Global Stability of a Mumps Transmission Model with Quarantine Measure  

作　　者：Yu-zhen BAI Xiao-jing WANG Song-bai GUO 

机构地区：[1]School of Science,Beijing University of Civil Engineering and Architecture,Beijing,102616,China [2]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing,100190,China

出　　处：《Acta Mathematicae Applicatae Sinica》2021年第4期665-672,共8页应用数学学报（英文版）

基　　金：This work is supported in part by the National Natural Science Foundation of China(Nos.11901027 and 11871093);the Scientific Research Project of Beijing Municipal Education Commission(No.KM201910016001);the Pyramid Talent Training Project of BUCEA(JDYC20200327);the Bill&Melinda Gates Foundation(INV-005834);the Fundamental Research Funds for Beijing Universities(X20083).

摘　　要：In this paper,a model of mumps transmission with quarantine measure is proposed and then the control reproduction number Rc of the model is obtained.This model admits a unique endemic equilibrium P*if and only if Rc>1,while the disease-free equilibrium P0 always exists.By using the technique of constructing Lyapunov functions and the generalized Lyapunov-LaSalle theorem,we first show that the equilibrium P0 is globally asymptotically stable(GAS)if Rc≤1;second,we prove that the equilibrium P*is GAS if Rc>1.Our results reveal that mumps can be eliminated from the community for Rc≤1 and it will be persistent for Rc>1,and quarantine measure can also effectively control the mumps transmission.

关 键 词：mumps transmission model control reproduction number quarantine measure global stability 

分 类 号：O175[理学—数学] R512.1[理学—基础数学]