Stability properties and Hopf bifurcation for a Hepatitis B infection model with exposed state and humoral immunity-response delay

Abstract

In this paper, a dynamics behavior of a delayed hepatitis B infection model with exposed state and humoral immunity is studied. The basic reproductive number R0and humoral immune reproductive number R1are introduced. By using suitable Lyapunov functional and LaSalle invariant principle, it is proved that when R0< 1, the infection-free equilibrium Q0is globally asymptotically stable; if R1<1<R0, the infected equilibrium without immunity Q1is globally asymptotically stable. When R1> 1, the sufficient conditions to the local stability of the infected equilibrium with immunity Q2can be obtained. The time delay can change the stability of Q2and lead to the existence of Hopf bifurcations. The stabilities of periodic solutions are also investigated. Finally, numerical simulations are carried out.