The transmission dynamic and optimal control of acute and chronic hepatitis B

In this article, we present the transmission dynamic of the acute and chronic hepatitis B epidemic problem and develop an optimal control strategy to control the spread of hepatitis B in a community. In order to do this, first we present the model formulation and find the basic reproduction number ....

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Bibliographic Details
Published in:Journal of biological dynamics 2017-01, Vol.11 (1), p.172-189
Main Authors: Khan, Tahir, Zaman, Gul, Chohan, M. Ikhlaq
Format: Article
Language:English
Subjects:
Basic Reproduction Number
Epidemic model
Epidemics
Hepatitis
Hepatitis B
Hepatitis B, Chronic - prevention & control
Hepatitis B, Chronic - transmission
Humans
Interferon
Mathematical models
Models, Biological
numerical simulation
optimal control strategy
stability analysis
Vaccination
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Summary:In this article, we present the transmission dynamic of the acute and chronic hepatitis B epidemic problem and develop an optimal control strategy to control the spread of hepatitis B in a community. In order to do this, first we present the model formulation and find the basic reproduction number . We show that if then the disease-free equilibrium is both locally as well as globally asymptotically stable. Then, we prove that the model is locally and globally asymptotically stable, if . To control the spread of this infection, we develop a control strategy by applying three control variables such as isolation of infected and non-infected individuals, treatment and vaccination to minimize the number of acute infected, chronically infected with hepatitis B individuals and maximize the number of susceptible and recovered individuals. Finally, we present numerical simulation to illustrate the feasibility of the control strategy.
ISSN:1751-3758
1751-3766
DOI:10.1080/17513758.2016.1256441