Global Stability and Hopf Bifurcation for a Virus Dynamics Model with General Incidence Rate and Delayed CTL Immune Response  

作　　者：Abdoul Samba Ndongo Abdoul Samba Ndongo(University de Nouakchott ALassriya, Faculty of Sciences, Department of Mathematics, Nouakchott, Mauritania)

机构地区：[1]University de Nouakchott ALassriya, Faculty of Sciences, Department of Mathematics, Nouakchott, Mauritania

出　　处：《Applied Mathematics》2021年第11期1038-1057,共20页应用数学（英文）

摘　　要：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 <span><em>E</em></span>^*<sub style="margin-left:-6px;">0</sub>, CTL-inactivated infection equilibrium <span><em>E</em></span>^*<sub style="margin-left:-6px;">1</sub> and CTL-activated infection equilibrium <span><em>E</em></span>^*<sub style="margin-left:-6px;">2</sub>. 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 <em>R</em>₀ and <em>R</em>₁, if <em>R</em>₀ <span style="font-size:12px;white-space:nowrap;">≤</span> 1, <span><em>E</em></span>^*<span style="margin-left:-6px;">₀ </span>is globally asymptotically stable, if <em>R</em>₁ <span style="font-size:12px;white-space:nowrap;">≤</span> 1 < <em>R</em>₀, <span><em>E</em></span>^*<span style="margin-left:-6px;">₁ </span>is globally asymptotically stable and if <em>R</em>₁ >1, <span><em>E</em></span>^*<span style="margin-left:-6px;">₂ </span>is globally asymptotically stable. But if the CTL immune response delay is different from zero, then the behaviour of the model at <span><em>E</em></span>^*<span style="margin-left:-6px;">₂ </span>changes completely, although <em>R</em>₁ > 1, a Hopf bifurcation at <span><em>E</em></span>^*<span style="margin-left:-6px;">₂ </span>is established. In the end, we present some numerical simulations.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 <span><em>E</em></span>^*<sub style="margin-left:-6px;">0</sub>, CTL-inactivated infection equilibrium <span><em>E</em></span>^*<sub style="margin-left:-6px;">1</sub> and CTL-activated infection equilibrium <span><em>E</em></span>^*<sub style="margin-left:-6px;">2</sub>. 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 <em>R</em>₀ and <em>R</em>₁, if <em>R</em>₀ <span style="font-size:12px;white-space:nowrap;">≤</span> 1, <span><em>E</em></span>^*<span style="margin-left:-6px;">₀ </span>is globally asymptotically stable, if <em>R</em>₁ <span style="font-size:12px;white-space:nowrap;">≤</span> 1 < <em>R</em>₀, <span><em>E</em></span>^*<span style="margin-left:-6px;">₁ </span>is globally asymptotically stable and if <em>R</em>₁ >1, <span><em>E</em></span>^*<span style="margin-left:-6px;">₂ </span>is globally asymptotically stable. But if the CTL immune response delay is different from zero, then the behaviour of the model at <span><em>E</em></span>^*<span style="margin-left:-6px;">₂ </span>changes completely, although <em>R</em>₁ > 1, a Hopf bifurcation at <span><em>E</em></span>^*<span style="margin-left:-6px;">₂ </span>is established. In the end, we present some numerical simulations.

关 键 词：Virus Dynamics Intracellular and CTL Immune Response Delays Lyapunov Function Global Asymptotic Stability Hopf Bifurcation 

分 类 号：O17[理学—数学]