中国物理B ›› 2005, Vol. 14 ›› Issue (7): 1370-1377.doi: 10.1088/1009-1963/14/7/018

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Cellular automata modelling of SEIRS

靳祯1, 刘权兴2   

  1. (1)Department of Applied Mathematics, North University of China,Taiyuan 030051, China; (2)Department of Chemical Engineering, North University of China, Taiyuan 030051, China
  • 收稿日期:2004-07-12 修回日期:2005-02-23 出版日期:2005-06-20 发布日期:2005-06-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10471040).

Cellular automata modelling of SEIRS

Liu Quan-Xing (刘权兴)a, Jin Zhen (靳祯)b    

  1. a Department of Chemical Engineering, North University of China, Taiyuan 030051, China; b Department of Applied Mathematics, North University of China,Taiyuan 030051, China
  • Received:2004-07-12 Revised:2005-02-23 Online:2005-06-20 Published:2005-06-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10471040).

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摘要： In this paper the SEIRS epidemic spread is analysed, and a two-dimensional probability cellular automata model for SEIRS is presented. Each cellular automation cell represents a part of the population that may be found in one of five states of individuals: susceptible, exposed (or latency), infected, immunized (or recovered) and death. Here studied are the effects of two cases on the epidemic spread. i.e. the effects of non-segregation and segregation on the latency and the infected of population. The conclusion is reached that the epidemic will persist in the case of non-segregation but it will decrease in the case of segregation. The proposed model can serve as a basis for the development of algorithms to simulate real epidemics based on real data. Last we find the density series of the exposed and the infected will fluctuate near a positive equilibrium point, when the constant for the immunized is less than its corresponding constant $\tau_{0}$. Our theoretical results are verified by numerical simulations.

关键词: cellular automata, epidemic, modelling, SEIRS modelling

Abstract: In this paper the SEIRS epidemic spread is analysed, and a two-dimensional probability cellular automata model for SEIRS is presented. Each cellular automation cell represents a part of the population that may be found in one of five states of individuals: susceptible, exposed (or latency), infected, immunized (or recovered) and death. Here studied are the effects of two cases on the epidemic spread. i.e. the effects of non-segregation and segregation on the latency and the infected of population. The conclusion is reached that the epidemic will persist in the case of non-segregation but it will decrease in the case of segregation. The proposed model can serve as a basis for the development of algorithms to simulate real epidemics based on real data. Last we find the density series of the exposed and the infected will fluctuate near a positive equilibrium point, when the constant for the immunized is less than its corresponding constant $\tau_{0}$. Our theoretical results are verified by numerical simulations.

Key words: cellular automata, epidemic, modelling, SEIRS modelling

中图分类号:  (General theory and mathematical aspects)

  • 87.10.-e
87.19.X- (Diseases) 87.23.Cc (Population dynamics and ecological pattern formation) 02.60.Cb (Numerical simulation; solution of equations)