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Optimal Control Strategy for the Transmission Dynamics of Typhoid Fever
American Journal of Applied Mathematics
Volume 7, Issue 2, April 2019, Pages: 37-48
Received: Apr. 13, 2019; Accepted: May 28, 2019; Published: Jun. 26, 2019
Author
Temesgen Debas Awoke, Department of Mathematics, College of Natural and Computational Science, Kotebe Metropolitan University, Addis Ababa, Ethiopia
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Abstract
The author developed a deterministic mathematical model for Typhoid fever disease dynamics that accounts for Vaccination and relapse of treatment. Three control strategies (vaccination, treatment of infection, screening and treatment of carriers) are applied to investigate the optimal intervention strategy of controlling Typhoid disease transmission. The aim of this study is to determine the optimal combination strategy of vaccination, treatment of infection, screening and treatment of carriers that will minimize the cost of those strategies and the number of Infective and Carriers. The author used Pontryagin’s maximum principle to characterize the optimal level of those three strategies. The result is simulated numerically using Runge-Kutta fourth order method through MATLAB software. Numerical results showed that implementation of all controls or a combination of vaccination, treatment of invectives as well as screening and treatment of carriers is the best strategy to eradicate the disease at an optimal level with minimum cost of interventions.
Keywords
"Typhoid Fever, Optimal Control, Pontryagin Maximum Principle, Equilibrium Point, Basic Reproduction Number, Numerical Simulation "
Temesgen Debas Awoke, Optimal Control Strategy for the Transmission Dynamics of Typhoid Fever, American Journal of Applied Mathematics. Vol. 7, No. 2, 2019, pp. 37-48. doi: 10.11648/j.ajam.20190702.11
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