Miao Hui, Teng Zhidong, Li Zhiming
College of Mathematics and System Sciences, Xinjiang University, Xinjiang, Urumqi 830046, China.
Comput Math Methods Med. 2016;2016:3903726. doi: 10.1155/2016/3903726. Epub 2016 Dec 15.
The dynamical behaviors for a five-dimensional viral infection model with three delays which describes the interactions of antibody, cytotoxic T-lymphocyte (CTL) immune responses, and nonlinear incidence rate are investigated. The threshold values for viral infection, antibody response, CTL immune response, CTL immune competition, and antibody competition, respectively, are established. Under certain assumptions, the threshold value conditions on the global stability of the infection-free, immune-free, antibody response, CTL immune response, and interior equilibria are proved by using the Lyapunov functionals method, respectively. Immune delay as a bifurcation parameter is further investigated. The numerical simulations are performed in order to illustrate the dynamical behavior of the model.
研究了一个具有三个时滞的五维病毒感染模型的动力学行为，该模型描述了抗体、细胞毒性T淋巴细胞（CTL）免疫反应以及非线性发生率之间的相互作用。分别建立了病毒感染、抗体反应、CTL免疫反应、CTL免疫竞争和抗体竞争的阈值。在某些假设下，分别使用Lyapunov泛函方法证明了无感染、无免疫、抗体反应、CTL免疫反应和内部平衡点全局稳定性的阈值条件。进一步研究了作为分岔参数的免疫时滞。进行了数值模拟以说明该模型的动力学行为。
