International Journal of Nonlinear Analysis and Applications
Analysis of a delayed HIV pathogenesis model with saturation incidence, both virus-to-cell and cell-to-cell transmission
Document Type : Research Paper
Authors
Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, India
Abstract
In this paper, we proposed and studied a delayed HIV pathogenesis model with saturation incidence, both virus-to-cell and cell-to-cell transmission. We address the basic reproduction number R0, the characteristic equations, and local stability of feasible equilibria are established. Where the delay incorporates both virus-to-cell and cell-to-cell transmission. Moreover, we discuss the existence of Hopf Bifurcation when a delay is used as a bifurcation parameter. Numerical simulations are performed to satisfy our theoretical results.
Keywords
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cell to-cell transmission, Nonlinear Anal. Real World Appl. 34 (2017), 75–96.
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[18] J.Y. Yang, X.Y. Wang and X.Z. Li, Hopf bifurcation for a model of HIV infection of CD4
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Cell-to-Cell Transmissions, Int. J. Bifurc. Chaos 28 (2018), no. 9, 1–20.
[20] X. Zhou, X. Song and X. Shi, Analysis of stability and Hopf bifurcationfor an HIV infection model with time
delay, Appl. Math. Comput. 199 (2008), 23–38.
parameters, SIAM J. Math. Anal. 33 (2002), 1144–1165.
[2] L. Cai, X. Li, M. Ghosh and B. Guo, Stability analysis of an HIV/AIDS epidemic model with treatment, J.
Comput. Appl. Math. 229 (2009), 313–323.
[3] R.V. Culshaw and S. Ruan, A delay differential equation model of HIV infection of CD4
+ T cells, Math. Biosci.
165 (2000), 27–39.
[4] X. Lai and X. Zou, Modeling cell-to-cell spread of HIV-1 with logistic target cell growth, J. Math. Anal. Appl.
426 (2015), 563–584.
[5] X. Lai and X. Zou, Modeling HIV-1 virus dynamics with both virus-to-cell infection and cell-to-cell transmission,
SIAM J. Appl. Math. 74 (2014), no. 3, 898–917.
[6] J.A. Levy, Pathogenesis of Human immunodeficiency virus infection, Microbiol. Rev. 57 (1993), no. 1, 183–289.
[7] M.Y. Li and H. Shu, Joint effects of mitosis and intracellular delay on viral dynamics: Two-parameter bifurcation
analysis, J. Math. Biol. 64 (2012), 1005–1020.
[8] M.Y. Li and H. Shu, Impact of intracellular delays and target-cell dynamicson in vivo viral infections, SIAM J.
Appl. Math. 70 (2010), no. 7, 2434–2448.
[9] F. Li and J. Wang, Analysis of an HIV infection model with logistic target-cell growth and cell-to-cell transmission,
Chaos Solution Fractals 81 (2015), 136–145.[10] J. Lin, R. Xu and X. Tian, Threshold dynamics of an HIV-1 virus model with both virus-to-cell and cell-to-cell
transmissions, intracellular delay, and humoral immunity, Appl. Math. Comput. 315 (2017), 516–530.
[11] Y. Lv, Z. Hu and F. Liao, The stability and Hopf bifurcation for an HIV model with saturated infection rate and
double delays, Int. J. Biomath. 11 (2018), no. 3, 1–43.
[12] A.S. Perelson, D.E. Kirschner and R.J. De Boer, Dynamics of HIV infection of CD4
+ T cells, Math. Biosci. 114
(1993), 81–125.
[13] S. Vinoth, T. Jayakumar and D. Prasantha Bharathi, Stability analysis of a Mathematical model for the dynamics
of HIV infection with cure rate, Int. J. Appl. Engin. Res. 14 (2019), no. 3 (Special Issue), 87–90.
[14] T. Wang, Z. Hu and F. Liao, Stability and Hopf bifurcation for a virus infection model with delayed humoral
immunity response, J. Math. Anal. Appl. 411 (2014), 63–74.
[15] J. Wang, J. Lang and X. Zou, Analysis of an age structured HIV infection model with virus-to-cell infection and
cell to-cell transmission, Nonlinear Anal. Real World Appl. 34 (2017), 75–96.
[16] R. Xu, Global stability of an HIV-1 infection model with saturation infection and intracellular delay, J. Math.
Anal. Appl. 375 (2011), 75–81.
[17] J. Xu and Y. Zhou, Bifurcation analysis of HIV-1 infection model with cell-To-cell transmission and immune
response delay, Math. Biosci. Engin. 13 (2016), no. 2, 343–367.
[18] J.Y. Yang, X.Y. Wang and X.Z. Li, Hopf bifurcation for a model of HIV infection of CD4
+ T-cells with virus
released delay, Discrete Dyn. Nature Soc. 2011 (2011), Article ID 649650, 1–24.
[19] X.Zhang and Z. Liu, Bifurcation Analysis of an Age Structured HIV Infection Model with Both Virus-to-Cell and
Cell-to-Cell Transmissions, Int. J. Bifurc. Chaos 28 (2018), no. 9, 1–20.
[20] X. Zhou, X. Song and X. Shi, Analysis of stability and Hopf bifurcationfor an HIV infection model with time
delay, Appl. Math. Comput. 199 (2008), 23–38.
)
Volume 13, Issue 2
July 2022Pages 1927-1936
- Receive Date: 23 January 2021
- Revise Date: 29 April 2021
- Accept Date: 11 May 2021