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

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  • Jairos Kahuru
  • Livingstone S. Luboobi
  • Yaw Nkansah-Gyekye

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.

Suggested Citation

  • Jairos Kahuru & Livingstone S. Luboobi & Yaw Nkansah-Gyekye, 2017. "Optimal Control Techniques on a Mathematical Model for the Dynamics of Tungiasis in a Community," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2017, pages 1-19, August.
    • Handle: RePEc:hin:jijmms:4804897
    DOI: 10.1155/2017/4804897
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    References listed on IDEAS

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    1. G. Devipriya & K. Kalaivani, 2012. "Optimal Control of Multiple Transmission of Water-Borne Diseases," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-16, July.
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