FUNCTIONAL LIMIT THEOREMS FOR NON-MARKOVIAN EPIDEMIC MODELS

Guodong Pang, Étienne Pardoux

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We study non-Markovian stochastic epidemic models (SIS, SIR, SIRS, and SEIR), in which the infectious (and latent/exposing, immune) periods have a general distribution. We provide a representation of the evolution dynamics using the time epochs of infection (and latency/exposure, immunity). Taking the limit as the size of the population tends to infinity, we prove both a functional law of large number (FLLN) and a functional central limit theorem (FCLT) for the processes of interest in these models. In the FLLN, the limits are a unique solution to a system of deterministic Volterra integral equations, while in the FCLT, the limit processes are multidimensional Gaussian solutions of linear Volterra stochastic integral equations. In the proof of the FCLT, we provide an important Poisson random measures representation of the diffusion-scaled processes converging to Gaussian components driving the limit process.

Original languageEnglish (US)
Pages (from-to)1615-1665
Number of pages51
JournalAnnals of Applied Probability
Volume32
Issue number3
DOIs
StatePublished - Jun 2022

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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