摘要：In this paper, we discuss a stochastic SIS epidemic model with vaccination. We investigate the asymptotic behavior according to the perturbation and the reproduction number R 0 $R_($ . When the perturbation is large, the number of infected decays exponentially to zero and the solution converges to the disease-free equilibrium regardless of the magnitude of R 0 $R_($ . Moreover, we get the same exponential stability and the convergence if R 0 1 $R_(>1$ . Furthermore, we prove that the system is persistent in the mean. Finally, the results are illustrated by computer simulations.
关键词：stochastic SIS epidemic model ; vaccination ; exponential stability ; persistent in mean ; Lyapunov function
