一类具有细胞与细胞传染和病毒与细胞传染的时滞HIV-1传染病模型（英文）
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摘要
研究一类具有细胞与细胞传染和病毒与细胞传染且带有免疫反应的时滞HIV-1传染病模型。通过比较原理和Hurwitz判据等方法,得到模型解的正性和有界性、无病平衡点P0全局稳定性、感染平衡点P*的局部稳定性和系统的一致持久性。通过构造合适的Lyapunov泛函,得到了P*全局渐近稳定的条件。数值模拟解释了分析结果。
Consider a delayed differential equation model of HIV-1 with cell-to-cell and virus-to-cell transmissions. At the same time,the immune response is included in the model. By using the comparison principle and Hurwitz criterion etc.,it is obtained that the positivity and boundedness of the solution,global stability of the infection-free steady state P0,local stability of the infected steady state P*and uniform persistence of the system. Some conditions which made P*globally asymptotically stable are obtained by constructing a suitable Lyapunov functional. Numerical simulations are performed to illustrate analytic results.
Consider a delayed differential equation model of HIV-1 with cell-to-cell and virus-to-cell transmissions. At the same time,the immune response is included in the model. By using the comparison principle and Hurwitz criterion etc.,it is obtained that the positivity and boundedness of the solution,global stability of the infection-free steady state P0,local stability of the infected steady state P*and uniform persistence of the system. Some conditions which made P*globally asymptotically stable are obtained by constructing a suitable Lyapunov functional. Numerical simulations are performed to illustrate analytic results.
引文
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[12]MITTLER J E,SULZERAC B,NEUMANNAD A U,et al.Influence of delayed viral production on viral dynamics in HIV-1 infected patients[J].Mathematical Biosciences,1998,152(2):143-163.
[13]WANG Y,BRAUER F,WU J H,et al.A delay-dependent model with HIV drug resistance during therapy[J].Journal of Mathematical Analysis and Applications,2014,414(2):514-531.
[14]HIRSCH W M,HANISCH H,GABRIEL J P.Differential equation models of some parasitic infections:methods for the study of asymptotic behavior[J].Communications on Pure and Applied Mathematics,1985,38(6):733-753.
[15]马知恩,周义仓.常微分方程定性与稳定性方法[M].北京:科学出版社,2001.
[16]LI X L,WEI J J.On the zeros of a fourth degree exponential polynomial with applications to a neural network model with delays[J].Chaos,Solitons&Fractals,2005,26(2):519-526.
[17]SMITH H L,ZHAO X Q.Robust persistence for semidynamical systems[J].Nonlinear Analysis:Theory,Methods&Applications,2001,49(7):6169-6179.
[2]HU Z X,LIU X D,WANG H,et al.Analysis of the dynamics of a delayed HIV pathogenesis model[J].Journal of Computational and Applied Mathematics,2010,234(2):461-476.
[3]XU R.Global dynamics of an HIV-1 infection model with distributed intracellular delays[J].Computers&Mathematics with Applications,2011,61(9):2799-2805.
[4]XU J,ZHOU Y.Bifurcation analysis of HIV-1 infection model with cell-to-cell transmission and immune response delay[J].Mathematical Biosciences and Engineering,2016,13(2):343-367.
[5]吕翠芳,袁朝晖,焦建军.HollingⅡ型发生率下常时滞HIV-1治疗模型的动力学行为研究[J].北华大学学报(自然科学版),2010,11(3):206-209.
[6]CULSHAW R V,RUAN S G.A delay-dierential equation model of HIV infection of CD4+T-cells[J].Mathematical Biosciences,2000,165(1):27-39.
[7]LAI X L,ZOU X F.Modeling HIV-1 virus dynamics with both virus-to-cell infection and cell-to-cell transmission[J].SIAM Journal on Applied Mathematics,2014,74(3):898-917.
[8]LI D,MA W B.Asymptotic properties of a HIV-1 infection model with time delay[J].Journal of Mathematical Analysis and Applications,2007,335(1):683-691.
[9]YANG Y,ZOU L,RUAN S G.Global dynamics of a delayed within-host viral infection model with both virus-to-cell and cell-to-cell transmissions[J].Mathematical Biosciences,2015,270(B):183-191.
[10]WANG Z,WANG W.Mathematical analysis of immune response of HIV-I including delay[J].Chinese Quarterly Journal of Mathematics,2010,25(1):45-51.
[11]PAEELEK K A,LIU S Q,PAHLEVANI F,et al.A model of HIV-1 infection with two time delays:mathematical analysis and comparison with patient data[J].Mathematical Biosciences,2012,235(1):98-109.
[12]MITTLER J E,SULZERAC B,NEUMANNAD A U,et al.Influence of delayed viral production on viral dynamics in HIV-1 infected patients[J].Mathematical Biosciences,1998,152(2):143-163.
[13]WANG Y,BRAUER F,WU J H,et al.A delay-dependent model with HIV drug resistance during therapy[J].Journal of Mathematical Analysis and Applications,2014,414(2):514-531.
[14]HIRSCH W M,HANISCH H,GABRIEL J P.Differential equation models of some parasitic infections:methods for the study of asymptotic behavior[J].Communications on Pure and Applied Mathematics,1985,38(6):733-753.
[15]马知恩,周义仓.常微分方程定性与稳定性方法[M].北京:科学出版社,2001.
[16]LI X L,WEI J J.On the zeros of a fourth degree exponential polynomial with applications to a neural network model with delays[J].Chaos,Solitons&Fractals,2005,26(2):519-526.
[17]SMITH H L,ZHAO X Q.Robust persistence for semidynamical systems[J].Nonlinear Analysis:Theory,Methods&Applications,2001,49(7):6169-6179.