Stability of an SEIR epidemic model with independent stochastic perturbations

Abstract

For an epidemic model of the type mentioned, we prove a theorem on almost sure exponential stability of the disease-free equilibrium. For small values of the diffusion parameter, ?, we describe the stability of the disease free equilibrium point in terms of an appropriate analogue, R? , of the basic reproduction number R0 of the deterministic special case. Whenever ? > 0 then R? < R0. For small values of ?, the stability theorem guarantees almost sure exponential stability whenever R? < 1. We also discuss the effect of increasing ?.