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  4. On the stability of a mathematical model for HIV(AIDS) - cancer dynamics

On the stability of a mathematical model for HIV(AIDS) - cancer dynamics

MMC.
2021;
Volume 8, Number 4
: pp. 783–796
https://doi.org/10.23939/mmc2021.04.783
Received: May 23, 2021
Accepted: June 07, 2021

Mathematical Modeling and Computing, Vol. 8, No. 4, pp. 783–796 (2021)

Authors:
  1. H. W. Salih
  2. A. Nachaoui
1
Mathematical department, Salahaddin University-Erbil, Erbil Kurdistan region Iraq
2
Laboratoire de Mathematiques Jean Leray, Universite de Nantes, France

In this work, we study an impulsive mathematical model proposed by Chavez et al. [1] to describe the dynamics of cancer growth and HIV infection, when chemotherapy and HIV treatment are combined.  To better understand these complex biological phenomena, we study the stability of equilibrium points.  To do this, we construct an appropriate Lyapunov function for the first equilibrium point while the indirect Lyapunov method is used for the second one.  None of the equilibrium points obtained allow us to study the stability of the chemotherapeutic dynamics, we then propose a bifurcation of the model and make a study of the bifurcated system which contributes to a better understanding of the underlying biochemical processes which govern this highly active antiretroviral therapy.  This shows that this mathematical model is sufficiently realistic to formulate the impact of this treatment.

equilibrium point
stability
HIV(AIDS)-cancer model
Lyapunov direct method
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