Stability and Hopf bifurcation of HIV-1 model with Holling II infection rate and immune delay

This paper aims to analyse stability and Hopf bifurcation of the HIV-1 model with immune delay under the functional response of the Holling II type. The global stability analysis has been considered by Lyapunov-LaSalle theorem. And stability and the sufficient condition for the existence of Hopf Bifurcation of the infected equilibrium of the HIV-1 model with immune response are also studied. Some numerical simulations verify the above results. Finally, we propose a novel three dimension system to the future study.

Effect of time delays in an HIV virotherapy model with nonlinear incidence

In this paper, we propose a mathematical model for HIV infection with delays in cell infection and virus production. The model examines a viral therapy for controlling infections through recombining HIV with a genetically modified virus. For this model, we derive two biologically insightful quantities (reproduction numbers) [Formula: see text] and [Formula: see text], and their threshold properties are discussed. When [Formula: see text], the infection-free equilibrium E₀ is globally asymptotically stable. If [Formula: see text] and [Formula: see text], the single-infection equilibrium E_s is globally asymptotically stable. When [Formula: see text], there occurs the double-infection equilibrium E_d, and there exists a constant R_b such that E_d is asymptotically stable if [Formula: see text]. Some simulations are performed to support and complement the theoretical results.