Journal of Applied Nonlinear Dynamics
Development of Optimal Strategy for Controlling Transmission Dynamics of HBV Epidemic Model
Journal of Applied Nonlinear Dynamics 11(2) (2022) 415425  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
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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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