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Open AccessArticle

Optimal Control of Drug Therapy in a Hepatitis B Model

Department of Mathematics and Computer Science, Hobart and William Smith Colleges, 300 Pulteney St., Geneva, NY 14456, USA
Department of Mathematics, Virginia Tech, 416 McBryde Hall, Blacksburg, VA 24061, USA
Department of Mathematics and Statistics, East Tennessee State University, Johnson City, TN 37614, USA
Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA
Authors to whom correspondence should be addressed.
Academic Editor: Yang Kuang
Appl. Sci. 2016, 6(8), 219;
Received: 23 May 2016 / Revised: 24 July 2016 / Accepted: 26 July 2016 / Published: 3 August 2016
(This article belongs to the Special Issue Dynamical Models of Biology and Medicine)
Combination antiviral drug therapy improves the survival rates of patients chronically infected with hepatitis B virus by controlling viral replication and enhancing immune responses. Some of these drugs have side effects that make them unsuitable for long-term administration. To address the trade-off between the positive and negative effects of the combination therapy, we investigated an optimal control problem for a delay differential equation model of immune responses to hepatitis virus B infection. Our optimal control problem investigates the interplay between virological and immunomodulatory effects of therapy, the control of viremia and the administration of the minimal dosage over a short period of time. Our numerical results show that the high drug levels that induce immune modulation rather than suppression of virological factors are essential for the clearance of hepatitis B virus. View Full-Text
Keywords: optimal control; hepatitis B; delay differential equations (DDE); immune response; drug therapy optimal control; hepatitis B; delay differential equations (DDE); immune response; drug therapy
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Forde, J.E.; Ciupe, S.M.; Cintron-Arias, A.; Lenhart, S. Optimal Control of Drug Therapy in a Hepatitis B Model. Appl. Sci. 2016, 6, 219.

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