Backward bifurcation,basic reinfection number and robustness of an SEIRE epidemic model with reinfection  

作　　者：Shaoli Wang Tengfei Wang Ya-Nen Qi Fei Xu 

机构地区：[1]School of Mathematics and Statistics Henan University Jinming Rd,Kaifeng 475001 Henan Province,P.R.China [2]Department of Mathematics WilfridLaurier University Waterloo,Ontario N2L 3C5,Canada

出　　处：《International Journal of Biomathematics》2023年第8期47-74,共28页生物数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(U21A20206);Natural Science Foundations of Henan(192102310089,202300410045).

摘　　要：Recent evidences show that individuals who recovered from COVID-19 can be reinfected.However,this phenomenon has rarely been studied using mathematical models.In this paper,we propose an SEIRE epidemic model to describe the spread of the epidemic with reinfection.We obtain the important thresholds R_(0)(the basic reproduction number)and R_(c)(a threshold less than one).Our investigations show that when R_(0)>1,the system has an endemic equilibrium,which is globally asymptotically stable.When R_(c)<R_(0)<1,the epidemic system exhibits bistable dynamics.That is,the system has backward bifurcation and the disease cannot be eradicated.In order to eradicate the disease,we must ensure that the basic reproduction number R_(0) is less than R_(c).The basic reinfection number is obtained to measure the reinfection force,which turns out to be a new tipping point for disease dynamics.We also give definition of robustness,a new concept to measure the dificulty of completely eliminating the disease for a bistable epidemic system.Numerical simulations are carried out to verify the conclusions.

关 键 词：SEIRE epidemic model global asymptotical stability backward bifurcation basic reinfection number ROBUSTNESS 

分 类 号：O175[理学—数学]