Volume 19, Number 1, Spring 2011
GLOBAL STABILITY OF THE ENDEMIC
EQUILIBRIUM OF A TUBERCULOSIS MODEL
WITH IMMIGRATION AND TREATMENT
HONGBIN GUO AND MICHAEL Y. LI
Abstract. Mathematical analysis is carried out for a tuberculosis (TB) model incorporating both latent and clinical stages, immigration and treatment. With immigration into the latent classes, we show that the model always has a unique endemic equilibrium and it is globally asymptotically stable. The global stability of the endemic equilibrium is proved using a global Lyapunov function.