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Optimal drug control in a four‐dimensional HIV infection model
Author(s) -
Shamsara Elham,
Afsharnezhad Zahra,
Effati Sohrab
Publication year - 2019
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2555
Subject(s) - hopf bifurcation , human immunodeficiency virus (hiv) , pontryagin's minimum principle , immunotherapy , immune system , optimal control , effector , drug , immunology , mathematics , virology , control theory (sociology) , biology , bifurcation , control (management) , computer science , mathematical optimization , physics , artificial intelligence , pharmacology , quantum mechanics , nonlinear system
Summary In this paper, we consider a four‐dimensional version of a human immunodeficiency virus (HIV) infection model, which is an extension of some previous three‐dimensional models. We approach the treatment problem by adding two controls u 1 and u 2 to the system for inhibiting viral production and preventing new infections. In fact, u 1 is added to components of uninfected and infected cells to represent the effect of chemotherapy on the interaction of uninfected CD4 + T cells with infected cells. u 2 is considered in the effector immune component as immunotherapy. The purpose of this work is to control the progress of the disease in a steady state. Hence, first, we obtain a relation between the two controls u 1 and u 2 such that a Hopf bifurcation occurs. Next, the Pontryagin minimum principle will be applied to derive the optimal therapy for HIV. At the end, numerical results are presented.