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, R σ , of the basic reproduction number R 0 of the deterministic special case. Whenever σ > 0 then R σ < R 0 . For small values of σ , the stability theorem guarantees almost sure exponential stability whenever R σ < 1 . We also discuss the effect of increasing σ .