Stability and hopf bifurcation analysis of an epidemiological model incorporating delay and media coverage

Abstract

In this paper, an epidemiological model with delay and media coverage is proposed and analyzed. Both the disease-free and endemic equilibria are found and their stability are studied by using the theory of differential equations. It is proved that the time delay may cause a stable equilibrium to become unstable, and Hopf bifurcation about endemic equilibrium can occur under certain conditions. The report ability of the media coverage plays an important role in the spreading of the diseases.