Delayed Model for HIV Infection with Drug Effects

被引：2
作者：
Sahani S.K. [1 ]
Yashi [1 ]
机构：
[1] Department of Mathematics, South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi
来源：
Differential Equations and Dynamical Systems | 2018年 / 26卷 / 1-3期
关键词：
Bifurcation; Combination therapy; Delay; Global stability; HIV; Immune response; Stability;
D O I：
10.1007/s12591-016-0341-7
中图分类号：
学科分类号：
摘要：
Delayed models are a better representation of the nature of HIV. In the present paper, a multi-delayed model of HIV with combination drug therapy has been analysed. Effect of the immune response in the form of effector cell response has also been included to make the model more justified. The threshold properties related with the basic reproduction number R0 have been discussed. The local and global properties of the model have been analysed. Extensive numerical simulations have been performed to show the impact of highly effective drug on the concentration of virus. The numerical simulations and the result proved has led to the conclusion that a highly effective drug when combined with a less effective drug, can very efficiently bring down the viral load to undetectable levels. © 2016, Foundation for Scientific Research and Technological Innovation.
引用
收藏
页码：57 / 80
页数：23
相关论文
共 45 条
  • [1] Allen L.J., Brauer F., Van den Driessche P., Wu J., Mathematical Epidemiology, (2008)
  • [2] Balasubramaniam P., Tamilalagan P., Prakash M., Bifurcation analysis of HIV infection model with antibody and cytotoxic T-lymphocyte immune responses and Beddington–DeAngelis functional response, Math. Methods Appl. Sci., 38, 7, pp. 1330-1341, (2015)
  • [3] Banks H., Bortz D., A parameter sensitivity methodology in the context of HIV delay equation models, J. Math. Biol., 50, 6, pp. 607-625, (2005)
  • [4] Banks H., Bortz D., Holte S., Incorporation of variability into the modeling of viral delays in HIV infection dynamics, Math. Biosci., 183, 1, pp. 63-91, (2003)
  • [5] Burg D., Rong L., Neumann A.U., Dahari H., Mathematical modeling of viral kinetics under immune control during primary HIV-1 infection, J. Theor. Biol., 259, 4, pp. 751-759, (2009)
  • [6] Castillo-Chavez C., Feng Z., Huang W., On the computation of r<sub>0</sub> and its role on global stability, Math. Approaches Emerg. Reemerg. Infect. Dis. Introd., 1, (2002)
  • [7] Ciupe M., Bivort B., Bortz D., Nelson P., Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models, Math. Biosci., 200, 1, pp. 1-27, (2006)
  • [8] Conway J.M., Perelson A.S., Post-treatment control of HIV infection, Proc. Natl. Acad. Sci., 112, 17, pp. 5467-5472, (2015)
  • [9] Culshaw R.V., Ruan S., A delay-differential equation model of HIV infection of CD4+ T-cells, Math. Biosci., 165, 1, pp. 27-39, (2000)
  • [10] Dixit N.M., Markowitz M., Ho D.D., Perelson A.S., Estimates of intracellular delay and average drug efficacy from viral load data of HIV-infected individuals under antiretroviral therapy, Antivir. Ther, 9, pp. 237-246, (2004)
12345