Abstract
A new version of the mathematical model for the optimal control of tuberculosis, incorporating vaccination, public health campaigns, case detection, quarantine, and sanitarium as control strategies, is developed and studied. The basic properties of the model in terms of existence and uniqueness, positivity, and boundedness of the solution were established. The model has two equilibrium points, namely the disease-free and endemic equilibrium points. Also, the reproduction number of the model was computed by the next-generation matrix method. The disease-free equilibrium point of the model was established to be locally and globally asymptotically stable provided that the basic reproduction number is less than unity and unstable otherwise. Furthermore, using the common quadratic Lyapunov function in conjunction with the Lassalle invariance principle, the endemic equilibrium point of the model is established to be globally asymptotically stable.