Abstract: We considered a class of SISVS epidemic system with random perturbation,  applied the new Lyapunov function to study the ergodicity of the system, and obtained the sufficient conditions for the existence and ergodicity of the stationary distribution of the stochastic epidemic system. The results show that the construction method of Lyapunov function improves the existing results of endemic equilibrium and the mortality, which depend on the deterministic models, and obtains more applicable conditions.

Key words: stochastic differential equation, Lyapunov function,  , SIS-VS epidemic model, station distribution, ergodicity