Hybrid on-off controls for an HIV model based on a linear control problem

Tae Soo Jang; Jungeun Kim; Hee-Dae Kwon; Jeehyun Lee

doi:10.4134/JKMS.2015.52.3.469

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2015; 52(3): 469-487

Printed May 1, 2015

https://doi.org/10.4134/JKMS.2015.52.3.469

Hybrid on-off controls for an HIV model based on a linear control problem

Tae Soo Jang, Jungeun Kim, Hee-Dae Kwon, and Jeehyun Lee

Inha University, Yonsei University, Inha University, Yonsei University

Abstract

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Abstract

We consider a model of HIV infection with various compartments, including target cells, infected cells, viral loads and immune effector cells, to describe HIV type 1 infection. We show that the proposed model has one uninfected steady state and several infected steady states and investigate their local stability by using a Jacobian matrix method. We obtain equations for adjoint variables and characterize an optimal control by applying Pontryagin's Maximum Principle in a linear control problem. In addition, we apply techniques and ideas from linear optimal control theory in conjunction with a direct search approach to derive on-off HIV therapy strategies. The results of numerical simulations indicate that hybrid on-off therapy protocols can move the model system to a ``healthy" steady state in which the immune response is dominant in controlling HIV after the discontinuation of the therapy.

Keywords: HIV dynamics, linear optimal control, STI, bang-bang control

MSC numbers: 49J15, 92C50, 93C15