A cellular automata model with probability infection and spatial dispersion |
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| Authors: | Jin Zhen Liu Quan-Xing Mainul Haque |
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| Affiliation: | School of Science, North University of China, Taiyuan 030051, China; Department of Mathematics, Krishnath College, Berhampore, Mursidabad, West Bengal, India-742101 |
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| Abstract: | In this article, we have proposed an epidemic model based on theprobability cellular automata theory. The essential mathematicalfeatures are analysed with the help of stability theory. We havegiven an alternative modelling approach for the spatiotemporal systemwhich is more realistic from the practical point of view. A discreteand spatiotemporal approach is shown by using cellular automatatheory. It is interesting to note that both the size of the endemicequilibrium and the density of the individuals increase with theincrease of the neighbourhood size and infection rate, but theinfections decrease with the increase of the recovery rate. Thestability of the system around the positive interior equilibrium hasbeen shown by using a suitable Lyapunov function. Finally,experimental data simulation for SARS disease in China in 2003 and abrief discussion are given. |
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| Keywords: | cellular automata SEIS model stability mean-field approximation spatial epidemic |
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