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

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.