ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Development of Optimal Strategy for Controlling Transmission Dynamics of HBV Epidemic Model

Journal of Applied Nonlinear Dynamics 11(2) (2022) 415--425 | DOI:10.5890/JAND.2022.06.011

Eihab B. M. Bashier$^{1, 2}$, Hasim A. Obaid$^2$

$^1$ Faculty of Education and Arts, Sohar University, P.O. Box 44, Postal Code: 311, Sohar, Oman

$^2$ Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Khartoum, P.O. Box

321, Postal Code: 11115, Khartoum, Sudan

Abstract

In this paper, the problem of controlling the transmission dynamics of HBV epidemics is formulated as an optimal control problem governed by a system of nonlinear differential equations. To reduce the HBV infection, we formulate two controls representing the increase of effort to immunize the new born individuals and isolating the infection carriers. The first order necessary conditions for optimal control are derived. The numerical simulations considered many scenarios and the controls are shown to be effective in reducing the number of infectious individuals. They showed that reducing the numbers of infected carriers can be achieved by applying the maximum controls for long periods of times and the immunization of new born individuals is more effective than isolating the infected individuals.

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