Mathematical modeling and analysis of the dynamics of hepatitis B with optimal control

Abstract

Limited resources hinder the control and prevention of hepatitis B in some communities in Ghana and the Brong Ahafo region is no different. In this paper, we formulated a model that explains the spread of hepatitis B and suggested an intervention to minimise its effect. We analysed the local and global stability of the disease as well as the basic reproduction number. It was established that the disease is locally asymptotically stable whenever the basic reproduction number is less than unity and unstable otherwise. Optimal control theory was incorporated to determine the best control strategy in combating the spread of hepatitis B in the environment. The following control strategies were employed; treatment, vaccination and prevention. The results of the numerical simulation showed that the best optimal control strategy in combating the spread of the infection was vaccination of susceptible and treatment of the infected population.