Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 296905, 12 pages
http://dx.doi.org/10.1155/2011/296905
Research Article

Modeling Transmission of Tuberculosis with MDR and Undetected Cases

Yongqi Liu,1 Zhendong Sun,1 Guiquan Sun,2 Qiu Zhong,3 Li Jiang,3 Lin Zhou,3 Yupeng Qiao,1 and Zhongwei Jia4

1College of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, China
2Department of Mathematics, North University of China, Taiyuan 030051, China
3Antituberculosis Research Institute of Guangdong Province, Guangzhou 510630, China
4National Institute on Drug Dependence, Peking University, Beijing 100083, China

Received 22 February 2011; Accepted 10 April 2011

Academic Editor: Guang Zhang

Copyright © 2011 Yongqi Liu 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

This paper presents a novel mathematical model with multidrug-resistant (MDR) and undetected TB cases. The theoretical analysis indicates that the disease-free equilibrium is globally asymptotically stable if 𝑅 0 < 1 ; otherwise, the system may exist a locally asymptotically stable endemic equilibrium. The model is also used to simulate and predict TB epidemic in Guangdong. The results imply that our model is in agreement with actual data and the undetected rate plays vital role in the TB trend. Our model also implies that TB cannot be eradicated from population if it continues to implement current TB control strategies.