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

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

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)469-487
Number of pages19
JournalJournal of the Korean Mathematical Society
Volume52
Issue number3
DOIs
Publication statusPublished - 2015 Jan 1

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Linear Control
Therapy
Control Problem
Model-based
Cell
Direct Search
HIV Infection
Optimal Control Theory
Immune Response
Jacobian matrix
Local Stability
Matrix Method
Maximum Principle
Infection
Optimal Control
Model
Numerical Simulation
Target

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Jang, Tae Soo ; Kim, Jungeun ; Kwon, Hee Dae ; Lee, Jeehyun. / Hybrid on-off controls for an hiv model based on a linear control problem. In: Journal of the Korean Mathematical Society. 2015 ; Vol. 52, No. 3. pp. 469-487.
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Hybrid on-off controls for an hiv model based on a linear control problem. / Jang, Tae Soo; Kim, Jungeun; Kwon, Hee Dae; Lee, Jeehyun.

In: Journal of the Korean Mathematical Society, Vol. 52, No. 3, 01.01.2015, p. 469-487.

Research output: Contribution to journalArticle

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