Abstract
A delayed HIV-1 infection model with CTL immune response is investigated. By using suitable Lyapunov functionals, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infection is less than or equal to unity; if the basic reproduction ratio for CTL immune response is less than or equal to unity and the basic reproduction ratio for viral infection is greater than unity, the CTL-inactivated infection equilibrium is globally asymptotically stable; if the basic reproduction ratio for CTL immune response is greater than unity, the CTL-activated infection equilibrium is globally asymptotically stable.
Highlights
Many mathematical models have been developed to describe the infection with HIV-1 human immunodeficiency virus 1
In 7, Nowak and Bangham considered an HIV-1 infection model with CTL immune response which is described by the following differential equations: xt λ − dx t − βx t v t, yt βx t v t − ay t − py t z t, 1.1 vt ky t − uv t, zt cy t z t − bz t, Discrete Dynamics in Nature and Society where x t, y t, v t, and z t represent the densities of uninfected target cells, infected cells, virions, and CTL cells at time t, respectively
We have studied the global dynamics of a delayed HIV-1 infection model with CTL immune response
Summary
Many mathematical models have been developed to describe the infection with HIV-1 human immunodeficiency virus 1. In 7 , Nowak and Bangham considered an HIV-1 infection model with CTL immune response which is described by the following differential equations: xt λ − dx t − βx t v t , yt βx t v t − ay t − py t z t , 1.1 vt ky t − uv t , zt cy t z t − bz t , Discrete Dynamics in Nature and Society where x t , y t , v t , and z t represent the densities of uninfected target cells, infected cells, virions, and CTL cells at time t, respectively.
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