An SEI infection model incorporating media impact

Abstract

To study the impact of media coverage on spread and control of infectious diseases, we use a susceptible-exposed-infective (SEI) model, including individuals' behavior changes in their contacts due to the inuences of media coverage, and fully investigate the model dynamics. We define the basic reproductive number R0 for the model, and show that the modeled disease dies out regardless of initial infections when R0 < 1, and becomes uniformly persistently endemic if R0 > 1. When the disease is endemic and the inuence of the media coverage is less than or equal to a critical number, there exists a unique endemic equilibrium which is asymptotical stable provided R0 is greater than and near one. However, if R0is larger than a critical number, the model can undergo Hopf bifurcation such that multiple endemic equilibria are bifurcated from the unique endemic equilibrium as the inuence of the media coverage is increased to a threshold value. Using numerical simulations we obtain results on the effects of media coverage on the endemic that the media coverage may decrease the peak value of the infectives or the average number of the infectives in different cases. We show, however, that given larger R0 the inuence of the media coverage may as well result in increasing the average number of the infectives, which brings challenges to the control and prevention of infectious diseases.