中国物理B ›› 2007, Vol. 16 ›› Issue (5): 1267-1275.doi: 10.1088/1009-1963/16/5/017

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A cellular automata model with probability infection and spatial dispersion

MainulHaque1, 靳\祯2, 刘权兴2   

  1. (1)Department of Mathematics, Krishnath College, Berhampore, Mursidabad, West Bengal, India-742101; (2)School of Science, North University of China, Taiyuan 030051, China\
  • 收稿日期:2006-06-18 修回日期:2006-11-29 出版日期:2007-05-20 发布日期:2007-05-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No~10471040), the Natural Science Foundation of Shan'xi Province, China (Grant No~2006011009), and part of this work have been done at the time when M. Haque was visiting North U

A cellular automata model with probability infection and spatial dispersion

Jin Zhen(靳祯)a)†, Liu Quan-Xing(刘权兴)a), and Mainul Haqueb)   

  1. a School of Science, North University of China, Taiyuan 030051, China; b Department of Mathematics, Krishnath College, Berhampore, Mursidabad, West Bengal, India-742101
  • Received:2006-06-18 Revised:2006-11-29 Online:2007-05-20 Published:2007-05-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No~10471040), the Natural Science Foundation of Shan'xi Province, China (Grant No~2006011009), and part of this work have been done at the time when M. Haque was visiting North U

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摘要： In this article, we have proposed an epidemic model based on the probability cellular automata theory. The essential mathematical features are analysed with the help of stability theory. We have given an alternative modelling approach for the spatiotemporal system which is more realistic from the practical point of view. A discrete and spatiotemporal approach is shown by using cellular automata theory. It is interesting to note that both the size of the endemic equilibrium and the density of the individuals increase with the increase of the neighbourhood size and infection rate, but the infections decrease with the increase of the recovery rate. The stability of the system around the positive interior equilibrium has been shown by using a suitable Lyapunov function. Finally, experimental data simulation for SARS disease in China in 2003 and a brief discussion are given.

关键词: cellular automata, SEIS model, stability, mean-field approximation, spatial epidemic

Abstract: In this article, we have proposed an epidemic model based on the probability cellular automata theory. The essential mathematical features are analysed with the help of stability theory. We have given an alternative modelling approach for the spatiotemporal system which is more realistic from the practical point of view. A discrete and spatiotemporal approach is shown by using cellular automata theory. It is interesting to note that both the size of the endemic equilibrium and the density of the individuals increase with the increase of the neighbourhood size and infection rate, but the infections decrease with the increase of the recovery rate. The stability of the system around the positive interior equilibrium has been shown by using a suitable Lyapunov function. Finally, experimental data simulation for SARS disease in China in 2003 and a brief discussion are given.

Key words: cellular automata, SEIS model, stability, mean-field approximation, spatial epidemic

中图分类号:  (Lattice theory and statistics)

  • 05.50.+q
02.50.Cw (Probability theory) 02.60.Cb (Numerical simulation; solution of equations) 05.45.-a (Nonlinear dynamics and chaos)