English

A SIR epidemic model on a refining spatial grid II-Central limit theorem

Probability 2024-12-10 v1

Abstract

A stochastic SIR epidemic model taking into account the heterogeneity of the spatial environment is constructed. The deterministic model is given by a partial differential equation and the stochastic one by a space-time jump Markov process. The consistency of the two models is given by a law of large numbers. In this paper, we study the deviation of the spatial stochastic model from the deterministic model by a functional central limit theorem. The limit is a distribution-valued Ornstein-Uhlenbeck Gaussian process, which is the mild solution of a stochastic partial differential equation.

Keywords

Cite

@article{arxiv.2412.06480,
  title  = {A SIR epidemic model on a refining spatial grid II-Central limit theorem},
  author = {Thierry Gallouët and Etienne Pardoux and Ténan Yeo},
  journal= {arXiv preprint arXiv:2412.06480},
  year   = {2024}
}
R2 v1 2026-06-28T20:27:52.375Z