Dynamics of stochastically perturbed SIS epidemic model with vaccination

Abstract

We introduce stochasticity into an SIS epidemic model with vaccination. The stochasticity in the model is a standard technique in stochastic population modeling. In the deterministic models, the basic reproduction number R 0 is a threshold which determines the persistence or extinction of the disease. When the perturbation and the disease-related death rate are small, we carry out a detailed analysis on the dynamical behavior of the stochastic model, also regarding of the value of R0. If R0 ≤ 1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model, whereas, if R 0 > 1, there is a stationary distribution, which means that the disease will prevail. The results are illustrated by computer simulations. © 2013 Yanan Zhao and Daqing Jiang.