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数学与物理
应用数学进展
Vol. 5 No. 3 (August 2016)
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带有无细胞传播、细胞传播和体液免疫反应的HIV/AIDS模型的稳定性分析
Stability Analysis of HIV/AIDS Model with Non-Cell-Propagation, Cell-Propagation and Humoral Immune Response
DOI:
10.12677/AAM.2016.53063
,
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被引量
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国家自然科学基金支持
作者:
阿斯亚•吾斯曼
,
夏米西努尔•阿布都热合曼
*
:新疆大学,数学与系统科学学院,新疆 乌鲁木齐
关键词:
药物疗法
;
细胞与细胞之间的传递
;
体液免疫
;
Lyapunov函数
;
全局稳定性
;
Drug Therapy
;
Cell-to-Cell Transmission
;
Humoral Immune
;
Lyapunov Function
;
Global Stability
摘要:
根据重要生物意义,我们研究了一类具有HIV感染经典细胞扩散与细胞之间传播以及具有治疗的HIV感染模型。本文我们首先讨论了解的正性和有界性。然后,给出了系统的平衡点和基本再生数
R
0
。当
R
0
<1
时,得到了系统无病平衡点的全局稳定性。当
R
1
<1
时,得到了无体液免疫平衡点的稳定性,而当
R
1
>1
时,得到了系统体液免疫平衡点的全局稳定性等结论。
Abstract:
Based on vital biological meanings, we consider a class of HIV infection models with both cell-free virus spread and cell-to-cell transmission. First of all, we show that all the solution to our system is positive and bounded. Then, we give the basic reproduction number
R
0
and we prove that if
R
0
<1
, the infection-free equilibrium is globally stable. And if
R
1
<1
, the endemic equilibrium with humoral immunity is locally asymptotically stable, if
R
1
>1
, the endemic equilibrium with humoral immunity is globally stable.
文章引用:
阿斯亚•吾斯曼, 夏米西努尔•阿布都热合曼. 带有无细胞传播、细胞传播和体液免疫反应的HIV/AIDS模型的稳定性分析[J]. 应用数学进展, 2016, 5(3): 523-535.
http://dx.doi.org/10.12677/AAM.2016.53063
参考文献
[
1
]
Mojaver, A. and Kheiri, H. (2015) Mathematical Analysis of a Class of HIV Infection Models of CD4+ T-Cells with Combined An-tiretroviral Therapy. Applied Mathematics and Computation, 259, 258-270.
http://dx.doi.org/10.1016/j.amc.2015.02.064
[
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]
Jones, L.E. and Perelson, A.S. (2007) Trensient Virema, Plasma Viral Load and Reservoir Replenishment in HIV Infected Patients on Antiretroviral Therapy. Journal of Acquired Immune Deficiency Syndromes, 45, 483-493.
[
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]
Wang, S.F. and Zou, D.Y. (2012) Global Stability of In-Host Viral Models with Humoral Immunity and Intracellular Delays. Applied Mathematical Modelling, 36, 1313-1322.
http://dx.doi.org/10.1016/j.apm.2011.07.086
[
4
]
Cai, L.M., Guo, S.L. and Wang, S.P. (2014) Analysis of an Extended HIV/AIDS Epidemic Model with Treatment. Applied Mathematics and Computation, 236, 621-627.
http://dx.doi.org/10.1016/j.amc.2014.02.078
[
5
]
Mukandavire, Z., Das, P., Chiyaka, C. and Nyabadza, F. (2010) Global Analysis of an HIV/AIDS Epidemic Model. World Journal of Modelling and Simulation, 6, 231-240.
[
6
]
El-Morshedy, H.A. (2014) Global Attractivity in a Population Model with Nonlinear Death Rate and Distributed Delays. Journal of Mathematical Analysis and Applications, 410, 642-658.
http://dx.doi.org/10.1016/j.jmaa.2013.08.060
[
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]
Hirsh, M.W., Hanisch, H. and Gabriel, J.-P. (1985) Differential Equation Models of Some Parasitic Infections: Methods for the Study of Asymptotic Behaviour. Communication on Pure and Applied Mathematics, 38, 733-753.
http://dx.doi.org/10.1002/cpa.3160380607
[
8
]
Mazurov, D., llinskaya, A., Heidecker, G., Lloyd, P. and Derse, D. (2010) Quantitative Comparison of HTLV-1 and HIV-1 Cell-to-Cell Infection with New Replication Dependent Vector. PLoS Pathogens, 6, e1000788.
http://dx.doi.org/10.1371/journal.ppat.1000788
[
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]
Johnson, D.C. and Huber, M.T. (2002) Directed Egress of Animal Viruses Promotes Cell-to-Cell Spread. Journal of Virology, 76, 1-8.
http://dx.doi.org/10.1128/JVI.76.1.1-8.2002
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