Spatial propagation in an epidemic model with nonlocal diffusion: The influences of initial data and dispersals

doi:10.1007/s11425-020-1740-1

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	Spatial propagation in an epidemic model with nonlocal diffusion: The influences of initial data and dispersals
	Xu, Wen-Bing 1,2; Li, Wan-Tong 2; Ruan, Shigui 3
	2020-09-11
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
页码	30
摘要	This paper studies an epidemic model with nonlocal dispersals. We focus on the influences of initial data and nonlocal dispersals on its spatial propagation. Here, initial data stand for the spatial concentrations of the infectious agent and the infectious human population when the epidemic breaks out and the nonlocal dispersals mean their diffusion strategies. Two types of initial data decaying to zero exponentially or faster are considered. For the first type, we show that spreading speeds are two constants whose signs change with the number of elements in some set. Moreover, we find an interesting phenomenon: the asymmetry of nonlocal dispersals can influence the propagating directions of the solutions and the stability of steady states. For the second type, we show that the spreading speed is decreasing with respect to the exponentially decaying rate of initial data, and further, its minimum value coincides with the spreading speed for the first type. In addition, we give some results about the nonexistence of traveling wave solutions and the monotone property of the solutions. Finally, some applications are presented to illustrate the theoretical results.
关键词	nonlocal dispersal epidemic model spreading speed initial data dispersal kernel
DOI	10.1007/s11425-020-1740-1
收录类别	SCI
语种	英语
资助项目	China Postdoctoral Science Foundation[2019M660047] ; National Natural Science Foundation of China[11731005] ; National Natural Science Foundation of China[11671180] ; National Science Foundation of USA[DMS-1853622]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000568498900001
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52164
专题	中国科学院数学与系统科学研究院
通讯作者	Li, Wan-Tong
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China 3.Univ Miami, Dept Math, Coral Gables, FL 33146 USA
推荐引用方式 GB/T 7714	Xu, Wen-Bing,Li, Wan-Tong,Ruan, Shigui. Spatial propagation in an epidemic model with nonlocal diffusion: The influences of initial data and dispersals[J]. SCIENCE CHINA-MATHEMATICS,2020:30.
APA	Xu, Wen-Bing,Li, Wan-Tong,&Ruan, Shigui.(2020).Spatial propagation in an epidemic model with nonlocal diffusion: The influences of initial data and dispersals.SCIENCE CHINA-MATHEMATICS,30.
MLA	Xu, Wen-Bing,et al."Spatial propagation in an epidemic model with nonlocal diffusion: The influences of initial data and dispersals".SCIENCE CHINA-MATHEMATICS (2020):30.