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Computational and Mathematical Methods in Medicine
Volume 2014 (2014), Article ID 932186, 15 pages
http://dx.doi.org/10.1155/2014/932186
Research Article

A Mathematical Study of a TB Model with Treatment Interruptions and Two Latent Periods

1School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
2College of Science, China University of Petroleum, Qingdao, Shandong 266580, China

Received 16 January 2014; Revised 21 March 2014; Accepted 23 April 2014; Published 22 May 2014

Academic Editor: Reinoud Maex

Copyright © 2014 Luju Liu and Yan 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

A TB transmission model which incorporates treatment interruptions and two latent periods is presented. The threshold parameter known as the control reproduction number and the equilibria for the model are determined, and the global asymptotical stabilities of the equilibria are studied by constructing the proper Lyapunov functions. The reproduction numbers and numerical simulations show that treatment of active TB cases always helps to control the TB epidemic, while treatment interruptions may have a negative, positive, or no effect on combating TB epidemic.