Mathematical Modeling of Cholera Transmission with Education Campaign and Treatment Through Quarantine
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Date
2019-06
Authors
Nyaberi, Halson Ogeto
Journal Title
Journal ISSN
Volume Title
Publisher
Kenyatta University
Abstract
Cholera, a water-borne disease characterized by intense watery diarrhea, a ects people in
regions with poor hygiene and untreated drinking water. This disease remains a menace
to public health globally and it is capable of causing high death rates if not adequately
controlled, leading to loss of individuals who are engaged in development projects and
hence crumbling communities' progress. In this research, we derived a system of ordinary
di erential equations from SIQR-B mathematical model to study the dynamics of cholera
transmission with health education campaign and treatment through quarantine as con-
trols against epidemic in Kenya. The e ective basic reproduction number is computed
using the next generation matrix method. The equilibrium points of the model are deter-
mined and their stability is analysed. Results of stability analysis show that the disease
free equilibrium is both locally and globally asymptotically stable R0 < 1 while the en-
demic equilibrium is both locally and globally asymptotically stable R0 > 1. Numerical
simulation carried out using MATLAB software shows that when health education cam-
paign is e cient, the number of cholera infected individuals decreases faster, implying
that health education campaign is vital in controlling the spread of cholera disease.
Description
A Project Submitted in Partial Fulfilment of the Requirements of the Award of
the Degree of Master of Science in Applied Mathematics in the School of
Pure and Applied Sciences of Kenyatta University, June 2019