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International Journal of Mathematics and Mathematical Sciences
Volume 2017, Article ID 4804897, 19 pages
https://doi.org/10.1155/2017/4804897
Research Article

Optimal Control Techniques on a Mathematical Model for the Dynamics of Tungiasis in a Community

1School of Computational and Communication Science and Engineering, Nelson Mandela African Institution of Science and Technology, P.O. Box 447, Arusha, Tanzania
2Department of Mathematics, Makerere University, P.O. Box 7062, Kampala, Uganda

Correspondence should be addressed to Jairos Kahuru; zt.ca.tsia-mn@kheznihs

Received 20 March 2017; Accepted 2 July 2017; Published 14 August 2017

Academic Editor: Nawab Hussain

Copyright © 2017 Jairos Kahuru et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Tungiasis is a permanent penetration of female sand flea “Tunga penetrans” into the epidermis of its host. It affects human beings and domestic and sylvatic animals. In this paper, we apply optimal control techniques to a Tungiasis controlled mathematical model to determine the optimal control strategy in order to minimize the number of infested humans, infested animals, and sand flea populations. In an attempt to reduce Tungiasis infestation in human population, the control strategies based on personal protection, personal treatment, educational campaign, environmental sanitation, and insecticidal treatments on the affected parts as well as on animal fur are considered. We prove the existence of optimal control problem, determine the necessary conditions for optimality, and then perform numerical simulations. The numerical results showed that the control strategy comprises all five control measures and that which involves the three control measures of insecticide control, insecticidal dusting on animal furs, and environmental hygiene has the significant impact on Tungiasis transmission. Therefore, fighting against Tungiasis infestation in endemic settings, multidimensional control process should be employed in order to achieve the maximum benefits.