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Bulletin of Mathematical Biology

, Volume 77, Issue 11, pp 2035–2071 | Cite as

Short- and Long-Term Optimal Control of a Mathematical Model for HIV Infection of \(CD4^{+}T\) Cells

  • Ana-Maria CroicuEmail author
Original Article

Abstract

The main goal of this study was to develop a theoretical short- and long-term optimal control treatment of HIV infection of \(CD4^{+}T\) cells. The aim of the mathematical model used herein is to make the free HIV virus particles in the blood decrease, while administering a treatment that is less toxic to patients. Pontryagin’s classical control theory is applied to a mathematical model of HIV infection of \(CD4^{+}T\) cells characterized by a system of nonlinear differential equations with the following unknown functions: the concentration of susceptible \(CD4^{+}T\) cells, \(CD4^{+}T\) cells infected by the HIV viruses and free HIV virus particles in the blood.

Keywords

HIV infection of \(CD4^{+}T\) cells System of nonlinear differential equations Optimal control State equations  Adjoint equations 

Notes

Acknowledgments

The author would like to thank the anonymous reviewers for the constructive feedback provided during the reviewing process.

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Copyright information

© Society for Mathematical Biology 2015

Authors and Affiliations

  1. 1.Kennesaw State UniversityKennesawUSA

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