[1]陈娟,戴斌祥,李文秀.一类具有媒体报道的传染病模型[J].集美大学学报(自然版),2019,24(1):64-67.
 CHEN Juan,DAI Binxiang,LI Wenxiu.A Class of Epidemic Model with Media Coverage[J].Journal of Jimei University,2019,24(1):64-67.
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一类具有媒体报道的传染病模型()
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《集美大学学报(自然版)》[ISSN:1007-7405/CN:35-1186/N]

卷:
第24卷
期数:
2019年第1期
页码:
64-67
栏目:
数理科学与信息工程
出版日期:
2019-01-28

文章信息/Info

Title:
A Class of Epidemic Model with Media Coverage
作者:
陈娟1戴斌祥2李文秀3
(1.集美大学理学院,福建 厦门361021;2.中南大学数学与统计学院,湖南 长沙 410083;3.湖南大学数学与计量经济学院,湖南 长沙 410082)
Author(s):
CHEN Juan1DAI Binxiang2LI Wenxiu3
(1.School of Science,Jimei University,Xiamen 361021,China;2.School of Mathematics and Statistics,Central South University,Changsha 410083,China;3.School of Mathematics and Econometrics,Hunan University,Changsha 410082,China)
关键词:
媒体报道传染病模型局部稳定性全局稳定性
Keywords:
media coverageepidemic modellocal stabilityglobal stability
文献标志码:
A
摘要:
将媒体报道量M视为时间t的函数,利用非连续函数β/(1+εMI)来刻画媒体报道对传染率的影响,建立了一个分段光滑的SIM传染病模型,给出了模型的非负平衡点的存在性。利用微分方程线性化稳定性理论分析,得到了系统的各平衡点局部稳定的阈值条件,并进一步利用Poincare-Bendixon定理给出了正平衡点全局渐近稳定的充分条件。
Abstract:
In this paper,the media coverage M is considered as a function of time t.Using discontinuous function β/(1+εMI) to describe the influence of media coverage on the infection rate,a piecewise-smooth SIM epidemic model is established.The existence of the nonnegative equilibrium of the model is given.The local stability of the equilibrium of the system is obtained by using the linear stability theory of differential equations.A sufficient condition for global asymptotic stability of positive equilibrium is given by using the Poincare-Bendixon theorem.
更新日期/Last Update: 2019-03-10