Analysis of variable structure of the disease spread with media impact

In order to show the characteristic of the impact on the spread of diseases by media coverage, we will propose a model with a piecewise continuous incidence rate in this paper. When the number of infected reaches the critical value, the effect of media coverage will appear. The existence and the stability of endemic equilibriums and sliding equilibrium depend on the critical value. With different critical values, the sliding mode area is changing and the model solutions will tend to the endemic equilibrium or sliding equilibrium. The result of the paper shows that if the critical value is selected and the parameters are proper, the final number of infected will be stable in the critical value chosen previously.