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

Thierry Gallouët; Etienne Pardoux; Ténan Yeo

doi:10.1007/s40072-024-00333-0

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arXiv · 2412.06480

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

Thierry Gallouët·Etienne Pardoux·Ténan Yeo

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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.

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Thierry Gallouët, Etienne Pardoux, Ténan Yeo. 2024-12-09. A SIR epidemic model on a refining spatial grid II-Central limit theorem. https://doi.org/10.1007/s40072-024-00333-0

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