title: Stability and Hopf Bifurcation in a Delayed HIV Infection Model with General Incidence Rate and Immune Impairment.
abstract: We investigate the dynamical behavior of a delayed HIV infection model with general incidence rate and immune impairment. We derive two threshold parameters, the basic reproduction number R 0 and the immune response reproduction number R 1. By using Lyapunov functional and LaSalle invariance principle, we prove the global stability of the infection-free equilibrium and the infected equilibrium without immunity. Furthermore, the existence of Hopf bifurcations at the infected equilibrium with CTL response is also studied. By theoretical analysis and numerical simulations, the effect of the immune impairment rate on the stability of the infected equilibrium with CTL response has been studied.
authors.affiliation: Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China.
authors.forename: Fuxiang
authors.initials: F
authors.lastname: Li
authors.affiliation: Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China.
authors.forename: Wanbiao
authors.initials: W
authors.lastname: Ma
authors.affiliation: Fundamental Science Department, North China Institute of Aerospace Engineering, Langfang, Hebei 065000, China.
authors.forename: Zhichao
authors.initials: Z
authors.lastname: Jiang
authors.affiliation: Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China.
authors.forename: Dan
authors.initials: D
authors.lastname: Li
mesh_terms: D050936:Basic Reproduction Number; D003198:Computer Simulation; D015658:HIV Infections / Q000453:epidemiology* / Q000276:immunology / Q000635:transmission; D006801:Humans; D015994:Incidence; D008954:Models, Biological; D018448:Models, Immunological; D015233:Models, Statistical; D013602:T-Lymphocytes, Cytotoxic / Q000276:immunology