Household epidemic models and McKean-Vlasov Poisson driven stochastic differential equations
Probability
2022-10-04 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1907.03001,
title = {Household epidemic models and McKean-Vlasov Poisson driven stochastic differential equations},
author = {Raphael Forien and Etienne Pardoux},
journal= {arXiv preprint arXiv:1907.03001},
year = {2022}
}