A Mathematical Model to Predict the Prevalence and Transmission Dynamics of Tuberculosis in Amansie West District, Ghana
I. K. Dontwi
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
W. Obeng-Denteh *
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
E. A. Andam
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
L. Obiri-Apraku
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
*Author to whom correspondence should be addressed.
Abstract
In this paper, a Susceptible - Exposed - Infected - Recovered (SEIR) epidemiological model is formulated to determine the transmission of tuberculosis. The equilibrium points of the model are found and their stability is investigated. By analyzing the model, a threshold parameter R0 was found which is the basic reproductive number. It is noted that when R0 < 1 the disease will fail to spread and when R0 > 1 the disease will persist in the population and become endemic. The model has two non–negative equilibria namely the disease – free equilibrium and the endemic equilibrium. The graphical solutions of the differential equations were developed using Matlab as well as the computer simulations.
Keywords: Differential equations, exposed and infected, simulation, transmission dynamics, tuberculosis.