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Optimal control applied on an HIV‐1 within‐host model
Author(s) -
Rahmoun Amel,
Ainseba Bedreddine,
Benmerzouk Djamila
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3628
Subject(s) - human immunodeficiency virus (hiv) , mathematics , host (biology) , basic reproduction number , stability (learning theory) , lyapunov function , simple (philosophy) , pill , optimal control , matrix (chemical analysis) , measure (data warehouse) , control (management) , mathematical optimization , control theory (sociology) , computer science , virology , medicine , nonlinear system , biology , artificial intelligence , population , pharmacology , philosophy , materials science , database , ecology , environmental health , composite material , epistemology , quantum mechanics , machine learning , physics
The treatment of human immunodeficiency virus (HIV) remains a major challenge, even if significant progress has been made in infection treatment by ‘drug cocktails’. Nowadays, research trend is to minimize the number of pills taken when treating infection. In this paper, an HIV‐1 within host model where healthy cells follow a simple logistic growth is considered. Basic reproduction number of the model is calculated using next generation matrix method, steady states are derived; their local, as well as global stability, is discussed using the Routh–Hurwitz criteria, Lyapunov functions and the Lozinskii measure approach. The optimal control policy is formulated and solved as an optimal control problem. Numerical simulations are performed to compare several cases, representing a treatment by Interleukin2 alone, classical treatment by multitherapy drugs alone, then both treatments at the same time. Objective functionals aim to (i) minimize infected cells quantity; (ii) minimize free virus particles number; and (iii) maximize healthy cells density in blood. Copyright © 2015 John Wiley & Sons, Ltd.