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

Abstract

A mathematical model of the human immunode…ciency virus infection with logistic growth, infected cells in eclipse phase and therapy is investigated. The model includes four nonlinear di¤erential 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 …rst 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, con…rming stability of the free and endemic equilibria and illustrating the e¤ectiveness of the two incorporated treatments via an e¢ cient optimal control.