Abstract and Applied Analysis
Volume 2010 (2010), Article ID 293747, 31 pages
doi:10.1155/2010/293747
Research Article

Stability of a Two-Strain Tuberculosis Model with General Contact Rate

Hai-Feng Huo,1 Shuai-Jun Dang,1 and Yu-Ning Li2

1Institute of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
2Department of Pediatrics, First Hospital of Lanzhou University, Lanzhou, Gansu 730000, China

Received 1 November 2010; Accepted 31 December 2010

Academic Editor: D. Anderson

Copyright © 2010 Hai-Feng Huo et al. 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 two-strain tuberculosis model with general contact rate which allows tuberculosis patients with the drug-sensitive Mycobacterium tuberculosis strain to be treated is presented. The model includes both drug-sensitive and drug-resistant strains. A detailed qualitative analysis about positivity, boundedness, existence, uniqueness and global stability of the equilibria of this model is carried out. Analytical results of the model show that the quantities R1 and R2, which represent the basic reproduction numbers of the sensitive and resistant strains, respectively, provide the threshold conditions which determine the competitive outcomes of the two strains. Numerical simulations are also conducted to confirm and extend the analytic results.