饱和接触率受媒体报道影响的SIR模型的研究  

Research on SIR Model with Saturating Contact Rate Affected Dy Media Coverage

作　　者：周苗 刘茂省[1] ZHOU Miao;LIU Mao-xing(School of Science,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《数学的实践与认识》2020年第20期148-155,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11571324,11701528);山西省“1331”重点创新团队;山西省自然科学基金项目(201801D121153);山西省131人才工程项目。

摘　　要：媒体报道在疾病的的预防和控制中起着至关重要的作用.通过构造合适的饱和接触率提出了一类SIR疾病传播模型,体现了媒体报道对疾病传播动力学的影响.首先计算基本再生数,分析平衡点的存在性;然后通过构造Lyapunov函数证明无病平衡点全局渐近稳定性;最后利用Routh-Hurwitz判据定理和第二加性复合矩阵分别证明了地方病平衡点的局部渐近稳定性和全局渐近稳定性.Media coverage plays a vital role in disease prevention and control.In this paper,a SIR disease transmission model is proposed by constructing a suitable saturating contact rate,which reflects the influence of media coverage on the dynamics of disease transmission.We first calculate the basic reproduction number and analyze the existence of the disease equilibrium point.Then the global asymptotic stability of the disease-free equilibrium was proved by Lyapunov function.Finally,the local asymptotic stability and global asymptotic stability of endemic equilibrium point are proved by using the Routh-Hurwitz criterion theorem and the second additive compound matrix,respectively.

关 键 词：媒体报道 饱和接触率 基本再生数 稳定性 

分 类 号：O175[理学—数学] R181[理学—基础数学]