A cellular automata model with probability infection and spatial dispersion |
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| Authors: | Jin Zhen Liu Quan-Xing and 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 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. |
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| Keywords: | cellular automata SEIS model stability mean-field approximation spatial epidemic |
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