河北工业科技2018，Vol.35Issue(1)：7-11,5.DOI:10.7535/hbgykj.2018yx01002
异质网络下含有相关系数的SIR传染病模型的建立和分析
Establishment and analysis of SIR epidemic model with correlation coefficient under heterogeneous network
摘要
Abstract
In the course of disease transmission,how much contact between the infected and the susceptible is key factor of infectious diseases prevalence.Therefore,in order to study the dynamic behavior of correlation coefficients and its influence on the dynamics of disease transmission,with the correlation coefficient between the state nodes as dynamic variables,the SIR epidemic dynamic models with correlation coefficient is constructed by using deconvolution approximation method on heteroge-neous network.The existence of each equilibrium of the model is analyzed,and the condition for the existence of positive corre-lation coefficients between the infected and susceptible individuals is derived.In the Poisson distribution,the three-dimensional variation plot of the correlation coefficient under the equilibrium state is simulated.Through biological meaning,the final size of the system is given by probabilistic method.Through analyzing the SIR epidemic model with correlation coefficient,the compli-cate dynamics behavior of the SIR epidemic model is obtained,namely when the infected individuals tends to be zero,the corre-lation coefficient between the infected and susceptible individuals is not zero.The study model has reference value in the dynam-ic research of controlling infectious disease transmission.关键词
微分动力系统/相关系数/反卷积逼近/最终规模/平衡点Key words
differential dynamical systems/correlation coefficient/deconvolution approximation/the final size/equilibrium point分类
数理科学引用本文复制引用
杨婵,张菊平..异质网络下含有相关系数的SIR传染病模型的建立和分析[J].河北工业科技,2018,35(1):7-11,5.基金项目
国家自然科学基金(11501339) （11501339）
山西省回国留学人员科研资助项目(2014-020) （2014-020）
