Mathematical Analysis of the Dynamics of HIV Infection with CTL Immune Response and Cure Rate

  • Sanaa Harroudi
  • Karam Allali


The mathematical model of the human immunodeficiency virus (HIV) pathogenesis with CTL (cytotoxic T lymphocytes) immune response and cure rate of infected cells is investigated. The model includes four nonlinear differential equations describing the evolution of uninfected cells, infected cells, free HIV viruses, and CTL immune response cells. The positivity and boundedness of solutions are established. The local stability for the disease-free steady state and for the infection steady states is studied. Finally, numerical simulations are performed to support our theoretical findings and to show the effectiveness of the cure rate in reducing the severity of the disease.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sanaa Harroudi
    • 1
  • Karam Allali
    • 1
  1. 1.Laboratory of Mathematics and Applications, Faculty of Sciences and TechnologiesUniversity Hassan II of CasablancaMohammediaMorocco

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