The asymptotic behavior and ergodicity of stochastically perturbed SVIR epidemic model.

In this paper, we introduce stochasticity into an SIR epidemic model with vaccination. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by the method of stochastic Lyapunov functions, we carry out a detailed analysis on the dynamical behavior of the stochastic model regarding of the basic reproduction number . If , the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model. If , there is a stationary distribution and the solution has the ergodic property, which means that the disease will prevail. [ABSTRACT FROM AUTHOR]