广东工业大学学报 ›› 2018, Vol. 35 ›› Issue (05): 51-59.doi: 10.12052/gdutxb.180058

• 综合研究 • 上一篇    下一篇

多因素制约下的SIR传染病模型的元胞自动机仿真模拟研究

郑三强, 韩晓卓   

  1. 广东工业大学 应用数学学院, 广东 广州 510520
  • 收稿日期:2018-03-22 出版日期:2018-07-10 发布日期:2018-07-18
  • 通信作者: 韩晓卓(1978-),女,副教授,主要研究方向为生物数学.E-mail:hanxzh@gdut.edu.cn E-mail:hanxzh@gdut.edu.cn
  • 作者简介:郑三强(1993-),男,硕士研究生,主要研究方向为生物数学.
  • 基金资助:
    国家自然科学基金资助项目（31670391）

A Simulation of Cellular Automata Based on the SIR Infectious Disease Model with Multifactorial Constraints

Zheng San-qiang, Han Xiao-zhuo   

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2018-03-22 Online:2018-07-10 Published:2018-07-18

HTML

PDF (PC)

3235

摘要： 针对多因素传染病的精确仿真，根据非高斯传染模型下模拟感染者的随机游走行为，通过构造传染病中心疫区的高斯压力死亡模型，采用基于sigmoid函数的痊愈率与不同隔离强度模拟感染者个体的被动转化行为，且其行为的发生服从动态泊松概率，建立了一类多因素制约下的元胞自动机传染病模型.通过对比实验发现，该模型的模拟仿真稳定，且能较精确仿真疫病传播的实际情况，相比目前的模型具有更高的精度.

关键词: 元胞自动机, 传染病模型, 高斯非邻体传染, 高斯压力, sigmoid函数

Abstract: Aiming at accurate simulation of multifactor infectious diseases and using Gauss-pressure model to simulate death in a central epidemic area, using the recovery rate and isolation intensity based on the sigmoid function to simulate the passive transformation of the infected individual, with the probability of the occurrence of its behavior obeying the dynamic probability, a multi-factor cellular automata infections disease model is established. Some comparison experiments are carried out on the model, and the results show that the model is more stable and more able than the current model to accurately simulate the actual situation of epidemic disease transmission.

Key words: cellular automata, epidemic model, Gaussian non-neighborhood infection, Gauss-pressure, sigmoid function

中图分类号: 

