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Computational and Mathematical Methods in Medicine
Volume 2016, Article ID 3410320, 10 pages
http://dx.doi.org/10.1155/2016/3410320
Research Article

A Dynamic Model of Human and Livestock Tuberculosis Spread and Control in Urumqi, Xinjiang, China

1Department of Public Health, Xinjiang Medical University, Urumqi 830011, China
2Urumqi Animal Disease Control and Diagnosis Center, Urumqi 830063, China
3Department of Mathematics, Yuncheng University, Yuncheng 044000, China
4Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China

Received 18 February 2016; Accepted 12 June 2016

Academic Editor: Konstantin Blyuss

Copyright © 2016 Shan 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

We establish a dynamical model for tuberculosis of humans and cows. For the model, we firstly give the basic reproduction number . Furthermore, we discuss the dynamical behaviors of the model. By epidemiological investigation of tuberculosis among humans and livestock from 2007 to 2014 in Urumqi, Xinjiang, China, we estimate the parameters of the model and study the transmission trend of the disease in Urumqi, Xinjiang, China. The reproduction number in Urumqi for the model is estimated to be 0.1811 (95% confidence interval: 0.123–0.281). Finally, we perform some sensitivity analysis of several model parameters and give some useful comments on controlling the transmission of tuberculosis.