Dynamics of a Delayed HIV-1 Infection Model with Saturation Incidence Rate and CTL Immune Response
Dynamics of a Delayed HIV-1 Infection Model with Saturation Incidence Rate and CTL Immune Response
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DOI：
10.1142/s0218127416502345
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发表时间：
2016-12
期刊：
影响因子：
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通讯作者：
Ting Guo;Haihong Liu;Chenglin Xu;Fang Yan
中科院分区：
文献类型：
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作者：
Ting Guo;Haihong Liu;Chenglin Xu;Fang Yan
本文研究了一个包含饱和感染率、CTL免疫反应和三个时滞（分别代表潜伏期、病毒产生期和免疫反应时滞）的五维病毒模型的动力学行为.我们开始这个模型证明的积极性和有界的解决方案。我们的模型承认三种可能的平衡解，即无感染平衡E0，无免疫反应的感染平衡E1和有免疫反应的感染平衡E2。通过分析相应的特征方程，分别证明了每个可行平衡点的局部稳定性和平衡点E2处的Hopf分支的存在性.进一步，利用波动引理和适当的李雅普诺夫泛函，证明了当病毒感染的基本再生数R0小于1时，E0是全局渐近稳定的.当免疫反应的基本再生数R1小于1，R0大于1时，平衡点E1是全局渐近稳定的。最后，进行了一些数值模拟，以说明理论结果。
In this paper, we investigate the dynamics of a five-dimensional virus model incorporating saturation incidence rate, CTL immune response and three time delays which represent the latent period, virus production period and immune response delay, respectively. We begin this model by proving the positivity and boundedness of the solutions. Our model admits three possible equilibrium solutions, namely the infection-free equilibrium E0, the infectious equilibrium without immune response E1 and the infectious equilibrium with immune response E2. Moreover, by analyzing corresponding characteristic equations, the local stability of each of the feasible equilibria and the existence of Hopf bifurcation at the equilibrium point E2 are established, respectively. Further, by using fluctuation lemma and suitable Lyapunov functionals, it is shown that E0 is globally asymptotically stable when the basic reproductive numbers for viral infection R0 is less than unity. When the basic reproductive numbers for immune response R1 is less than unity and R0 is greater than unity, the equilibrium point E1 is globally asymptotically stable. Finally, some numerical simulations are carried out for illustrating the theoretical results.