Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response

Author:

Wang Haibin1ORCID,Xu Rui1

Affiliation:

1. Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, No. 97 Heping West Road, Shijiazhuang, Hebei 050003, China

Abstract

An HIV-1 infection model with latently infected cells and delayed immune response is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria is established and the existence of Hopf bifurcations at the CTL-activated infection equilibrium is also studied. By means of suitable Lyapunov functionals and LaSalle’s invariance principle, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infectionR01; if the basic reproduction ratio for viral infectionR0>1and the basic reproduction ratio for CTL immune responseR11, the CTL-inactivated infection equilibrium is globally asymptotically stable. If the basic reproduction ratio for CTL immune responseR1>1, the global stability of the CTL-activated infection equilibrium is also derived when the time delayτ=0. Numerical simulations are carried out to illustrate the main results.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Modelling and Simulation

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