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Computational and Mathematical Methods in Medicine
Volume 2016, Article ID 8713924, 12 pages
http://dx.doi.org/10.1155/2016/8713924
Research Article

Seasonality Impact on the Transmission Dynamics of Tuberculosis

1Science College, Air Force Engineering University, Xi’an, Shaanxi 710051, China
2College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, Shaanxi 710062, China
3Centre for Disease Modelling, York University, Toronto, ON, Canada M3J 1P3
4School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
5Institute of Tuberculosis Prevention and Treatment in Shaanxi, Xi’an, Shaanxi 710048, China

Received 10 November 2015; Revised 14 January 2016; Accepted 1 February 2016

Academic Editor: Ruy M. Ribeiro

Copyright © 2016 Yali Yang 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

The statistical data of monthly pulmonary tuberculosis (TB) incidence cases from January 2004 to December 2012 show the seasonality fluctuations in Shaanxi of China. A seasonality TB epidemic model with periodic varying contact rate, reactivation rate, and disease-induced death rate is proposed to explore the impact of seasonality on the transmission dynamics of TB. Simulations show that the basic reproduction number of time-averaged autonomous systems may underestimate or overestimate infection risks in some cases, which may be up to the value of period. The basic reproduction number of the seasonality model is appropriately given, which determines the extinction and uniform persistence of TB disease. If it is less than one, then the disease-free equilibrium is globally asymptotically stable; if it is greater than one, the system at least has a positive periodic solution and the disease will persist. Moreover, numerical simulations demonstrate these theorem results.