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Emergence of Strange Spatial Pattern in a Spatial Epidemic Model |
| SUN Gui-Quan;JIN Zhen;LIU Quan-Xing;LI Li |
| Department of Mathematics, North University of China, Taiyuan 030051 |
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SUN Gui-Quan, JIN Zhen, LIU Quan-Xing et al 2008 Chin. Phys. Lett. 25 2296-2299 |
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Abstract Pattern formation of a spatial epidemic model with nonlinear incidence rate kI2S/(1+αI2) is investigated. Our results show that strange spatial dynamics, i.e., filament-like pattern, can be obtained by both mathematical analysis and numerical simulation, which are different from the previous results in the spatial epidemic model such as stripe-like or spotted or coexistence of both pattern and so on. The obtained results well extend the finding of pattern formation in the epidemic model and may well explain the distribution of the infected of some epidemic.
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| Keywords:
87.23.Cc
82.40.Ck
05.45.Pq
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Received: 25 February 2008
Published: 31 May 2008
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| PACS: |
87.23.Cc
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(Population dynamics and ecological pattern formation)
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82.40.Ck
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(Pattern formation in reactions with diffusion, flow and heat transfer)
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05.45.Pq
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(Numerical simulations of chaotic systems)
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[1] Sun G, Jin Z, Liu Q X and Li L 2007 J. Stat. Mech.P11011
[2] Liu Q X and Jin Z 2007 J. Stat. Mech. P05002
[3] Hanski I 1983 Ecology 64 493
[4] Hastings A 1990 Ecology 71 426
[5] Liu W M, Hethcote H W and Levin S A 1987 J. Math.Biol. 25 359
[6] Ruan S and Wang W 2003 J. Diff. Equations 188135
[7] Turing A M 1952 Philos. Trans. R. Soc. London B 237 7
[8] Baurmann M, Gross T and Feudel U 2007 J. Theor.Biol. 245 200
[9] Segel L A and Jackson J L 1972 J. Theor. Biol. 37 545
[10] Pascual M 1993 Proc. R. Soc. London B 251 1
[11] Medvinsky A B, Petrovskii S V, Tikhonova I A, Malchow Hand Li B L 2002 SIAM Rev. 44 311
[12] Murray J D 1993 Mathematical Biology 2nd edn(Berlin: Springer)
[13] Arag$\acute{o$n J L, Torres M, Gil D, Barrio R A andMaini P K 2002 Phys. Rev. E 65 051913
[14] Cross M C and Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[15] Leppnen T 2004 PhD Thesis (Helsinki University ofTechnology, Finland)
[16] Dushoff J, Plotkin J B, Levin S A and Earn D J D 2004 Proc. Natl. Acad. Sci. U.S.A. 101 16915 |
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