| 一类具免疫应答和非线性感染函数的时滞HIV-1感染模型的全局稳定性 |
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| 引用本文： | 常侠,袁朝晖.一类具免疫应答和非线性感染函数的时滞HIV-1感染模型的全局稳定性[J].经济数学,2011(4):1-5. |
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| 作者姓名： | 常侠 袁朝晖 |
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| 作者单位： | 桂林电子科技大学数学与计算科学学院;湖南大学数学与计量经济学院 |
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| 基金项目： | 广西自然科学基金(2010GXNSFC013012) |
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| 摘 要： | 考虑到HIV-1感染过程中免疫反应和非线性感染函数,建立了一类具有三个分布时滞的HIV-1感染动力学模型.得到了关于病毒感染的基本再生数R0和CTLs免疫反应的基本再生数R1 ＜R0.通过构造Lyapunov泛函证明了系统具有阈值动力学性质,即当R0≤1时,系统存在全局渐近稳定的无感染平衡点；当R1≤1＜R0时,系统出...
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| 关 键 词： | 时滞 稳定性 Lyapunov泛函 免疫反应 |
Global Stability of a Delayed HIV-1 Infection Model with Immune Response and Nonlinear Infection Function |
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| CHANG Xi,YUAN Zhao-hui.Global Stability of a Delayed HIV-1 Infection Model with Immune Response and Nonlinear Infection Function[J].Mathematics in Economics,2011(4):1-5. |
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| Authors: | CHANG Xi YUAN Zhao-hui |
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| Institution: | 1.Department of Mathematics,Guilin University of Electronic Science and Technology College,Guilin,Guangxi 541004,China;2.College of Mathematics and Econometrics,Hunan University,Changsha,Hunan 410082,China) |
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| Abstract: | Based on immune response and nonlinear infection function in HV-1 infection,an HIV-1 infection model with three distributed delays was established. The basic reproduction number R0 for viral infection and R1 〈R0 for CTLs response were obtained. By constructing Lyapunov functions, it is shown that the model exhibits a threshold dynamics., the uninfected equilibrium exists and is globally asymptotically stable if Ro ≤1 ;the infected equilibrium without immune response exists and is globally asymptotically stable if R1 ≤1≤Ro ; the infected equilibrium with immune response is globally asymptotically stable if R1 〉1. |
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| Keywords: | delays stability Lyapunov function immune response |
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