【摘要】 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E₀、无免疫感染平衡点E₁、免疫感染平衡点E₂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E₂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。更多还原

【Abstract】 Consider a delayed HIV model with Logistic growth and saturated CTL-immune response. The existence conditions of the infection-free equilibrium E₀,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 theorem. Finally,numerical simulations are carried out to illustrate the mathematical conclusions.更多还原