Global stability for a tuberculosis model

A deterministic model is developed to describe the effects of vaccination and treatment on the spread of tuberculosis. It is shown that the basic reproduction number characterizes the disease transmission dynamics: if R0≤1R0≤1, there exists only the disease-free equilibrium which is globally asymptotically stable, and if R0>1R0>1 then there is a disease endemic equilibrium and the disease persists. Global stability of the endemic equilibrium is also discussed. Analysis of the dependence of R0R0 on the vaccination rate, vaccine efficacy and treatment rate shows that the spread of tuberculosis can be controlled if the vaccine rate or the efficacy or the treatment rate reaches a certain threshold.