Stability Properties and Hopf Bifurcation of a Delayed HIV Dynamics Model with Saturation Functional Response, Absorption Effect and Cure Rate

Abstract

In this paper, stability properties of an HIV infection model with saturation functional response, logistic proliferation term of susceptible CD4+T cells, cure rate of infected CD4+T cell, virus absorption effect, intracellular delay, and maturation delay are investigated. According to our mathematical analysis, the basic reproduction number R0 of the model completely determines its stability features. Using the characteristic equation of the model, we establish that the infection-free equilibrium point and the infected equilibrium point are locally asymptotically stable when R0 ≤ 1 and R0 > 1, respectively. By means of appropriate Lyapunov functionals and LaSalle’s invariance principle for delay models, if R0 ≤ 1, we study the global asymmetric stability of the infection-free equilibrium point of the model. When R0 > 1, we establish the occurrence of Hopf bifurcations and determine conditions for the permanence of the model. Finally, numerical simulations are also presented to confirm the analytical results.