Stability of an SEIR epidemic model with indepenent 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, σ, we describe the stability of the disease free equilibrium point in terms of an appropriate analogue, Rσ , of the basic reproduction number R0 of the deterministic special case. Whenever σ > 0 then Rσ < R0. For small values of σ, the stability theorem guarantees almost sure exponential stability whenever Rσ < 1. We also discuss the effect of increasing σ.