Modeling Jiggers’ Infestation with Incomplete Recoveries Incorporating the Flea Population; A Case Study of Murang’a County, Kenya

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dc.contributor.advisorKennedy Awuoren_US
dc.contributor.authorAgutu, Arthur Omondi
dc.date.accessioned2024-05-31T13:01:32Z
dc.date.available2024-05-31T13:01:32Z
dc.date.issued2023-09
dc.descriptionA Project Submitted in Partial Fulfillment of the Requirements for the Award of the Degree of Master of Science (Applied Mathematics) in the School of Pure and Applied Sciences of Kenyatta University, September 2023en_US
dc.description.abstractSand flea insect thrives in hot and humid regions full of dust particles. It attacks humans leading to jiggers infection (tungiasis). Spread of jiggers has been recorded in Caribbean, South American and African countries. In Kenya, Murang'a, Homabay and Siaya Counties are among the top regions affected by tungiasis infections. Poverty, lack of sufficient awareness, improper sanitation, and poor control methods are the major reasons for the unending spread of jiggers in Kenya. Prevention and treatment measures have been put in place by the government and NGO's to combat the unending new infections, yet the recoveries are still incomplete. A number of mathematical frameworks have been put in place to unravel the cyclic behavior of this infectious disease. However, a comparative study of the dynamical behavior of the disease in both human and flea population has not been conducted. In this research, we designed a model of jiggers infestation which incorporates the human and sand flea population in Muranga County, Kenya. We derived an ODE system from SEIR-FLA mathematical model to investigate the dynamics of jiggers infestation which incorporates both the human and flea population in Muranga County, Kenya. We used the Mathematica software tools to determine the effective basic reproduction number by applying the next generation matrix method. We applied the MATLAB software to generate the solutions of equations. Results confirmed local stability of JFE when Ro = 4.9827¢ — 13 as t — oo for all the Susceptible, Exposed, Infectious, Recovered human compartments and the Egg, Larval, Adult sand flea compartments. All state variables are positive at all times ¢, and numerical analysis of the invariant region reveals that the model is well-posed. These findings confirm that treatment aid in reducing incomplete recoveries of jiggers infestation.en_US
dc.description.sponsorshipKenyatta Universityen_US
dc.identifier.urihttps://ir-library.ku.ac.ke/handle/123456789/28060
dc.language.isoenen_US
dc.publisherKenyatta Universityen_US
dc.subjectModeling Jiggers’ Infestationen_US
dc.subjectIncomplete Recoveriesen_US
dc.subjectIncorporatingen_US
dc.subjectFlea Populationen_US
dc.subjectMurang’a Countyen_US
dc.subjectKenyaen_US
dc.titleModeling Jiggers’ Infestation with Incomplete Recoveries Incorporating the Flea Population; A Case Study of Murang’a County, Kenyaen_US
dc.typeThesisen_US
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