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Modeling the impact of immigration on the epidemiology of tuberculosis |
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| Authors: | Jia Zhong-Wei Tang Gong-You Jin Zhen Dye Christopher Vlas Sake J Li Xiao-Wen Feng Dan Fang Li-Qun Zhao Wen-Juan Cao Wu-Chun |
| Institution: | a School of Information Engineering, Beijing University of Posts and Telecommunications, 10 Xitucheng Road, Beijing 100876, PR China b Beijing Institute of Microbiology and Epidemiology, State Key Laboratory of Pathogen and Biosecurity, 20 Dongda Street, Fengtai District, Beijing 100071, PR China c College of Information Science and Engineering, Ocean University of China, 238 Songling Road, Qingdao 266100, PR China d Department of Mathematics, North University of China, Taiyuan 030051, PR China e Communicable Disease Control, Prevention and Eradication, World Health Organization, 1211 Geneva 27, Switzerland f Department of Public Health, Erasmus MC, University Medical Center Rotterdam, P.O. Box 2040, 3000 CA Rotterdam, The Netherlands g Institute of Remote Sensing Applications Chinese Academy of Sciences, P.O. Box 9718, Beijing 100101, PR China |
| Abstract: | This paper presents two new theoretical frameworks to investigate the impact of immigration on the transmission dynamics of tuberculosis. For the basic model, we present new analysis on the existence and stability of equilibria. Then, we use numerical simulations of the model to illustrate the behavior of the system. We apply the model to Canadian reported data on tuberculosis and observe a good agreement between the model prediction and the data. For the extended model, which incorporated the recruitment of the latent and infectious in immigrants to the basic model, we find that the usual threshold condition does not apply and a unique equilibrium exists for all parameter values. This indicates that the disease does not disappear and becomes endemic in host areas. This finding is also supported by numerical simulations with the extended model. Our study suggests that immigrants have a considerable influence on the overall transmission dynamics behavior of tuberculosis. |
| Keywords: | Tuberculosis Immigrant Endemic equilibrium Threshold parameter Global asymptotic stability |
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