一类具有追踪隔离及媒体效应的SEQIR传染病模型动力学分析

A Class of SEQIR Infectious Disease Models with Tracking Isolation Rate and Media Effect

为了研究追踪隔离以及媒体效应对疾病传播的影响,基于经典的SIR传染病模型,建立了一类具有追踪隔离及媒体效应的SEQIR传染病模型。利用下代矩阵方法给出了模型的基本再生数R_(0),基于R_(0)给出模型无病平衡点以及地方病平衡点的存在性。当R_(0)<1时,无病平衡点是全局渐近稳定的;当R_(0)>1时,模型存在唯一的地方病平衡点,利用数值模拟得到了地方病平衡点的全局渐近稳定性。借助数值模拟,分析了追踪隔离以及媒体效应对疾病传播的影响,提高媒体报道中相关信息的准确率,可以提高染病者的追踪隔离率,减少感染人数,从而控制疾病的传播。

In order to study the impact of tracking isolation and media effect on disease transmission,a class of SEQIR infectious disease model with tracking isolation and media effect is developed based on the classical SIR infectious disease model.Firstly,the basic regeneration number R_(0)of the model is given by the next-generation matrix method,and the existence of the disease-free equilibrium point and the endemic equilibrium point of the model is given based on the basic regeneration number R_(0).When R_(0)<1,the disease-free equilibrium point is global asymptotically stable,and when R_(0)>1,the model has a unique endemic equilibrium point,and the global asymptotic stability of the endemic equilibrium point is obtained by numerical simulation.Finally,with the help of numerical simulation,the effects of tracking isolation and media effects on disease transmission are analyzed.