general. The epidemic model includes the generalized non–Markovian SIR, SEIR, SIS, SIRS models with infection-age dependent infectivity. In the FCLTs for the generalized SIR and SEIR models, the limits of the diffusion-scaled fluctuations of the infectivity and susceptible processes are a unique solution to a two-dimensional Gaussian-driven stochastic Volterra integral equations, and then given these solutions, the limits for the infected (exposed/infectious) and recovered processes are Gaussian processes expressed in terms of the solutions to those stochastic Volterra integral equations. We also present the FCLTs for the generalized SIS and SIRS models.
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U2 - 10.1080/17442508.2022.2124870
DO - 10.1080/17442508.2022.2124870
M3 - Article
AN - SCOPUS:85139157221
SN - 1744-2508
VL - 95
SP - 819
EP - 866
JO - Stochastics
JF - Stochastics
IS - 5
ER -