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

• Main Authors: Tahir Khan, Gul Zaman, M. Ikhlaq Chohan
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2017-01-01
• Series: Journal of Biological Dynamics
• Subjects: Epidemic model; basic reproduction number; stability analysis; optimal control strategy; numerical simulation
• Online Access: http://dx.doi.org/10.1080/17513758.2016.1256441

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 $ R_0 $ . We show that if $ R_0\leq 1, $ 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 $ R_0>1 $ . 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.