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Household epidemic models and McKean-Vlasov Poisson driven stochastic differential equations
Raphael Forien, Etienne Pardoux · 2019-07-06 · via math.PR updates on arXiv.org

This paper presents a new view of household epidemic models, where the interaction between the households is of mean field type. We thus obtain in the limit of infinitely many households a nonlinear Markov process solution of a McKean - Vlasov type Poisson driven SDE, and a propagation of chaos result. We also define a basic reproduction number R0, and show that if R0>1, then the nonlinear Markov process has a unique non trivial ergodic invariant probability measure, whereas if R0<=1, it converges to 0 as t tends to infinity.

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