Abstract
The main purpose of this paper is to explore the global behavior of a stochastic SIRS epidemic model with media coverage. The value of this research has 2 aspects: for one thing, we use Markov semigroup theory to prove that the basic reproduction number can be used to control the dynamics of stochastic system. If , the stochastic system has a disease‐free equilibrium, which implies the disease will die out with probability one. If , under the mild extra condition, the stochastic differential equation has an endemic equilibrium, which is globally asymptotically stable. For another, it is known that environment fluctuations can inhibit disease outbreak. Although the disease is persistent when R0 > 1 for the deterministic model, if , the disease still dies out with probability one for the stochastic model. Finally, numerical simulations were carried out to illustrate our results, and we also show that the media coverage can reduce the peak of infective individuals via numerical simulations.
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