American Institute of Mathematical Sciences

Advanced
September  2009, 12(2): 511-524. doi: 10.3934/dcdsb.2009.12.511

Dynamics of a HIV-1 Infection model with cell-mediated immune response and intracellular delay

Huiyan Zhu 1, and  Xingfu Zou 2,

1. 

School of Mathematics and Physics, Nanhua University, Hengyang, Hunan 421001, China
2. 

Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7

Received  October 2008 Revised  January 2009 Published  July 2009

In this paper, we consider a mathematical model for HIV-1 infection with intracellular delay and cell-mediated immune response. A novel feature is that both cytotoxic T lymphocytes (CTLs) and the intracellular delay are incorporated into the model. We obtain a necessary and sufficient condition for the global stability of the infection-free equilibrium and give sufficient conditions for the local stability of the two infection equilibria: one without CTLs being activated and the other with. We also perform some numerical simulations which support the obtained theoretical results. These results show that larger intracellular delay may help eradicate the virus, while the activation of CTLs can only help reduce the virus load and increase the healthy CD$_4^+$ cells population in the long term sense.
Keywords: Stability., intracellular delay, immune response, HIV-1 infection.
Mathematics Subject Classification: Primary: 92B05,92C50; Secondary: 92D2.
Citation: Huiyan Zhu, Xingfu Zou. Dynamics of a HIV-1 Infection model with cell-mediated immune response and intracellular delay. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 511-524. doi: 10.3934/dcdsb.2009.12.511
[1]

Jinliang Wang, Lijuan Guan. Global stability for a HIV-1 infection model with cell-mediated immune response and intracellular delay. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 297-302. doi: 10.3934/dcdsb.2012.17.297
[2]

Jinhu Xu, Yicang Zhou. Bifurcation analysis of HIV-1 infection model with cell-to-cell transmission and immune response delay. Mathematical Biosciences & Engineering, 2016, 13 (2) : 343-367. doi: 10.3934/mbe.2015006
[3]

Zhijun Liu, Lianwen Wang, Ronghua Tan. Spatiotemporal dynamics for a diffusive HIV-1 infection model with distributed delays and CTL immune response. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021159
[4]

Rachid Ouifki, Gareth Witten. A model of HIV-1 infection with HAART therapy and intracellular delays. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 229-240. doi: 10.3934/dcdsb.2007.8.229
[5]

Aiping Wang, Michael Y. Li. Viral dynamics of HIV-1 with CTL immune response. Discrete & Continuous Dynamical Systems - B, 2021, 26 (4) : 2257-2272. doi: 10.3934/dcdsb.2020212
[6]

Shengqiang Liu, Lin Wang. Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy. Mathematical Biosciences & Engineering, 2010, 7 (3) : 675-685. doi: 10.3934/mbe.2010.7.675
[7]

Yun Tian, Yu Bai, Pei Yu. Impact of delay on HIV-1 dynamics of fighting a virus with another virus. Mathematical Biosciences & Engineering, 2014, 11 (5) : 1181-1198. doi: 10.3934/mbe.2014.11.1181
[8]

Haitao Song, Weihua Jiang, Shengqiang Liu. Virus dynamics model with intracellular delays and immune response. Mathematical Biosciences & Engineering, 2015, 12 (1) : 185-208. doi: 10.3934/mbe.2015.12.185
[9]

Gesham Magombedze, Winston Garira, Eddie Mwenje. Modelling the immunopathogenesis of HIV-1 infection and the effect of multidrug therapy: The role of fusion inhibitors in HAART. Mathematical Biosciences & Engineering, 2008, 5 (3) : 485-504. doi: 10.3934/mbe.2008.5.485
[10]

Nikolay Pertsev, Konstantin Loginov, Gennady Bocharov. Nonlinear effects in the dynamics of HIV-1 infection predicted by mathematical model with multiple delays. Discrete & Continuous Dynamical Systems - S, 2020, 13 (9) : 2365-2384. doi: 10.3934/dcdss.2020141
[11]

Hee-Dae Kwon, Jeehyun Lee, Myoungho Yoon. An age-structured model with immune response of HIV infection: Modeling and optimal control approach. Discrete & Continuous Dynamical Systems - B, 2014, 19 (1) : 153-172. doi: 10.3934/dcdsb.2014.19.153
[12]

Jeng-Huei Chen. An analysis of functional curability on HIV infection models with Michaelis-Menten-type immune response and its generalization. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2089-2120. doi: 10.3934/dcdsb.2017086
[13]

Lianwen Wang, Zhijun Liu, Yong Li, Dashun Xu. Complete dynamical analysis for a nonlinear HTLV-I infection model with distributed delay, CTL response and immune impairment. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 917-933. doi: 10.3934/dcdsb.2019196
[14]

Yu Ji, Lan Liu. Global stability of a delayed viral infection model with nonlinear immune response and general incidence rate. Discrete & Continuous Dynamical Systems - B, 2016, 21 (1) : 133-149. doi: 10.3934/dcdsb.2016.21.133
[15]

Yuan Yuan, Xianlong Fu. Mathematical analysis of an age-structured HIV model with intracellular delay. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021123
[16]

Alexander Rezounenko. Stability of a viral infection model with state-dependent delay, CTL and antibody immune responses. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1547-1563. doi: 10.3934/dcdsb.2017074
[17]

Bing Li, Yuming Chen, Xuejuan Lu, Shengqiang Liu. A delayed HIV-1 model with virus waning term. Mathematical Biosciences & Engineering, 2016, 13 (1) : 135-157. doi: 10.3934/mbe.2016.13.135
[18]

Loïc Barbarroux, Philippe Michel, Mostafa Adimy, Fabien Crauste. A multiscale model of the CD8 T cell immune response structured by intracellular content. Discrete & Continuous Dynamical Systems - B, 2018, 23 (9) : 3969-4002. doi: 10.3934/dcdsb.2018120
[19]

Mudassar Imran, Hal L. Smith. The dynamics of bacterial infection, innate immune response, and antibiotic treatment. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 127-143. doi: 10.3934/dcdsb.2007.8.127
[20]

Cameron Browne. Immune response in virus model structured by cell infection-age. Mathematical Biosciences & Engineering, 2016, 13 (5) : 887-909. doi: 10.3934/mbe.2016022

2020 Impact Factor: 1.327

Tools

Metrics

  • PDF downloads (143)
  • HTML views (0)
  • Cited by (79)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences