Author(s)

Abdoul Samba Ndongo

Department of Mathematics, Faculty of Sciences, University of Nouakchott Al Aasriya, Nouakchott, Mauritania.

In this work, we investigate an HIV-1 infection model with a general incidence rate and delayed CTL immune response. The model admits three possible equilibria, an infection-free equilibrium E^*₀, CTL-inactivated infection equilibrium E^*₁ and CTL-activated infection equilibrium E^*₂. We prove that in the absence of CTL immune delay, the model has exactly the basic behaviour model, for all positive intracellular delays, the global dynamics are determined by two threshold parameters R₀ and R₁, if R₀ ≤ 1, E^*₀ is globally asymptotically stable, if R₁ ≤ 1 < R₀, E^*₁ is globally asymptotically stable and if R₁ >1, E^*₂ is globally asymptotically stable. But if the CTL immune response delay is different from zero, then the behaviour of the model at E^*₂ changes completely, although R₁ > 1, a Hopf bifurcation at E^*₂ is established. In the end, we present some numerical simulations.

Virus Dynamics, Intracellular and CTL Immune Response Delays, Lyapunov Function, Global Asymptotic Stability, Hopf Bifurcation

Ndongo, A. (2021) Global Stability and Hopf Bifurcation for a Virus Dynamics Model with General Incidence Rate and Delayed CTL Immune Response. Applied Mathematics, 12, 1038-1057. doi: 10.4236/am.2021.1211068.