河北工业科技2018，Vol.35Issue(2)：84-90,7.DOI:10.7535/hbgykj.2018yx02002
具有季节性和接种疫苗的元胞自动机传染病模型
A cellular automata model for epidemics with seasonal and vaccination
摘要
Abstract
In order to study the influence on the infectious desease control of a class of SIR epidemic models with seasonal and vaccination based on two-dimensional cellular automaton,a nonlinear discrete model is established by means of mean-field approximation.The model is analyzed mathematically.By calculating the spectral radius of the Jacobian matrix with the disease-free equilibrium,the local stability of the disease-free equilibrium is obtained.The relationship between the number of infected persons at the positive equilibrium point and the structure of the cell neighborhood is obtained by numerical simulating.And the effects of different initial patient settings on the disease transmission speed and the different vaccination rates on disease spread are considered.Through numerical simulation,the conclusion is gotten that when the initial patient is distributed at a central distribution,the speed of transmission is less than the velocity of the infectious disease when the initial patient is randomly distributed;with the increase of vaccination rate,the infectious disease transmission speed will decrease,which has greater impact on the initial distribution of patients as the center of cellular automaton.The study model has reference value in the dynamic research of controlling infectious disease transmission.关键词
微分动力学系统/元胞自动机/SIR模型/季节性/接种疫苗/平均场近似Key words
differential dynamical systems/cellular automata/SIR model/seasonality/vaccination/mean-field approximation分类
数理科学引用本文复制引用
王燕,刘茂省,李有文..具有季节性和接种疫苗的元胞自动机传染病模型[J].河北工业科技,2018,35(2):84-90,7.基金项目
山西省自然科学基金(2005011009) （2005011009）
山西省131人才工程项目 （）
山西省留学回国人员科技活动择优资助项目 （）
山西省回国留学人员科研资助项目(2016-086) （2016-086）
