One subject of spatial epidemiology is spatial variation in disease risk or incidence. The spread of epidemics can result in strong spatial patterns of such risk or incidence: for example, pathogen dispersal might be highly localized, vectors or reservoirs for pathogens might be spatially restricted, or susceptible hosts might be clumped. Here, spatial pattern of an epidemic model with nonlinear incidence rates is investigated. The conditions for Hopf bifurcation and Turing bifurcation are gained and, in particular, exact Turing domain is found in the two parameters space. Furthermore, numerical results show that force of infection, namely beta, plays an important role in the spatial pattern. More specifically, different patterns emerge as beta increases. The mathematical analysis and numerical results well extend the finding of pattern formation in the epidemic models and may well explain the field observed in some areas.
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Xuchang Univ, Sch Sci, Xuchang 461000, Peoples R China
Northwestern Polytech Univ, Dept Appl Math, Xian 710072, Peoples R ChinaXuchang Univ, Sch Sci, Xuchang 461000, Peoples R China
Zheng, Qianqian
Pandey, Vikas
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Univ Calif Los Angeles, David Geffen Sch Med, Los Angeles, CA 90095 USAXuchang Univ, Sch Sci, Xuchang 461000, Peoples R China
Pandey, Vikas
Shen, Jianwei
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North China Univ Water Resources & Elect Power, Sch Math & Stat, Zhengzhou 450046, Peoples R ChinaXuchang Univ, Sch Sci, Xuchang 461000, Peoples R China
Shen, Jianwei
Xu, Yong
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Northwestern Polytech Univ, Dept Appl Math, Xian 710072, Peoples R ChinaXuchang Univ, Sch Sci, Xuchang 461000, Peoples R China
Xu, Yong
Guan, Linan
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North China Univ Water Resources & Elect Power, Sch Math & Stat, Zhengzhou 450046, Peoples R ChinaXuchang Univ, Sch Sci, Xuchang 461000, Peoples R China
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North Univ China, Dept Math, Taiyuan 030051, Shanxi, Peoples R ChinaNorth Univ China, Dept Math, Taiyuan 030051, Shanxi, Peoples R China
Li, Jing
Sun, Gui-Quan
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Shanxi Univ, Complex Syst Res Ctr, Taiyuan 030006, Shanxi, Peoples R China
Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R ChinaNorth Univ China, Dept Math, Taiyuan 030051, Shanxi, Peoples R China
Sun, Gui-Quan
Jin, Zhen
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Shanxi Univ, Complex Syst Res Ctr, Taiyuan 030006, Shanxi, Peoples R China
Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R ChinaNorth Univ China, Dept Math, Taiyuan 030051, Shanxi, Peoples R China
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N Univ China, Dept Math, Taiyuan 030051, Shanxi, Peoples R China
N Univ China, Sch Mechatron Engn, Taiyuan 030051, Shanxi, Peoples R ChinaN Univ China, Dept Math, Taiyuan 030051, Shanxi, Peoples R China
Sun, Gui-Quan
Li, Li
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N Univ China, Dept Math, Taiyuan 030051, Shanxi, Peoples R ChinaN Univ China, Dept Math, Taiyuan 030051, Shanxi, Peoples R China
Li, Li
Jin, Zhen
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N Univ China, Dept Math, Taiyuan 030051, Shanxi, Peoples R ChinaN Univ China, Dept Math, Taiyuan 030051, Shanxi, Peoples R China
Jin, Zhen
Li, Bai-Lian
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Univ Calif Riverside, Ecol Complex & Modeling Lab, Dept Bot & Plant Sci, Riverside, CA 92521 USAN Univ China, Dept Math, Taiyuan 030051, Shanxi, Peoples R China
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Wenzhou Univ, Coll Math & Informat Sci, Wenzhou 325035, Peoples R ChinaWenzhou Univ, Coll Math & Informat Sci, Wenzhou 325035, Peoples R China
Wang Wei-Ming
Liu Hou-Ye
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Wenzhou Univ, Coll Math & Informat Sci, Wenzhou 325035, Peoples R ChinaWenzhou Univ, Coll Math & Informat Sci, Wenzhou 325035, Peoples R China
Liu Hou-Ye
Cai Yong-Li
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Wenzhou Univ, Coll Math & Informat Sci, Wenzhou 325035, Peoples R ChinaWenzhou Univ, Coll Math & Informat Sci, Wenzhou 325035, Peoples R China
Cai Yong-Li
Li Zhen-Qing
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Chinese Acad Sci, Inst Bot, State Key Lab Vegetat & Environm Change, Beijing 100093, Peoples R ChinaWenzhou Univ, Coll Math & Informat Sci, Wenzhou 325035, Peoples R China
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Wenzhou Univ, Coll Math & Informat Sci, Wenzhou 325035, Peoples R China
Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R ChinaWenzhou Univ, Coll Math & Informat Sci, Wenzhou 325035, Peoples R China
Wang, Weiming
Lin, Yezhi
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Wenzhou Univ, Coll Math & Informat Sci, Wenzhou 325035, Peoples R ChinaWenzhou Univ, Coll Math & Informat Sci, Wenzhou 325035, Peoples R China
Lin, Yezhi
Wang, Hailing
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City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R ChinaWenzhou Univ, Coll Math & Informat Sci, Wenzhou 325035, Peoples R China
Wang, Hailing
Liu, Houye
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Wenzhou Univ, Coll Math & Informat Sci, Wenzhou 325035, Peoples R ChinaWenzhou Univ, Coll Math & Informat Sci, Wenzhou 325035, Peoples R China
Liu, Houye
Tan, Yongji
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Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R ChinaWenzhou Univ, Coll Math & Informat Sci, Wenzhou 325035, Peoples R China
机构:
College of Mathematics and Information Science,Wenzhou UniversityCollege of Mathematics and Information Science,Wenzhou University
王玮明
刘厚业
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College of Mathematics and Information Science,Wenzhou UniversityCollege of Mathematics and Information Science,Wenzhou University
刘厚业
蔡永丽
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College of Mathematics and Information Science,Wenzhou UniversityCollege of Mathematics and Information Science,Wenzhou University
蔡永丽
李镇清
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机构:
State Key Laboratory of Vegetation and Environmental Change,Institute of Botany,Chinese Academy of SciencesCollege of Mathematics and Information Science,Wenzhou University