Analysis of Transmission Dynamics of Tuberculosis (TB) Using Differential Equations: A Case Study Of Amansie West District, Ghan

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In this thesis, a Susceptible – Exposed - Infected - Recovered (SEIR) epidemiological model was formulated to determine the transmission of tuberculosis. The equilibrium points of the model were found and their stability was investigated. By analyzing the model, we found a threshold parameter R0, the basic reproductive number. It was noted that when R0 < 1 the disease will fail to spread and when R0 > 1 the disease will persist in the population and become an endemic. The model had two non – negative equilibria namely the disease – free equilibrium and the endemic equilibrium. Using the Routh - Hurwitz stability theorem and computer simulations, it was observed that the number of immunized individuals in the population will increase the level of immunity. The graphical solutions of the differential equations were developed using Matlab as well as the computer simulations. The Appendix contains the Matlab codes used in the computer simulations.
A Thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirement for the degree of Master of Science in Industrial Mathematics,