一类具有时滞及非线性感染率的病毒感染模型的稳定性及分支分析

基金项目:

国家自然科学基金项目(11071013)

详细信息

Stability Properties and Hopf Bifurcation of a Class of Viral Infection Model with Intracellular Delay and Nonlinear Incidence

Department of Applied Mathematics,School of Mathematics and Physics,University of Science and Technology Beijing

摘要: 将时滞及饱和发生率引入到一类具有初级细胞毒性T淋巴细胞(CTLp)和效应细胞毒性T淋巴细胞(CTLe)免疫反应的病毒感染模型,证明了改进后模型无病毒感染平衡点及无免疫平衡点的全局渐近稳定性.同时,给出了免役应答平衡点(正平衡点)产生Hopf分支的充分条件.最后,数值模拟验证了理论结果.
- 非线性感染率 /
- 时滞 /
- 稳定性 /
- Hopf分支
Abstract: Intracellular delay and nonlinear infection rate were introduced into a class of viral infection model with primary and secondary CTL response to viral infections.Global asymptotic stability of the infection free equilibrium and the no-immune response equilibrium were discussed.Then，the conditions for the existence of Hopf bifurcation near the positive equilibrium were given.Finally，numerical simulations verified the theoretical results.
- nonlinear infection rate /
- intracellular delay /
- stability /
- Hopf bifurcation

[1]	陈兰荪，宋新宇，陆征一．数学生态学模型与研究方法［M］．成都: 四川科学技术出版社，2003．
[2]	陈兰荪，孟新柱，焦建军．生物动力学［M］．北京: 科学出版社，2009．