Dynamics Analysis of an Epidemiological Model with Media Impact and Two Delays

This paper is concerned with exploring the global dynamics of SEIR epidemic model with media impact, which incorporates latency and relapse delays. The permanence of the model is carefully discussed. By suitable Lyapunov functionals, we establish the global stability of the equilibria. It is found that the basic reproduction number completely determines the threshold dynamics of the SEIR model. Finally, the impact of media on the epidemic spread is studied, which reveals that timely response of media and individuals may play a more key role in disease control