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ISRN Biomathematics
Volume 2013 (2013), Article ID 912835, 6 pages
http://dx.doi.org/10.1155/2013/912835
Research Article

Optimal Antiviral Treatment Strategies of HBV Infection Model with Logistic Hepatocyte Growth

1Département de Mathématiques et Informatique, Faculté des Sciences Ben M’Sik, Université Hassan II Mohammadia, Casablanca, Morocco
2Département de Mathématiques et Informatique, Faculté des Sciences, Université Chouaib Doukkali, El Jadida, Morocco

Received 1 May 2013; Accepted 19 June 2013

Academic Editors: M. Brumen and J. R. C. Piqueira

Copyright © 2013 Hassan Laarabi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This study considers an optimal therapy strategy for HBV infection by incorporating two controls laws into a previous hepatitis B viral infection model with logistic hepatocyte growth. Our goal is to maximize the number of healthy cells and to minimize the cost of the therapy. In this context, the existence of an optimal control is proved. The optimal control is obtained by solving the optimality system which was composed of three nonlinear ODEs with initial conditions and three nonlinear adjoint ODEs with transversality conditions. The results were analysed and interpreted numerically using MATLAB.