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

[1] E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent
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 2022
Pages 1927-1936
  • Receive Date: 23 January 2021
  • Revise Date: 29 April 2021
  • Accept Date: 11 May 2021