An SIRS Epidemiological Model with Nonlinear Incidence Rate Incorporating Media Coverage

In this paper, an SIRS epidemiological model with nonlinear incidence rate incorporating media coverage is investigated and the threshold of the existence of various equilibria are found. By means of constructing Dulac function and combing with the local stability of the corresponding linear system, one can verify that the disease-free equilibrium is globally asymptotically stable if the reproduction number R₀ is less than unity, and the endemic equilibrium is globally asymptotically when it exists. From the analysis and simulation, we can find that though the media coverage is not a determined fact to eradicate the infection of the diseases, to a certain extent, the effective media coverage can postpone the arrival of the infection peak, and a fewer number of individuals become infected in the course of transmission.