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。
In this paper,the media coverage M is considered as a function of time t.Using discontinuous functionβ/(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.
作者
陈娟
戴斌祥
李文秀
CHEN Juan;DAI Binxiang;LI Wenxiu(School of Science,Jimei University,Xiamen 361021,China;School of Mathematics and Statistics,Central South University,Changsha 410083,China;School of Mathematics and Econometrics,Hunan University,Changsha 410082,China)
出处
《集美大学学报（自然科学版）》
CAS
2019年第1期64-67,共4页
Journal of Jimei University：Natural Science
基金
国家自然科学基金项目(51479215
11271371)
