Skip Navigation Links
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Dynamics of an HIV pathogenesis Model with Absorption and Saturation Incidence

Discontinuity, Nonlinearity, and Complexity 10(1) (2021) 19--29 | DOI:10.5890/DNC.2021.03.002

Vinoth Sivakumar , Jayakumar Thippan, Prasantha Bharathi Dhandapani

Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, India

Download Full Text PDF



In this paper, the dynamics of an HIV infection model with absorption and saturation incidence are proposed and analyzed. Further, we introduce a time delay to the model, which describes a time between infected cells and excretion of the viral particles. This model is used to explain existence, characteristic equations, and stability of infected and disease free steady states. Numerical simulations are provided to illustrate the theoretical results.


  1. [1]  Culshaw, R.V. and Ruan, S. (2000), A delay differential equation model of HIV infection of CD4+ T cells, Math Biosci, 165 , 27-39.
  2. [2]  Mittler, J.E., Sulzer, B., Neumann, A.U., and Perelson, A.S. (1998), Influence of delayed viral production on viral dynamics in HIV-1 infected patients, Mathematical Biosciences, 152(2), 143-163.
  3. [3]  Perelson, A.S., Kirschner, D.E., and De Boer, R. (1993), Dynamics of HIV infection of CD4+ T cells, Math Biosci, 114, 81-125.
  4. [4]  Wang, X. and Song, X. (2007), Global stability and periodic solution of a model for HIV infection of CD4+ T cells, Applied Mathematics and Computation, 189(2),1331-1340.
  5. [5]  Nowak, M.A., Bonhoeffer, S., Hill, A.M., Boehme, R., and Thomas, H.C. (1996), Viral dynamics in hepatitis B virus infection, Proceedings of the National Academy of Sciences of the United States of America, 93, 4398-4402.
  6. [6]  Srivastava, P.Kr. and Chandra, P. (2010) , Modeling the dynamics of HIV and CD4+ T cells during primary infection, Nonlinear Analysis. Real World Applications , 11, 612-618.
  7. [7]  Song, X. and Neumann, A.U. (2007), Global stability and periodic solution of the viral dynamics, J. Math. Anal. Appl, 329, 281-297.
  8. [8]  Hu, Z.X., Zhang, J.J., Wang, H., and Ma, W.B. (2014), Dynamics analysis of a delayed viral infection model with logistic growth and immune impairment, Appl Math Model, 38,524-534.
  9. [9]  Jia, J. and Li, J. (2017), Stability and Hopf bifurcation of a delayed viral infection model with logistic growth and saturated immune impairment, Math Meth Appl Sci, 1-11.
  10. [10]  Wang, L. and Li, M.Y. (2006), Mathematical analysis of the global dynamics of a model for HIV infection of CD4$^{+}$ T cells, Mathematical Biosciences, 200(1),44-57.
  11. [11]  Wang, Y., Zhou, Y., Wu, J., and Heffernan, J. (2009), Oscillatory viral dynamics in a delayed HIV pathogenesis model, Math. Biosci, 219,104-112.
  12. [12]  Zhou, X.Y., Shi, X.Y., and Song, X.Y. (2009), A differential equation model of HIV infection of CD4+ T-cells with cure rate , J Appl Math Comput.,31,51-70.
  13. [13]  Xu, R. (2011), Global stability of an HIV-1 infection model with saturation infection and intracellular delay, J. Math. Anal. Appl., 375, 75-81.
  14. [14] Van den Driessche, P. and Watmough, J.(2002), Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math.Biosci, 180(1-2),29-48.
  15. [15]  Li, M.Y. and Muldowney, J.S. (1996), A geometric approach to the global stability problems, SIAM J. Math. Anal, 27, 1070-1083.
  16. [16]  Martin Jr, R.H. (1974), Logarithmic norms and projections applied to linear differential systems, J. Math. Anal. Appl, 45, 432-454.
  17. [17]  Dieudonne, J. (1960), Foundations of Modern Analysis, Academic Press: New York,.
  18. [18]  Song, Y.L. and Yuan, S.L. (2006), Bifurcation analysis in a predator-prey system with time delay, J. Nonlinear Anal Real World Appl, 7, 265-284.