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Comput Math Methods Med. 2014;2014:475451. doi: 10.1155/2014/475451. Epub 2014 Apr 9.

Mathematical modeling of transmission dynamics and optimal control of vaccination and treatment for hepatitis B virus.

Author information

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

Abstract

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.

PMID:
24812572
PMCID:
PMC4000643
DOI:
10.1155/2014/475451
[Indexed for MEDLINE]
Free PMC Article

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