Global stability of a SEIR epidemic model with infectious force in latent period and infected period under discontinuous treatment strategy  

作　　者：Yanjun Zhao Huilai Li Wenxuan Li Yang Wang 

机构地区：[1]College of Humanities and Sciences Northeast Normal University Changchun 130117,P.R.China [2]College of Mathematics,Jilin University Changchun 130022,P.R.China [3]College of Mathematics,Jilin Normal University Siping 136000,P.R.China

出　　处：《International Journal of Biomathematics》2021年第5期221-238,共18页生物数学学报（英文版）

基　　金：supported by the National Nature Science Foundation of China(11271154).

摘　　要：We consider a SEIR epidemic model with infectious force in latent period and infected period under discontinuous treatment.The treatment rate has at most a finite number of jump discontinuities in every compact interval.By using Lyapunov theory for discontinuous differential equations and other techniques on non-smooth analysis,the basic reproductive number Ro is proved to be a sharp threshold value which completely determines the dynamics of the model.If Ro<1,then there exists a disease-free equilibrium which is globally stable.If Ro>1,the disease-free equilibrium becomes unstable and there exists an endemic equilibrium which is globally stable.We discuss that the disease will die out in a finite time which is impossible for the corresponding SEIR model with continuous treatment.Furthermore,the numerical simulations indicate that strengthening treatment measure after infective individuals reach some level is beneficial to disease control.

关 键 词：Latent period infected period discontinuous treatment globally stable global convergence in finite time 

分 类 号：O17[理学—数学]