Spreading speeds of epidemic models with nonlocal delays

doi:10.3934/mbe.2019380

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	Spreading speeds of epidemic models with nonlocal delays
	Lin, Guo 1; Pan, Shuxia 2; Yan, Xiang-Ping 3
刊名	MATHEMATICAL BIOSCIENCES AND ENGINEERING
	2019
卷号	16 期号:6 页码:7562-7588
关键词	auxiliary equation nonmonotone system asymptotic spreading
ISSN号	1547-1063
DOI	10.3934/mbe.2019380
英文摘要	We estimate the spreading speeds in diffusive epidemic models with nonlocal delays, nonlinear incidence rate and constant recruitment rate. The purpose is to model the process that the infective invades the habitat of the susceptible, and they coexist eventually. In order to focus on our idea, a system with a nonlinear incidence rate is firstly studied, which implies a saturation level of the infective individuals and monotone incidence rate. When the initial value of the infective has nonempty compact support, we prove the rough spreading speed that equals the minimal wave speed of traveling wave solutions in the known results. Then for a general (nonmonotone) incidence rate, we obtain the spreading speeds by constructing auxiliary systems admitting a monotone incidence rate, and prove the convergence of solutions on any compact spatial interval. Furthermore, some numerical examples are given to estimate the invasion speed and show the nontrivial effect of time delay and spatial nonlocality, which implies that the stronger spatial nonlocality leads to larger spreading speeds.
资助项目	Foundation of a Hundred Youth Talents Training Program of Lanzhou Jiaotong University[152022]
WOS研究方向	Mathematical & Computational Biology
语种	英语
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
WOS记录号	WOS:000487331700072
状态	已发表
内容类型	期刊论文
源URL	[http://119.78.100.223/handle/2XXMBERH/32261]
专题	理学院
通讯作者	Lin, Guo
作者单位	1.Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China 2.Lanzhou Univ Technol, Sch Sci, Lanzhou 730050, Gansu, Peoples R China 3.Lanzhou Jiaotong Univ, Dept Math, Lanzhou 730070, Gansu, Peoples R China
推荐引用方式 GB/T 7714	Lin, Guo,Pan, Shuxia,Yan, Xiang-Ping. Spreading speeds of epidemic models with nonlocal delays[J]. MATHEMATICAL BIOSCIENCES AND ENGINEERING,2019,16(6):7562-7588.
APA	Lin, Guo,Pan, Shuxia,&Yan, Xiang-Ping.(2019).Spreading speeds of epidemic models with nonlocal delays.MATHEMATICAL BIOSCIENCES AND ENGINEERING,16(6),7562-7588.
MLA	Lin, Guo,et al."Spreading speeds of epidemic models with nonlocal delays".MATHEMATICAL BIOSCIENCES AND ENGINEERING 16.6(2019):7562-7588.