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)
a School of Science, North University of China, Taiyuan 030051, China; b Department of Mathematics, Krishnath College, Berhampore, Mursidabad, West Bengal, India-742101
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.
Received: 18 June 2006
Revised: 29 November 2006
Accepted manuscript online:
Fund: 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
Cite this article:
Jin Zhen(靳祯), Liu Quan-Xing(刘权兴), and Mainul Haque A cellular automata model with probability infection and spatial dispersion 2007 Chinese Physics 16 1267
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