PHD-Department of Mathematics

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Browsing PHD-Department of Mathematics by Subject "Infestation"

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    Modelling Jiggers Infestation and Interventions in Humans: A Case Study of Murang'a County, Kenya
    (Kenyatta University, 2020-06) Matendechere, Nancy Imbusi
    Tungiasis is a parasitic skin disease caused by jiggers, also known as sandeas. The disease predominantly a ects impoverished populations living in Sub-Saharan Africa, the Caribbean and South America.In areas especially with limited or no interventions, jiggers infestationremains a problem. Mathematical models have been used for decades to inform public health policies and have been useful for the evaluation of control strategies and interventions. While some studies may have been done on jiggers, majority of them focused on social aspects of the disease. Very few mathematical models have been done on jiggers infestation. Considering the results and the interventions that come from models on vector borne diseases, a model on jiggers infestation and interventions in humans would be useful for the policy makers and government to intervene and come up with a solution to this menace. In this thesis, we present two deterministic mathematical models. First, we present a deterministic model with four compartments that represent the dynamics of the human population and an age-structured model for flea. Second, we incorporated media campaigns in the first model with the aim of investigating the potential role of awareness through media campaigns on jiggers infestation dynamics. We introduce a class of those that are aware in which the awareness does not completely protect individuals from jiggers. The model equilibria are computed and stability analyses carried out based on the reproduction number R0. Sensitivity analysis is performed on the model parameters and the results suggest that the executive infestation contact rate, as well as the rate at which the larvae develop into adult fleas are the main parameters that fuel jiggers infestation. Bifurcation analysis reveals that the model has an intrinsic backward bifurcation whenever the parameter that accounts for the proportion of larvae that develop into adult female fleas involved in jiggers transmission is included. The model points to control of the flea through treatment of infested humans and enhancing efficacy of media campaigns.