Dynamic Research Of Two Kinds Of COVID-19 Models And Empirical Analysis

The COVID-19 outbreak at the end of 2019 had a huge impact on people around the world,threatening their lives and health seriously.At the beginning of the epidemic,non-pharmaceutical interventions(NPIs)were taken by many countries to control the development of the COVID-19.With the successful development of the vaccine,the prevention and control of the epidemic entered a stage where NPIs and vaccination were taken together,and the epidemic gradually stabilized.However,with the development of the epidemic,variants have emerged and become more infectious,but the effectiveness of existing COVID-19 vaccine against variants has been reduced,which led to a large-scale outbreak and brought new challenges to the prevention of pandemic transmission.In this paper,two kinds of COVID-19transmission models are established to explore effective measures to control the development of the epidemic and provide theoretical support for the actual epidemic prevention and control.The main research work is as follows:(1)According to prevention and control interventions of the epidemic,a kind of COVID-19 transmission model with quarantine and vaccination is proposed.The basic reproduction number is obtained by using the next generation matrix method and it is discussed that the equilibrium is existent.The global asymptotic stability of the disease-free equilibrium is proved by using Lasalle invariant set principle.In addition,the sensitivity analysis of the basic reproduction number is carried out,and the stability of disease-free equilibrium is verified by numerical simulation.Finally,the effects of quarantine and vaccination on controlling the spread of the epidemic are discussed.(2)Considering the combined effects of quarantine,vaccination and variants of the COVID-19,a kind of COVID-19 transmission model applicable to the outbreak phase is established.The disease-free equilibrium and the basic reproduction number of the model are given.By using Routh-Hurwitz criterion and Lyapunov function method,respectively,the local and global asymptotic stabilities of the disease-free equilibrium are proved,and the existence of the endemic equilibrium is also discussed.Finally,numerical simulations are carried out to illustrate our main results.(3)The COVID-19 pandemic mainly caused by Delta variant in South Korea is analyzed by using the model applicable to the outbreak phase.The parameters to be estimated are obtained by two-stage fitting.The epidemic situation is predicted,and the prediction result is basically consistent with the actual data,which verifies the applicability of the model.In addition,the sensitivity analysis of the basic reproduction number is carried out by PRCC and the results show that the proportion of quarantine q,contact rate c,probability of infection β and vaccination rate ζ_v are the key factors affecting the development of the outbreak.Finally,the effects of quarantine and vaccination on the control of the COVID-19 are discussed by numerical simulations.The results show that improving the intensity of quarantine and enhancing the effectiveness of quarantine can greatly slow down the development of the epidemic.Meanwhile,accelerating vaccination and improving the effectiveness and durability of vaccine can effectively control the spread of the COVID-19.