一类具有Hill型感染率的HIV模型的动力学分析

Dynamic analysis of a HIV model with Hill type infection rate

首先考虑了一类具有Hill感染率的HIV模型,给出了平衡点的具体表达式,分析了系统解的正性和有界性,并得到了无病平衡点局部和全局稳定的条件,以及正平衡点局部稳定的条件.然后考虑了对应的时滞系统,给出了平衡点稳定的充分条件,并讨论了正平衡点处的分支现象.最后借助计算机数值模拟验证了结论的正确性.

Firstly, a class of HIV model with Hill type infection rate is considered, the exact forms of equilibria are obtained, the positivity and boundedness of solution are analyzed, and the condition for local and global stability of the infection-free equilibrium are obtained, the conditions for local stability of the positive equilibrium are also given. Secondly, the corresponding delay system is taken into consideration, the sufficient conditions for stability of equilibria are provided, and the bifurcation of the positive equilibrium is discussed. Finally, the correctness of the conclusions are verified by computer numerical simulition.