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PATTERN SELECTION IN AN EPIDEMIC MODEL WITH SELF AND CROSS DIFFUSION

WEIMING WANG

College of Mathematics and Information Science, Wenzhou University, Wenzhou, 325035, P R China

School of Mathematical Sciences, Fudan University, Shanghai, 200433, P R China

Corresponding author.

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YEZHI LIN

College of Mathematics and Information Science, Wenzhou University, Wenzhou, 325035, P R China

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HAILING WANG

Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

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HOUYE LIU

College of Mathematics and Information Science, Wenzhou University, Wenzhou, 325035, P R China

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, and

YONGJI TAN

School of Mathematical Sciences, Fudan University, Shanghai, 200433, P R China

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https://doi.org/10.1142/S0218339011003555Cited by:22 (Source: Crossref)

Abstract

In this paper, we have presented Turing pattern selection in a spatial epidemic model with zero-flux boundary conditions, for which we have given a general survey of Hopf and Turing bifurcations, and have derived amplitude equations for the excited modes. Furthermore, we present novel numerical evidence of typical Turing patterns, and find that the model dynamics exhibits complex pattern replication: on increasing the control parameter r, the sequence "H₀-hexagons → H₀-hexagon-stripe mixtures → stripes → H_π-hexagon-stripe mixtures → H_π-hexagons" is observed. This may enrich the research of the pattern formation in diffusive epidemic models.

Keywords:

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