On HIV Model with Adaptive Immune Response, Two Saturated Rates and Therapy

¹ Laboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University HassanII of Casablanca, PO Box 146, Mohammedia, Morocco
² Department of SEG, Polydisciplinary Faculty, University Chouaib Doukkali, El Jadida, Morocco

^* Corresponding author. E-mail: allali@hotmail.com

Abstract

The mathematical model of the human immunodeficiency virus (HIV) pathogenesis with the adaptive immune response, two saturated rates and therapy is presented and studied in this work. The adaptive immune response is represented by the cytotoxic T-lymphocytes (CTL) cells and the antibodies; the two saturated rates describe the viral infection and the CTL proliferation. Two kinds of treatments are incorporated into the model; the objective of the first one is to reduce the number of infected cells, while the aim of the second one is to block the free viruses. The positivity and boundedness of solutions are established. The local stability of the disease free steady state and the infection steady states are studied. Numerical simulations are performed to show the behavior of solutions and the effectiveness of the incorporated therapy in controlling the HIV replication which can improves significantly the patient's life quality.