A Note on Stability Properties of a Delayed Viral Infection Model with Lytic Immune Response

摘要

Based on biological meanings, a recent paper [Stability properties and Hopf bifurcation of a delayed viral infection model with lytic immune resposne, J. Math. Anal. Appl. 373 (2010)345-355] considered a delayed viral infection model with lytic immune response. Using stability switch criteria, one of main results in that paper is proved and conjectured, that is, there exists a Hopf bifurcation of the positive equilibrium. However, By Direct Lyapunov Method, in this note we construct Lyapunov functions to demonstrate that the positive equilibrium is global asymptotically stable when it exists, which implies Hopf bifurcation does not occur. And numerical simulations are given to confirm it. Finally, we discuss that the immune activation delay can bring periodic solutions.