Modeling Jiggers’ Infestation with Incomplete Recoveries Incorporating the Flea Population; A Case Study of Murang’a County, Kenya
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Date
2023-09
Authors
Agutu, Arthur Omondi
Journal Title
Journal ISSN
Volume Title
Publisher
Kenyatta University
Abstract
Sand 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.
Description
A 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 2023
Keywords
Modeling Jiggers’ Infestation, Incomplete Recoveries, Incorporating, Flea Population, Murang’a County, Kenya