具有Logistic增长和饱和CTL免疫反应的时滞HIV模型的稳定

Stability analysis of delayed HIV model with Logistic growth and saturated CTL-immune response

研究具有Logistic增长和饱和CTL免疫反应及其免疫时滞的HIV病毒模型。讨论在不同情况下无病平衡点E_0、无免疫感染平衡点E_1、免疫感染平衡点E_2的存在条件,通过分析特征方程,建立三个平衡点的局部渐近稳定性;讨论免疫感染平衡点E_2附近存在Hopf分支的充分条件,通过规范型方法及中心流定理,分析Hopf分支的方向和稳定性。数值模拟验证了主要结论的正确性。

Consider a delayed HIV model with Logistic growth and saturated CTL-immune response. The existence conditions of the infection-free equilibrium Eo, the immune-exhausted equilibrium E1 and the infected equilibrium with immunity E2 are shown. The locally asymptotically stability conditions of the trivial equilibrium are established by analyzing the characteristic equations. The sufficient condition under which there appears Hopf bifurcations near the infected equilibrium with immunity E2. The direction and stability of bifurcation periodic solutions are also studied by the norm-form method and central flow theo- rem. Finally, numerical simulations are carried out to illustrate the mathematical conclusions.