摘要Pattern formation of a spatial epidemic model with both self- and cross-diffusion is investigated. From the Turing theory, it is well known that Turing pattern formation cannot occur for the equal self-diffusion coefficients. However, combined with cross-diffusion, the system will show emergence of isolated groups, i.e., stripe-like or spotted or coexistence of both, which we show by both mathematical analysis and numerical simulations. Our study shows that the interaction of self- and cross-diffusion can be considered as an important mechanism for the appearance of complex spatiotemporal dynamics in epidemic models
Abstract：Pattern formation of a spatial epidemic model with both self- and cross-diffusion is investigated. From the Turing theory, it is well known that Turing pattern formation cannot occur for the equal self-diffusion coefficients. However, combined with cross-diffusion, the system will show emergence of isolated groups, i.e., stripe-like or spotted or coexistence of both, which we show by both mathematical analysis and numerical simulations. Our study shows that the interaction of self- and cross-diffusion can be considered as an important mechanism for the appearance of complex spatiotemporal dynamics in epidemic models
LI Li;JIN Zhen;SUN Gui-Quan. Spatial Pattern of an Epidemic Model with Cross-diffusion[J]. 中国物理快报, 2008, 25(9): 3500-3503.
LI Li, JIN Zhen, SUN Gui-Quan. Spatial Pattern of an Epidemic Model with Cross-diffusion. Chin. Phys. Lett., 2008, 25(9): 3500-3503.
[1] Bernoulli D 1760 M\'{em. Math. Phys. Acad. R. Sci.Paris p 1 [2] Hufnagel L, Brockmann D, and Geisel T 2004 Proc.Natl. Acad. Sci. U.S.A. 101 15124 [3] Keeling M J, Woolhouse M E J, Shaw D J, Matthews L,Chase-Topping M, Haydon D T, Cornell S J, Kappey J, Wilesmith J,and Grenfell B T 2001 Science 294 813 [4] Smith D L, Lucey B, Waller L A, Childs J E, and Real L A\newblock 2002 Proc. Natl. Acad. Sci. U.S.A. 99 3668 [5] Keeling M J, Woolhouse M E J, May R M, Davies G andGrenfell B T 2003 Nature 421 136 [6] Hanski I 1983 Ecology 64 493 [7] Hastings A 1990 Ecology 71 426 [8] Conroy M J, Cohen Y, James F C, Matsinos Y G and Maurer BA 1995 Ecol. Appl. 5 17 [9] Kot M, Lewis M A and van den Driessche P 1996 Ecology 77 2027 [10] Ruckelshaus M, Hartway C and Kareiva P 1997 Conserv. Biol. 11 1298 [11] Fagan W F, Lewis M A, Neubert M G and vanden Driessche P 2002 Ecol. Lett. 5 148 [12] Liu W m, Levin S A and Iwasa Y 1987 J. Math. Biol. 25 359 [13] Liu W m, Hethcote H W, Levin S A 1986 J. Math.Biol. 23 187 [14] Sun G, Jin Z, Liu Q X and Li L 2007 J. Stat. Mech.P11011 [15] Sun G Q, Jin Z, Liu Q X and Li L 2008 Chin. Phys.Lett. 25 2296 [16] Ouyang Q 2000 Pattern Formation in aReaction-Diffusion Systems (Shanghai: Scientific and TechnologicalEducation Publishing House) (in Chinese) [17]Murray J D 1993 Mathematical Biology 2nd edn(Berlin: Springer)
2008, Vol. 25 
