Traveling waves of the spread of avian influenza
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- by Zhi-Cheng Wang, Jianhong Wu and Rongsong Liu PDF
- Proc. Amer. Math. Soc. 140 (2012), 3931-3946 Request permission
Abstract:
This paper gives a proof for the existence and nonexistence of traveling wave solutions of a reaction-convection epidemic model for the spatial spread of H5N1 avian influenza involving a wide range of bird species and environmental contamination. The threshold condition for the existence of traveling waves coincides with the basic reproduction number exceeding one. The existence of wave solutions is obtained by constructing an invariant cone of initial functions defined on a large spatial domain, applying a fixed point theorem on this cone and then a limiting argument. The invariant cone is based on the information of initial growth pattern of the epidemic and the final size estimation during the entire course of the outbreak.References
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Additional Information
- Zhi-Cheng Wang
- Affiliation: School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, People’s Republic of China
- MR Author ID: 782911
- Email: wangzhch@lzu.edu.cn
- Jianhong Wu
- Affiliation: Centre for Disease Modeling, York Institute for Health Research and Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada
- Email: wujh@mathstat.yorku.ca
- Rongsong Liu
- Affiliation: Department of Mathematics and Department of Zoology and Physiology, University of Wyoming, Laramie, Wyoming 82072
- Email: Rongsong.Liu@uwyo.edu
- Received by editor(s): January 26, 2010
- Received by editor(s) in revised form: May 11, 2011
- Published electronically: March 22, 2012
- Additional Notes: The first author was supported in part by the NSF of China (11071105), by FRFCU (lzujbky-2011-27) and by the Program for New Century Excellent Talents in University (NCET-2010-0470).
The second author was supported in part by CRC, NSERC, CIHR, MITACS and GEOIDE
The third author was supported in part by the University of Wyoming’s EPScoR start-up fund. - Communicated by: Yingfei Yi
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 3931-3946
- MSC (2010): Primary 35K57, 92D30; Secondary 34K10
- DOI: https://doi.org/10.1090/S0002-9939-2012-11246-8
- MathSciNet review: 2944733