Stability of an SEIR epidemic model with independent stochastic perturbations

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.