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Cross diffusion-induced pattern in an SI model. (English) Zbl 1200.92038
Summary: A spatial SI epidemic model with self and cross diffusion is investigated. For the no cross diffusion system, there is no Turing pattern in the spatially extended model with equal self diffusion coefficients. While considering cross diffusion of the susceptible, we obtain typical Turing patterns. The results well enrich the finding in the epidemic model and may well explain the field observed in other areas.
35Q92PDEs in connection with biology and other natural sciences
68U10Image processing (computing aspects)
[1]Anderson, R. M.; May, R. M.: Infectious diseases of humans, Dynamics and control (1991)
[2]Castets, V.; Dulos, E.; Boissonade, J.; De Kepper, P.: Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern, Phys. rev. Lett. 64, 2953-2956 (1990)
[3]Chung, J. M.; Peacock-Lopez, E.: Bifurcation diagrams and Turing patterns in a chemical self-replicating reaction – diffusion system with cross diffusion, J. chem. Phys. 127, 174903 (2007)
[4]Courchamp, F.; Pontier, D.; Langlais, M.; Artois, M.: Population dynamics of feline immunodeficiency virus within populations of cats, J. theor. Biol. 175, 553-560 (1995)
[5]Cross, M. C.; Hohenberg, P. C.: Pattern formation outside of equilibrium, Rev. mod. Phys. 65, 851-1112 (1993)
[6]Diekmann, O.; Kretzschmar, M.: Pattern in effects of infectious diseases on population growth, J. math. Biol. 29, 539-570 (1991) · Zbl 0732.92024 · doi:10.1007/BF00164051
[7]Earn, D. J. D.; Rohani, P.; Bolker, B. M.; Grenfell, B. T.: A simple model for complex dynamical transitions in epidemics, Science 287, 667-670 (2000)
[8]L. Edelstein-Keshet, Mathematical Models in Biology, Random, New York, 1988. · Zbl 0674.92001
[9]I.R. Epstein, J.A. Pojman, Introduction to Nonlinear Chemical Dynamics, Oscillations, Waves, Patterns, and Chaos, Oxford, New York, 1998.
[10]P. Gray, S.K. Scott, Chemical Oscillations and Instabilities, Oxford, Oxford, 1990.
[11]Hilker, F. M.; Langlais, M.; Petrovskii, S. V.; Malchow, H.: A diffusive SI model with allee effect and application to FIV, Math. biosci. 206, 61-80 (2007) · Zbl 1124.92044 · doi:10.1016/j.mbs.2005.10.003
[12]T. Leppnen, Computational Studies of Pattern Formation in Turing Systems, Ph.D. Thesis, Helsinki University of Technology, Finland, 2004.
[13]Li, L.; Jin, Z.; Sun, G. -Q.: Spatial pattern of an epidemic model with cross-diffusion, Chin. phys. Lett. 25, 3500-3503 (2009)
[14]Liu, Q. -X.; Jin, Z.: Formation of spatial patterns in an epidemic model with constant removal rate of the infectives, J. stat. Mech., P05002 (2007)
[15]Liu, W. -M.; Hethcote, H. W.; Levin, S. A.: Influence of nonlinear incidence rates upon the behaviour of SIRS epidemiological models, J. math. Biol. 23, 187-204 (1986) · Zbl 0582.92023 · doi:10.1007/BF00276956
[16]Liu, W. -M.; Levin, S. A.; Lwasa, Y.: Dynamical behavior of epidemiological model with nonlinear incidence rate, J. math. Biol. 25, 359-380 (1987) · Zbl 0621.92014 · doi:10.1007/BF00277162
[17]Murray, J. D.: Mathematical biology II: Spatial models and biomedical applications, Biomathematics 18 (2003)
[18]Ouyang, Q.; Swinney, H. L.: Transition from a uniform state to hexagonal and striped Turing patterns, Nature 352, 610-612 (1991)
[19]Strogatz, S. H.: Nonlinear dynamics and chaos, (1994)
[20]Sun, G.; Jin, Z.; Liu, Q. -X.; Li, L.: Pattern formation in a spatial SCI model with non-linear incidence rates, J. stat. Mech., P11011 (2007)
[21]Sun, G. -Q.; Jin, Z.; Liu, Q. -X.; Li, L.: Spatial pattern in an epidemic system with cross-diffusion of the susceptible, J. biol. Sys. 17, 141-152 (2009)
[22]Turing, A. M.: The chemical basis of morphogenesis, Phil. trans. Roy. soc. London B 237, 37-72 (1952)