Optimal Control Techniques on a Mathematical Model for the Dynamics of Tungiasis in a Community. (14th August 2017)

• Record Type: Journal Article
• Authors: Kahuru, Jairos; Luboobi, Livingstone S.; Nkansah-Gyekye, Yaw
• Other Names: Hussain Nawab Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2017(2017)
• Publication Date: 2017-08-14
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2017/4804897
• Languages: English
• ISSNs: 0161-1712

Abstract

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.