A SEIR Model to Control Varicella Transmission in Ghana
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Date
2015-03-03
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Abstract
In this thesis, a SEIR epidemiological model is formulated to help control the
transmission of varicella, using clinical varicella data from Ghana Health Service.
The thesis is based on the assumption that the population is constant with birth
rate equals death rate. First it is shown that there exists a domain where the
model is epidemiologically and mathematically well-posed as desired in any pop-
ulation dynamics. Qualitative results show that the model has the disease-free
equilibrium point which is locally asymptotically stable for R0 < 1 and unstable
for R0 > 1. The Routh-Hurwitz criterion is used to show that the model has an
endemic equilibrium point which is locally asymptotically stable when R0 > 1.
The basic reproduction number for Ghana is found to be R0 = 1:2869, whiles the
herd immunity threshold is found to be HI = 22:3%. Numerical simulation of
the model, using MATLAB and a fouth order Runge-Kuta method suggests that
one practical measure, to bring the transmission of the disease under control is
early detection of the infectious, for isolated supervised treatment. It is concluded
that vaccination is the most important factor to control the spread of varicella
in case of an outbreak and that 22:3% of the susceptible population needs to be
vaccinated in order to bring the disease under control.
Description
A Thesis Submitted to the Department Of Mathematics, Kwame Nkrumah University of Science and Technology In Partial Fulfillment of the requirements for the Award of the Degree Of M.Phil Applied Mathematics.