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|Title: ||Modeling the spread of tuberculosis in Central Region using the susceptible-exposed-infected-susceptible (SEIS) mathematical model|
|Authors: ||Sarkodie, Eric|
|Issue Date: ||16-Oct-2014|
|Abstract: ||Tuberculosis (TB) is a growing problem worldwide, with an estimated one-third of the world’s population currently infected.
In this thesis we modify the non-constant population SEIS model developed by Castillo-Chavez to a constant population model to predict the spread of tuberculosis in the Central Region of Ghana using data from the Central regional Health Directorate, Cape Coast.
We discuss the mathematics behind the model and various tools for judging effectiveness of policies and control methods.
The model has two equilibrium states namely, the disease – free and the endemic equilibrium points. The stability of each equilibrium point is discussed and the endemic equilibrium has been found to be stable while that of the disease-free was unstable. The basic reproduction number (R_o) was estimated to be 2. The disease was found to persist with R_o >1 whenever the transmission rate was increased or the recovery rate reduced but turned to die out with R_o <1, whenever the transmission rate was reduced or the recovery rate increased.
The results of our sensitivity analysis showed that the most sensitive parameter that controls the spread of tuberculosis in Central Region is the initial infection rate of the susceptible, σ. Decreasing the value of σ at the same rate as the other parameter values completely decreases the proportions of both the infective and the exposed more effectively than any parameter value.
From the analysis and discussions of the model, SEIS epidemiological model is a good model to study the spread of tuberculosis in Ghana.|
|Description: ||A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology,
in partial fulfilment of the requirement for the degree of
Master of Science in Industrial Mathematics, 2014|
|Appears in Collections:||College of Science|
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