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 descri...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.展开更多
In this paper,we evaluate the effect of the state of emergency for the first wave of COVID-19 in Japan,2020 from the viewpoint of mathematical modelling.In Japan,it was announced during the period of the state of emer...In this paper,we evaluate the effect of the state of emergency for the first wave of COVID-19 in Japan,2020 from the viewpoint of mathematical modelling.In Japan,it was announced during the period of the state of emergency from April 7 to May 25,2020 that the 80%reduction of the contact rate is needed to control the outbreak.By numerical simulation,we show that the reduction rate seems to have reached up to 86%.Moreover,we estimate the control reproduction number R c during the period of the state of emergency as R c?0:36(95%CI,0.34e0.39),and show that the effective reproduction number R e after the lifting of the state of emergency could be greater than 1.This result suggests us that the second wave of COVID-19 in Japan could possibly occur if any effective intervention will not be taken again.展开更多
基金supported by the National Natural Science Foundation of China(U21A20206)Natural Science Foundations of Henan(192102310089,202300410045).
文摘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.
基金This work was partially supported by the Japan Society for the Promotion of Science(JSPS)KAKENHI grant number 19K14594.
文摘In this paper,we evaluate the effect of the state of emergency for the first wave of COVID-19 in Japan,2020 from the viewpoint of mathematical modelling.In Japan,it was announced during the period of the state of emergency from April 7 to May 25,2020 that the 80%reduction of the contact rate is needed to control the outbreak.By numerical simulation,we show that the reduction rate seems to have reached up to 86%.Moreover,we estimate the control reproduction number R c during the period of the state of emergency as R c?0:36(95%CI,0.34e0.39),and show that the effective reproduction number R e after the lifting of the state of emergency could be greater than 1.This result suggests us that the second wave of COVID-19 in Japan could possibly occur if any effective intervention will not be taken again.
