摘要
在疾病传播过程中,染病者和易感者有多大的倾向接触是传染病是否流行的关键因素。为了研究相关系数在疾病传播过程中的动力学行为以及其对于传染病传播动力学特性的影响,将状态节点之间的相关系数作为动态变量,利用二元组的反卷积逼近方法,在异质网络上建立了含有相关系数的SIR传染病动力学模型,分析了系统平衡点的存在性,给出了染病者与易感者之间相关系数存在正值的条件。在泊松分布下,模拟出了平衡状态下相关系数的三维变化图。通过生物学意义,用概率的方法,给出了系统的最终规模。结果表明,通过分析含有相关系数的SIR传染病模型,得到SIR传染病模型复杂的动力学性态,即当染病者数量趋于零时,染病者与易感者之间的相关系数不为零。研究模型在控制传染病传播的动力学研究方面具有一定的参考价值。
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 heterogeneous network. The existence of each equilibrium of the model is analyzed,and the condition for the existence of positive correlation 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 complicate dynamics behavior of the SIR epidemic model is obtained,namely when the infected individuals tends to be zero,the correlation coefficient between the infected and susceptible individuals is not zero. The study model has reference value in the dynamic research of controlling infectious disease transmission.
出处
《河北工业科技》
CAS
2018年第1期7-11,共5页
Hebei Journal of Industrial Science and Technology
基金
国家自然科学基金(11501339)
山西省回国留学人员科研资助项目(2014-020)
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
differential dynamical systems
correlation coefficient
deconvolution approximation
the final size
equilibrium point
