title: Seasonality Impact on the Transmission Dynamics of Tuberculosis.
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.
authors.affiliation: Science College, Air Force Engineering University, Xi'an, Shaanxi 710051, China; College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, China; Centre for Disease Modelling, York University, Toronto, ON, Canada M3J 1P3.
authors.forename: Yali
authors.identifier: 0000-0002-7944-3618
authors.initials: Y
authors.lastname: Yang
authors.affiliation: Science College, Air Force Engineering University, Xi'an, Shaanxi 710051, China.
authors.forename: Chenping
authors.identifier: 0000-0001-8713-9475
authors.initials: C
authors.lastname: Guo
authors.affiliation: School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China.
authors.forename: Luju
authors.identifier: 0000-0003-4585-6999
authors.initials: L
authors.lastname: Liu
authors.affiliation: Institute of Tuberculosis Prevention and Treatment in Shaanxi, Xi'an, Shaanxi 710048, China.
authors.forename: Tianhua
authors.identifier: 0000-0002-6180-0381
authors.initials: T
authors.lastname: Zhang
authors.affiliation: Institute of Tuberculosis Prevention and Treatment in Shaanxi, Xi'an, Shaanxi 710048, China.
authors.forename: Weiping
authors.identifier: 0000-0002-5105-5031
authors.initials: W
authors.lastname: Liu
mesh_terms: D000465:Algorithms; D050936:Basic Reproduction Number; D002681:China; D003141:Communicable Diseases / Q000453:epidemiology; D003198:Computer Simulation; D058872:Epidemics; D006801:Humans; D015994:Incidence; D008962:Models, Theoretical; D009169:Mycobacterium tuberculosis; D012621:Seasons; D012984:Software; D013997:Time Factors; D014397:Tuberculosis, Pulmonary / Q000453:epidemiology* / Q000635:transmission*