A MATHEMATICAL MODEL FOR TUBERCULOSIS INFECTION TRANSMISSION DYNAMICS IN THE PRESENCE OF TESTING AND THERAPY, ISOLATION AND TREATMENT

Abstract

In this study, a mathematical model for Tuberculosis infection transmission dynamics is developed by incorporating testing and therapy of latent individuals, the isolation of infectious individuals and the treatment of the isolated individuals. The basic reproduction number was computed using the next generation matrix method. Analysis of the model at the disease-free equilibrium state and the endemic equilibrium states shows that it is locally and globally asymptomatically stable whenever the basic reproduction number is less than unity at the disease -free equilibrium state and locally and globally asymptotically stable whenever the basic reproduction number is greater than unity. The result from the sensitivity index of  show that the infection transmission parameter and other control parameters such as early detection and therapy, the isolation of infected individuals and treatment are crucial parameters to tuberculosis management.  It is shown from numerical simulations that the early detection and therapy, isolation and treatment of infected individuals will reduce the infection transmission. Further numerical results show that the combination of early detection and therapy, isolation and treatment of infectious individuals will decrease the infection transmission and its eventual eradication from the human population.