OPTIMAL CONTROL OF AN HIV INFECTION MODEL WITH
THE CTL RESPONSE AND TWO SATURATED RATES
Bouchra Lahmidani1, Othmane Baiz2,
Youssef Tabit3, Driss El Moutawakil4
1 Univ. Sultan Moulay Slimane, Equipe de recherche MATIC
FPK, MOROCCO
2 Univ. Ibn Zohr, FP of Ouarzazate, MOROCCO
3 Univ. Hassan II, ENCG Casablanca, MOROCCO
4 Univ. Sultan Moulay Slimane, Equipe de recherche MATIC
FPK, MOROCCO

Abstract

In this paper, we study a mathematical model that describes the Human Immunodeficiency Virus (HIV) pathogenesis with Cytotoxic T Lymphocytes (CTL) response. This model includes the cure of infected cells, two saturated rates describing viral infection, CTL proliferation and two treatments. These latter represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. First, we derive the positivity and boundedness of solutions for nonnegative initial data, which is consistent with the biological studies. Furthermore, we prove the existence of the optimal control pair, and its characterization is obtained by using the Pontryagin's maximum principle. Finally, the optimality system is derived and illustrated by a numerical example. The obtained results show that the optimal treatment strategies reduce the viral load and then increase the uninfected CD4^{+}T cells as well as cytotoxic T-lymphocyte immune response, this improves the patient life quality.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 6
Year: 2021

DOI: 10.12732/ijam.v34i6.4

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