Modelling the impact of protection and treatment strategies on transmission dyanamics of malaria in Ghana
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Date
NOVEMBER, 2015
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Abstract
Eradicating malaria from Ghana has proven to be a difficult challenge not only to the
researchers and health organizations but also to government .Despite great advances
over the last decade, including the training of all health staff to control the disease,
Ghana remains one of the countries worst affected by malaria. The goal of this thesis is
to develop a mathematical model to help to assess the potential impact of protection and
treatment strategies on the dynamics of malaria in Ghana. A basic deterministic malaria
model SEIR model was first formulated. The model consists of seven non-linear
differential equations which describe the dynamics of malaria with 4 variables for
humans and 3 variables for mosquitoes. Analysis of the model showed that there exists a
domain where the model is epidemiologically and mathematically well-posed. Key to the
analysis is the definition of the basic reproductive number 0 R , which was derived by use
of next generation method. The basic reproduction number for Ghana is found to be
R0 = 0.7397 hence malaria can be eliminated from Ghana. The disease-free equilibrium
point is asymptotically stable. This means that malaria free society can be achieved.
In order to assess the potential impact of protection and treatment strategies on the
transmission dynamics of malaria, two intervention strategies ,the protected and treated
classes were added to the basic malaria model to formulate SPEITR model which
consists of nine non-linear differential equations.
Description
A thesis submitted to the Department of Mathematics,
Kwame Nkrumah University of Science and Technology in
partial fufillment of the requirement for the degree
of Master of Philosophy (Applied Mathematics).