Effect of Control on the Mathematical Model of Hepatitis B Virus with Infective Migrant
Folahan S. Akinboro *
Department of Geomatics, Faculty of Environmental Sciences, University of Benin, Nigeria.
T. O. Oluyo
Department of Pure and Applied Mathematics, Faculty of Applied Sciences, Ladoke Akintola Univeristy of Technology, Ogbomoso, Nigeria.
O. O. Kehinde
Department of Mathematics, University of the Western Cape, Western Cape, South Africa.
S. Alao
Department of Pure and Applied Mathematics, Faculty of Applied Sciences, Ladoke Akintola Univeristy of Technology, Ogbomoso, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The transmission dynamics of Hepatitis B Virus in a population with infective immigrant is presented with the inclusion of an optimal control strategy to curtail the spread of the virus. To understand the spread of this infection, we develop a mathematical model with control variables of migrant screening and public sensitization. The optimality system is characterized using Pontryagin’s maximum principle and solve numerically with an implicit finite difference method. Result of the numerical simulation is presented to illustrate the feasibility of this control strategy. The analysis reveals that combination of both control variables could be the most fruitful way to reduce the incidence of Hepatitis B virus.
Keywords: Mathematical model, hepatitis B virus, infective immigrant, Pontryagin’s maximum principle, optimal control, finite difference.