Pattern formation of an epidemic model with diffusion

被引:124
|
作者
Sun, Gui-Quan [1 ]
机构
[1] N Univ China, Dept Math, Taiyuan 030051, Shanxi, Peoples R China
基金
中国国家自然科学基金;
关键词
Spatial epidemic model; Nonlinear incidence rates; Pattern formation; EMERGING INFECTIOUS-DISEASES; SPATIAL DYNAMICS; SMALLPOX; TRANSMISSION; BEHAVIOR; FOOT;
D O I
10.1007/s11071-012-0330-5
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
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.
引用
收藏
页码:1097 / 1104
页数:8
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