具有Logistic增长和时滞的HIV-1感染模型的Hopf分支

Hopf bifurcation analysis in a HIV-1 infection model with delays and logistic growth

研究目标细胞具有Logistic增长、细胞间可以传播的、带有两个时滞的HIV-1病毒感染模型,两个时滞分别为细胞因病毒引起感染过程的时滞和病毒在感染细胞内繁殖的时滞。讨论在不同情况下各个平衡点存在的条件,通过分析特征方程,建立三个平衡点的局部稳定性和把两个时滞作为分支参数时Hopf分支的存在性。结论显示:两个时滞对琐细平衡点和边界平衡点的局部稳定性没有影响,但可能使正平衡点扰动,进而可能存在周期解。数值模拟验证了所得结论。

Consider the dynamical behavior of a HIV-1 infection model with Logistic growth for target cells and two discrete delays, namely the infection delay caused by free virus and the virus production delay. It is shown that the existence of the positive equilibriums in different conditions. By analyzing the characteristic equations, the local stability of the three equilibriums of the model and the existence of Hopf bifurcations when two delays are used as the bifurcation parameter are established. The results exhibit that both delays do not affect the stability of the boundary equilibrium. However, they are able to destabilize the positive equilibrium and cause periodic solutions. Numerical simulations are carried out to explain the mathematical conclusions.