MATHEMATICAL MODEL OF THE SPREAD OF TUBERCULOSIS USING DIFFERENTIAL EQUATIONS
Abstract
In this project work we formulate a mathematical model of Tuberculosis us-ing differential equations. The model is constructed using the SIR model which described the disease transmission through contact with infected per-son or through pets, also infected person are hospitalized and then removed or recovered. We show that the solutions are bounded and positive. we find two equilibrium points (disease free equilibrium and endemic equilibrium). We also move forward to find the basic reproduction number R0 using the next generation matrix method, we establish the local stability of the dis-ease free equilibrium and endemic equilibrium, the DFE was shown to be stable likewise the endemic equilibrium. Sensitivity analysis was conducted to verify the parameters that are sensitive to the model using the method of normalized forward sensitivity index. Some numerical simulations were carried out to support the theoretical aspect of the work.
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