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

Thierry Gallouët , Étienne Pardoux (1) , Ténan Yeo

1 I2M - Institut de Mathématiques de Marseille

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.

Domaines: Mathématiques [math]

Thierry Gallouët, Étienne Pardoux, Ténan Yeo. A SIR epidemic model on a refining spatial grid II-central limit theorem. Stochastics and Partial Differential Equations: Analysis and Computations, 2024, ⟨10.1007/s40072-024-00333-0⟩. ⟨hal-04826748⟩