A stochastic epidemic model incorporating media coverage

Abstract

In this paper, we investigate the effects of environment fluctuations on disease dynamics through studying the stochastic dynamics of an SIS model incorporating media coverage. The value of this study lies in two aspects: Mathematically, we show that the disease dynamics the SDE model can be governed by its related basic reproduction number RS 0 : if R S 0 ≤1, the disease will die out stochastically, but if RS 0 >1, the disease will break out with probability one. Epidemiologically, we partially provide the effects of the environment fluctuations affecting spread of the disease incorporating media coverage. First, noise can suppress the disease outbreak. Notice that RS 0 1, it has endemic stationary distribution, which leads to the stochastically persistence of the disease. In order to understand the role of media coverage on disease dynamics, we present some numerical simulations to validate the analytical findings. It is interesting to note that although some parameters have no role in determining Rs 0, however the strength of noise to the susceptible population and the parameters characterizing media affect play crucial role in determining the long term dynamics of the system.