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Computational and Mathematical Methods in Medicine
Volume 2014, Article ID 475451, 15 pages
Research Article

Mathematical Modeling of Transmission Dynamics and Optimal Control of Vaccination and Treatment for Hepatitis B Virus

1Department of Mathematics Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
2Department of Mathematical Sciences, Payame Noor University, Iran
3Research Center for Infection Control and Hand Hygiene, Mashhad University of Medical Sciences, Mashhad, Iran
4Payame Noor University, Khorasan Razavi, Mashhad, Iran

Received 30 December 2013; Accepted 26 February 2014; Published 9 April 2014

Academic Editor: Chris Bauch

Copyright © 2014 Ali Vahidian Kamyad 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.


Hepatitis B virus (HBV) infection is a worldwide public health problem. In this paper, we study the dynamics of hepatitis B virus (HBV) infection which can be controlled by vaccination as well as treatment. Initially we consider constant controls for both vaccination and treatment. In the constant controls case, by determining the basic reproduction number, we study the existence and stability of the disease-free and endemic steady-state solutions of the model. Next, we take the controls as time and formulate the appropriate optimal control problem and obtain the optimal control strategy to minimize both the number of infectious humans and the associated costs. Finally at the end numerical simulation results show that optimal combination of vaccination and treatment is the most effective way to control hepatitis B virus infection.