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Seasonality Impact on the Transmission Dynamics of Tuberculosis


Affiliations
1 Science College, Air Force Engineering University, Xi’an, Shaanxi 710051, China
2 School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
3 Institute of Tuberculosis Prevention and Treatment in Shaanxi, Xi’an, Shaanxi 710048, China
 

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.
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  • Seasonality Impact on the Transmission Dynamics of Tuberculosis

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Authors

Yali Yang
Science College, Air Force Engineering University, Xi’an, Shaanxi 710051, China
Chenping Guo
Science College, Air Force Engineering University, Xi’an, Shaanxi 710051, China
Luju Liu
School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
Tianhua Zhang
Institute of Tuberculosis Prevention and Treatment in Shaanxi, Xi’an, Shaanxi 710048, China
Weiping Liu
Institute of Tuberculosis Prevention and Treatment in Shaanxi, Xi’an, Shaanxi 710048, China

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.