The effect of media coverage on threshold dynamics for a stochastic SIS epidemic model

Abstract

Media coverage is one of the important measures for controlling infectious diseases, but the effect of media coverage on diseases spreading in a stochastic environment still needs to be further investigated. Here, we present a stochastic susceptible–infected–susceptible (SIS) epidemic model incorporating media coverage and environmental fluctuations. By using Feller’s test and stochastic comparison principle, we establish the stochastic basic reproduction number R0s, which completely determines whether the disease is persistent or not in the population. If R0s≤1, the disease will go to extinction; if R0s=1, the disease will also go to extinction in probability, which has not been reported in the known literatures; and if R0s>1, the disease will be stochastically persistent. In addition, the existence of the stationary distribution of the model and its ergodicity are obtained. Numerical simulations based on real examples support the theoretical results. The interesting findings are that (i) the environmental fluctuation may significantly affect the threshold dynamical behavior of the disease and the fluctuations in different size scale population, and (ii) the media coverage plays an important role in affecting the stationary distribution of disease under a low intensity noise environment.