Mathematical Modelling of Tungiasis Disease Dynamics Incorporating Hygiene as a Control Strategy.

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Mbuthia, Faith Kabura
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Kenyatta University
Despite the intensive research that has been done on tungiasis, a lot remains to be done, especially on hygiene as a control strategy. Protection measures include, but not limited to; vaccination against tetanus in areas that are tungiasis-endemic, regular application of natural repellants like coconut oil and neem and regularly spraying domestic animals such as cats and dogs that act as reservoirs to tunga penetrants. Families in prone areas can also be provided with shoes, house floors that are sealed, clean water and soap. In this research, we particularly concentrate on hygiene as a control strategy. We have formulated a model which is mathematical in nature. The model is based on a system of ordinary differential equations, which are used to study the dynamics of tungiasis disease, incorporating hygiene as protection against infection as a control measure. We have determined the steady state of the model and also carried out stability analysis. This has helped in determining the conditions that favor the infection of tungiasis in a community. We are then able to determine the effect of hygiene of a population against infection of tungiasis. We have established the endemic equilibrium point and also the disease free equilibrium point, which are found to be asymptotically stable. The basic reproduction number, RO, is calculated using the next generation matrix. Numerical simulation of the model carried out showed that protection against infection using proper hygiene measures leads to a decrease in the spread of tungiasis.
A Research Project Submitted in Partial Fulfilment of the Requirements for the Award of The Degree of Master of Science in Applied Mathematics in the School of Pure and Applied Sciences of Kenyatta University. March, 2019