Optimal control of HIV dynamic using embedding method
type: Item
instance of: scholarly article
title: Optimal control of HIV dynamic using embedding method
zbMATH Open document ID: 1219.92049
DOI: 10.1155/2011/674318
author: Yong-Cai Geng
author: Sumit K. Garg
published in: Computational \& Mathematical Methods in Medicine
publication date: 2011-06-06T00:00:00Z
full work available at URL: https://eudml.org/doc/231523
review text: Summary: The present study proposes an optimal control problem, with the final goal of implementing an optimal treatment protocol which could maximize the survival time of patients and minimize the cost of drug utilizing a system of ordinary differential equations which describes the interaction of the immune system with the human immunodeficiency virus (HIV). The optimal control problem transfers into a modified problem in the measure space using an embedding method in which the existence of optimal solutions is guaranteed by compactness of the space. Then the metamorphosed problem is approximated by a linear programming (LP) problem, and by solving this LP problem a suboptimal piecewise constant control function, which is more practical from the clinical viewpoint, is achieved. The comparison between the immune system dynamics in treated and untreated patients is introduced. Finally, the relationships between the healthy cells and the virus are shown.
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 49N90
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 5904396
Wikidata QID: Q41760351
MaRDI profile type: Publication
OpenAlex ID: W2067341023
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DBLP publication ID: journals/cmmm/ZareiKF11
description: scientific article; zbMATH DE number 5904396