Optimal Control of an HIV Infection Model with Logistic Growth, CTL Immune Response and Infected Cells in Eclipse Phase

  • Jaouad Danane
  • Karam Allali


This paper deals with an optimal control problem for an HIV infection model with logistic growth, cytotoxic T-lymphocytes (CTL) immune response, and infected cells in eclipse phase. The model under consideration describes the interaction between the uninfected cells, the latently infected cells, the productively infected cells, the free viruses, and the CTL cells. The two treatments represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. Existence of the optimal control pair is established and the Pontryagin’s minimum principle is used to characterize these two optimal controls. The optimality system is derived and solved numerically using the forward and backward difference approximation. Finally, numerical simulations are performed in order to show the role of optimal therapy in controlling the infection severity.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

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