  • TP301.1
[1] SCHNECKENREITHER G, POPPER N, ZAUNER G, et al. Modelling SIR-type epidemics by ODEs, PDEs, difference equations and cellular automata-a comparative study[J]. Simulation Modelling Practice & Theory, 2008, 16(8):1014-1023
[2] 余雷, 薛惠锋, 高晓燕,等. 基于元胞自动机的传染病传播模型研究[J]. 计算机工程与应用, 2007, 43(2):196-198 YU L, XUE H F, GAO X Y, et al. Epidemic spread model based on cellular automata[J]. Computer Engineering and Applications, 2007, 43(2):196-198
[3] 谭欣欣, 戴钦武, 史鹏燕,等. 基于元胞自动机的个体移动异质性传染病传播模型[J]. 大连理工大学学报, 2013, 53(6):908-914 TAN X X, DAI Q W, SHI P Y, et al. CA-based epidemic propagation model with inhomogeneity and mobility[J]. Journal of Dalian University of Technology, 2013, 53(6):908-914
[4] WHITE S H, REY A M D, SÁNCHEZ G R. Modeling epidemics using cellular automata[J]. Applied Mathematics & Computation, 2007, 186(1):193-202
[5] VENKATACHALAM S, MIKLER A R. An infectious disease outbreak simulator based on the cellular automata paradigm[C]//Innovative Internet Community Systems, International workshop, Iics 2004, Guadalajara, Mexico, June 21-23, 2004, Revised Papers. DBLP, 2004:198-211.
[6] LI S, NIENKE H, NIKO S, et al. Consequences of landscape fragmentation on lyme disease risk:a cellular automata approach[J]. Plos One, 2012, 7(6):e39612-e39612
[7] SANTOS L B L, COSTA M C, PINHO S T R, et al. Periodic forcing in a three-level cellular automata model for a vector-transmitted disease[J]. Physical Review E Statistical Nonlinear & Soft Matter Physics, 2009, 80(2):016102
[8] 李璐, 宣慧玉, 高宝俊. 基于元胞自动机的异质个体HIV/AIDS传播模型[J]. 系统管理学报, 2008, 17(6):704-710 LI L, XUAN H Y, GAO B J. CA-based heterogeneous epidemic model for HIV/AIDS transmission[J]. Journal of Systems & Management, 2008, 17(6):704-710
[9] 王仲君, 张莉丽. 具有年龄结构的异质元胞自动机HIV传播模型[J]. 武汉理工大学学报(信息与管理工程版), 2014, 36(2):145-149 WANG Z J, ZHANG L L. A heterogeneous cellular automata model with age structure for HIV transmission[J]. Journal of Wuhan University of Technology (Information & Management Engineering), 2014, 36(2):145-149
[10] 张丽娟. 一类复杂系统下元胞自动机传染病模型的控制和预测[J]. 运筹与模糊学, 2017, 07(4):91-103 ZHANG L J. Control and prediction of cellular automata epidemic model under a complex system[J]. Operations Research and Fuzziology, 2017, 07(4):91-103
[11] 关超, 彭云, 袁文燕. 基于元胞自动机带有干预机制的传染病模型[J]. 北京化工大学学报(自然科学版), 2011, 38(6):109-113 GUAN C, PENG Y, YUAN W Y. A cellular automaton model with medical intervention for epidemic propagation[J]. Journal of Beijing University of Chemical Technology (Natural Science Edition), 2011, 38(6):109-113
[12] CHOPARD B, DROZ M. 物理系统的元胞自动机模拟[M]. 祝玉学, 赵学龙, 译. 北京:清华大学出版社, 2003:10-12.
[13] WOLFRAM S, MALLINCKRODT A J. Cellular automata and complexity[J]. Computers in Physics, 1995, 9(1):55-55
[14] 靳祯. 网络传染病动力学建模与分析[M]. 北京:科学出版社, 2014.
[15] 田蓓蓓, 李青, 周美莲. 复杂网络上病毒传播的元胞自动机模拟[J]. 计算机工程, 2008, 34(23):78-279 TIAN B B, LI Q, ZHOU M L. Simulation of cellular automata for virus propagation on complex network[J]. Computer Engineering, 2008, 34(23):78-279
[16] WOLFRAM S. Cellular automata as models of complexity[J]. Nature, 1984, 311(5985):419-424
[17] WOLFRAM S. Theory and applications of cellular automata[J]. World Scientific, 1986, 43(12):1346-1357
[18] 金小刚. 基于Matlab的元胞自动机的仿真设计[J]. 计算机仿真, 2002, 19(4):27-30 JING X G. The simulation of cellular automata based on matlab[J]. Computer Simulation, 2002, 19(4):27-30
[19] 游爱丽. 基于元胞自动机的SIR传染病模型[D]. 乌鲁木齐:新疆大学数学与系统科学学院, 2010.
[20] APENTENG O O. The use of cellular automata for modelling (Sir)N diseases with migratory reinfection[C]//International Conference on Computer Research and Development. New York:ASME, 2013.
[21] SATSUMA J, WILLOX R, RAMANI A, et al. Extending the SIR epidemic model[J]. Physica A Statistical Mechanics & Its Applications, 2004, 336(3):369-375
[22] SIRAKOULIS G C, KARAFYLLIDIS I, THANAILAKIS A. A cellular automaton model for the effects of population movement and vaccination on epidemic propagation[J]. Ecological Modelling, 2000, 133(3):209-223
[23] MITCHELL M, CRUTCHFIELD J P, HRABER P T. Evolving cellular automata to perform computations:mechanisms and impediments[J]. Physica D Nonlinear Phenomena, 1994, 75(1-3):361-391
[1] 高京广； 孙有发； 张成科； . 变种群量的SIRS型传染病模型及控制策略[J]. 广东工业大学学报, 2008, 25(3): 31-35.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2017 《广东工业大学学报》编辑部
地址：广州市东风东路729号广东工业大学 邮编：510090
电话：020-37626653,020-37626139,020-37626396
邮箱：xbzrb@gdut.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发