Sanaa HARROUDİ, Jaouad DANANE, Karam ALLALİ

Analysis and optimal control of an HIV model with logistic growth and infected cells in eclipse phase

A mathematical model of the human immunodeficiency virus infection with logistic growth, infected cells in eclipse phase and therapy is investigated. The model includes four nonlinear differential equations describing the evolution of uninfected CD4⁺ T cells, infected CD4⁺ T cells in latent stage, productively infected CD4⁺ T cells and free virus. Two types of treatments are incorporated into the model; the purpose of the first one consists to block the viral proliferation while the role of the second is to prevent new infections. The positivity and boundedness of solutions are established. The local stability of the disease free steady state and the infection steady states are studied. An optimal control problem is proposed and investigated. Numerical simulations are performed, confirming stability of the free and endemic equilibria and illustrating the effectiveness of the two incorporated treatments via an efficient optimal control.

Keywords:

HIV infection, logistic growth treatment, stability, optimal control,

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Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics-Cover

ISSN: 1303-5991
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 1948
Yayıncı: Ankara Üniversitesi

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