Modelling prevention and control of jigger infestation in Mayuge district: a mathematical approach

Volume 22, Issue 3, pp 252--265 http://dx.doi.org/10.22436/jmcs.022.03.05

Publication Date: August 17, 2020 Submission Date: February 17, 2017 Revision Date: November 12, 2018 Accteptance Date: November 22, 2018

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Authors

Betty Nannyonga - Department of Mathematics, School of Physical Sciences, College of Natural Sciences, Makerere University, P.O. Box 7062, Kampala, Uganda. John M. Mango - Department of Mathematics, School of Physical Sciences, College of Natural Sciences, Makerere University, P.O. Box 7062, Kampala, Uganda. Sylvester Rugeihyamu - Department of Mathematics, University of Dar Es Salaam, P.O. Box 35091, Dar es Salaam, Tanzania.

Abstract

Tungiasis is a disease caused by the smallest jigger flea and found in many poor communities. Although its control involves wearing closed shoes or extraction of the flea using a very cheap sterile safety pin, the disease continues to cause death or rotting away of infested people. Numerous super infestation and deaths have been reported in Uganda, in particular, Mayuge district. This has posed a major threat to the already wanting education standards in the region. In this study, a mathematical model is presented aimed at assessing the effects of persistent jigger infestation in Mayuge district, and how it could be controlled. We use to controls, one to prevent the adult female flea from burrowing into the human host, and the other by extraction of the embedded flea from the infected human and killing the eggs to prevent further infection. Results show that without control, the disease-free equilibrium point is stable for those values of \(0.3 <\mathcal{R}_0 < 1, \) otherwise it is unstable. With maximum control, the disease-free is stable for values of \(0.0103 <\mathcal{R}_0 < 1.\) Numerical results show that if the infection rate \(\beta\) is less than 0.3, with other parameters kept constant, \(\mathcal{R}_0\) can be controlled to less than unity and jigger infestation stopped. Numerical results further indicate that to avoid super infestation, all efforts to extract the jigger once embedded must be enforced. With the current presence of super infestation in Mayuge district, a single individual can cause more than 7 new infestations. To control this, efforts must be made to reduce the current prevalence of jigger infestation from 0.25 to 0.004. We conclude from the study that jigger infestation has an important social dimension and affects human rights. It is a zoonosis and considering its links with poverty, requires multi-disciplinary research in which public health, social sciences, health education, and animal husbandry need to interact.

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Keywords

• Tunga penetrans
• mathematical modelling

MSC

•  49J75
•  92B05
•  92D30
•  93A30

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