Abstract:

This paper considers a stochastic SIS epidemic model with virus auto variation, in which the recovery rate is influenced by white noise. First, we prove the global existence, uniqueness of the positive solution, and show that the diseasefree equilibrium is stochastically asymptotical stability when max｛R1,R2｝≤1. Then we point out when the white noise σ1 is large enough, the virus tends to disappear. Finally, the numerical simulations are carried out to support our results.

Key words: stochastic SIS epidemic model; Lyapunov function; It formula; asymptotic behavior