具有免疫反应的时滞HIV感染模型的稳定性
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摘要
建立了具有免疫反应的时滞HIV感染模型,讨论了系统解的非负性和有界性,得到了确定模型动力学性态的基本再生数。通过构造适当的Lyapunov泛函,利用La Salle不变原理证明了无病平衡点的全局渐近稳定性,并用数值模拟验证了结果。
In this paper,we built a delay infection model with immune response and discussed the nonnegativity and boundedness of the solution. The basic reproduction number is obtained,which determines the dynamical behaviors of the infection model. By constructing suitable Lyapunov functions and applying La Salle's invariance principle we have proven that the infection-free equilibrium is globally asymptotically stable. Then numerical simulations are carried out to support the result.
In this paper,we built a delay infection model with immune response and discussed the nonnegativity and boundedness of the solution. The basic reproduction number is obtained,which determines the dynamical behaviors of the infection model. By constructing suitable Lyapunov functions and applying La Salle's invariance principle we have proven that the infection-free equilibrium is globally asymptotically stable. Then numerical simulations are carried out to support the result.
引文
[1]李益群,李建全,李琳.一类具有CTL作用的HIV感染模型的全局稳定性[J].生物数学学报,2013,28(3):467-472.
[2]LYU Cui-fang,HUANG Li-hong,YUAN Zhao-hui.Global stability for an HIV-1 infection model with Beddington-De Angelis incidence rate and CTL immune response[J].Communications in Nonlinear Science and Numerical Simulation,2014,19(1):121-127.
[3]HUANG Dong-wei,ZHANG Xiao,GUO Yong-feng,et al.Analysis of an HIV infection model with treatments and delayed immune response[J].Applied Mathematical Modelling,2016,40(4):3081-3089.
[4]NOWAK M A,BONHOEFFER S,HILL A M,et al.Viral Dynamics in hepatitis B virus infection[J].Proceedings of the National Academy of Sciences,1996(9):398-402.
[5]眭鑫,刘贤宁,周林.具有潜伏细胞和CTL免疫反应的HIV模型的稳定性分析[J].西南大学学报:自然科学版,2012,34(5):23-27.
[6]郑重武,张凤琴.一类具有感染时滞的HIV模型的稳定性分析[J].数学的实践与认识,2010,40(13):247-252.
[7]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,2011,28(4):1-5.
[8]TIAN Xiao-hong,XU Rui.Global stability and Hopf bifurcation of an HIV-1 infection model with saturation incidence and delayed CTL immune response[J].Applied Mathematics and Computation,2014,237(7):146-154.
[9]陈美玲.具免疫应答的时滞HIV感染模型动力学性质研究[D].衡阳:南华大学,2010.
[10]曹艳红.具有免疫应答和细胞内部时滞的HIV感染模型的稳定性分析[D].衡阳:南华大学,2011.
[2]LYU Cui-fang,HUANG Li-hong,YUAN Zhao-hui.Global stability for an HIV-1 infection model with Beddington-De Angelis incidence rate and CTL immune response[J].Communications in Nonlinear Science and Numerical Simulation,2014,19(1):121-127.
[3]HUANG Dong-wei,ZHANG Xiao,GUO Yong-feng,et al.Analysis of an HIV infection model with treatments and delayed immune response[J].Applied Mathematical Modelling,2016,40(4):3081-3089.
[4]NOWAK M A,BONHOEFFER S,HILL A M,et al.Viral Dynamics in hepatitis B virus infection[J].Proceedings of the National Academy of Sciences,1996(9):398-402.
[5]眭鑫,刘贤宁,周林.具有潜伏细胞和CTL免疫反应的HIV模型的稳定性分析[J].西南大学学报:自然科学版,2012,34(5):23-27.
[6]郑重武,张凤琴.一类具有感染时滞的HIV模型的稳定性分析[J].数学的实践与认识,2010,40(13):247-252.
[7]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,2011,28(4):1-5.
[8]TIAN Xiao-hong,XU Rui.Global stability and Hopf bifurcation of an HIV-1 infection model with saturation incidence and delayed CTL immune response[J].Applied Mathematics and Computation,2014,237(7):146-154.
[9]陈美玲.具免疫应答的时滞HIV感染模型动力学性质研究[D].衡阳:南华大学,2010.
[10]曹艳红.具有免疫应答和细胞内部时滞的HIV感染模型的稳定性分析[D].衡阳:南华大学,2011.