Dynamical Behaviors of a New Sis Epidemic Model on Scale-Free Networks With Stochastic Perturbation

Abstract

A new SIS epidemic model on scale-free networks with stochastic perturbation is considered. We deduce that dynamical behaviors of the model are related to the basic reproduction number R 0 of the corresponding deterministic model. Under the conditions that the intensities of white noises interference are sufficiently weak, the solution of the model oscillates around the disease-free equilibrium of the corresponding deterministic model when R 0 < 1, whereas, the disease will be persistent when R 0 > 1.