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