Jia-Bing Wang, Wan-Tong Li, Guo-Bao Zhang
Abstract:
This article concerns the spatial dynamics of a nonlocal
dispersal vector disease model with spatio-temporal delay.
We establish the existence of spreading speeds and construct some new
types of solutions which are different from the traveling wave solutions.
To obtain the existence of spreading speed, we follow the truncating approach
to develop a comparison principle and to construct a suitable sub-solution.
Our result indicates that the spreading speed coincides with the minimal wave
speed of the regular traveling waves. The solutions are constructed
by combining regular traveling waves and the spatially independent solutions
which provide some new transmission forms of the disease.
Submitted February 2, 2015. Published May 5, 2015.
Math Subject Classifications: 35K57, 35R20, 92D25.
Key Words: global solution; nonlocal dispersal;
vector disease model; spatio-temporal delay.
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Jia-Bing Wang School of Mathematics and Statistics Lanzhou University Lanzhou, Gansu 730000, China email: jbwang11@lzu.edu.cn |
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Wan-Tong Li School of Mathematics and Statistics Lanzhou University Lanzhou, Gansu 730000, China email: wtli@lzu.edu.cn |
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Guo-Bao Zhang College of Mathematics and Statistics Northwest Normal University Lanzhou, Gansu 730070, China email: zhanggb2011@nwnu.edu.cn |
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