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


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.


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



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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