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Journal of Applied Mathematics
Volume 2012, Article ID 571469, 15 pages
http://dx.doi.org/10.1155/2012/571469
Research Article

Global Stability of a SLIT TB Model with Staged Progression

Department of Mathematics, North University of China, Shanxi, Taiyuan 030051, China

Received 14 January 2012; Revised 28 July 2012; Accepted 16 August 2012

Academic Editor: Vu Phat

Copyright © 2012 Yakui Xue and Xiaohong Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Because the latent period and the infectious period of tuberculosis (TB) are very long, it is not reasonable to consider the time as constant. So this paper formulates a mathematical model that divides the latent period and the infectious period into n-stages. For a general n-stage stage progression (SP) model with bilinear incidence, we analyze its dynamic behavior. First, we give the basic reproduction number . Moreover, if , the disease-free equilibrium is globally asymptotically stable and the disease always dies out. If , the unique endemic equilibrium is globally asymptotically stable and the disease persists at the endemic equilibrium.