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Zbl 1194.92066
Sun, Gui-Quan; Li, Li; Jin, Zhen; Li, Bai-Lian
Effect of noise on the pattern formation in an epidemic model. (English)
[J] Numer. Methods Partial Differ. Equations 26, No. 5, 1168-1179 (2010). ISSN 0749-159X; ISSN 1098-2426/e

Summary: We present novel numerical evidence of a complicated phenomenon controlled by noise in a spatial epidemic model. The number of the spot is decreased as the noise intensity being increased, which we show by performing a series of numerical simulations. Moreover, when the noise intensity and temporal correlation are both large enough, the model dynamics exhibits a noise controlled transition from spotted patterns to stripe growth. In addition, we show in detail the number of the spotted and stripe patterns, with the identification of a wide range of noise intensity and temporal correlations. The obtained results show that noise plays an important role in the pattern formation of the epidemic model, which may provide guidance to prevent and control the spread of disease.

MSC 2000:: *92D30 Epidemiology
60H15 Stochastic partial differential equations
65C20 Models (numerical methods)

Keywords: epidemic model; noise; transition; pattern formation

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