Electron. J. Diff. Equ., Vol. 2015 (2015), No. 122, pp. 1-28.

Spatial dynamics of a nonlocal dispersal vector disease model with spatio-temporal delay

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
Wan-Tong Li
School of Mathematics and Statistics
Lanzhou University
Lanzhou, Gansu 730000, China
email: wtli@lzu.edu.cn
Guo-Bao Zhang
College of Mathematics and Statistics
Northwest Normal University
Lanzhou, Gansu 730070, China
email: zhanggb2011@nwnu.edu.cn

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