GLOBAL PROPERTIES OF A MODEL OF IMMUNE EFFECTOR RESPONSES TO VIRAL INFECTIONS
Xia Wang and
Xinyu Song ()
Additional contact information Xia Wang: Department of Mathematics, Xinyang Normal University, Xinyang 464000 Henan, P. R. China
Xinyu Song: Department of Mathematics, Xinyang Normal University, Xinyang 464000 Henan, P. R. China; College of Mathematics and Information Science, Henan University, Kaifeng 475001 Henan, P. R. China
This article proposes a mathematical model which has been used to investigate the importance of lytic and non-lytic immune responses for the control of viral infections. By means of Lyapunov functions, the global properties of the model are obtained. The virus is cleared if the basic reproduction number R0 ≤ 1 and the virus persists in the host if R0 > 1. Furthermore, if R0 > 1 and other conditions hold, the immune-free equilibrium E0 is globally asymptotically stable. The equilibrium E1 exists and is globally asymptotically stale if the CTL immune response reproductive number R1 < 1 and the antibody immune response reproductive number R2 > 1. The equilibrium E2 exists and is globally asymptotically stable if R1 > 1 and R2 < 1. Finally, the endemic equilibrium E3 exists and is globally asymptotically stable if R1 > 1 and R2 > 1.