具有Logistic增长和两时滞的HTLV-I感染模型的Hopf分支

Hopf Bifurcation Analysis in a HTLV-I Infection Model with Logistic Growth and Two Delays

研究了具有Logistic增长和考虑感染细胞的产生及CTL免疫反应所需时滞的HTLV-I感染模型.讨论了平衡点的存在性,以及平衡点E0、无病平衡点E1和地方病平衡点E*的存在条件,并通过特征方程分析了3个平衡点的局部渐近稳定性和两个时滞在不同情况下对E*的影响以及Hopf分支的存在性.结果表明:两个时滞对E0和E1的局部稳定性没有影响,但可能使E*扰动产生周期解.最后用Matlab对本文的结论进行了数值模拟.

In this paper,we establish a HTLV-I model with Logistic growth and two time delays,namely an intracellular delay and a CTL immune response delay.The existence of the disease-free equilibriumE0,E1 and the endemic equilibriumE^* is discussed.By analyzing the characteristic equations,the local asymptotical stability of the three equilibriums and the existence of Hopf bifurcations when two delays are used as the bifurcation parameter are established.The results show that two delays do not affect the asymptotical stability of the boundary equilibrium,but they may destabilize the endemic equilibrium and cause periodic solutions.Numerical simulation are carried out to explain the mathematical conclusions.