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.
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).
