Journal
NONLINEAR DYNAMICS
Volume 69, Issue 3, Pages 1097-1104Publisher
SPRINGER
DOI: 10.1007/s11071-012-0330-5
Keywords
Spatial epidemic model; Nonlinear incidence rates; Pattern formation
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Funding
- National Natural Science Foundation of China [11147015, 11171314]
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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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