An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks

Abstract

<abstract><p>An SIS epidemic model with time delay and stochastic perturbation on scale-free networks is established in this paper. And we derive sufficient conditions guaranteeing extinction and persistence of epidemics, respectively, which are related to the basic reproduction number $ R_0 $ of the corresponding deterministic model. When $ R_0 &lt; 1 $, almost surely exponential extinction and $ p $-th moment exponential extinction of epidemics are proved by Razumikhin-Mao Theorem. Whereas, when $ R_0 &gt; 1 $, the system is persistent in the mean under sufficiently weak noise intensities, which indicates that the disease will prevail. Finally, the main results are demonstrated by numerical simulations.</p></abstract>