Study On The Dynamics Of COVID-19 Epidemic Models

In order to study the spread trend of the coronavirus disease 2019(COVID-19),and explore the influences of isolation,vaccination and the environmental viruses on the transmission of COVID-19,furthermore,seek optimal strategies for prevention and control,we establish three classes of infectious diseases models,then carry out dynamic analysis and numerical simulations.The researches include the followings:The first part mainly introduces the development process of COVID-19,the spread status and the current research situation of COVID-19 infectious disease at home and abroad,and the related theories are provided.In the second part,based on the transmission mechanism of the COVID-19,we develop a kind of SEIAHRMSq Eq infectious disease model with isolation and treatment measures,then calculate the control reproduction number and analyze the sensitivity of parameters of the control reproduction number,finally,numerical simulations are carried out.The results show that the scale of outbreak can be decreased by reducing the contact rate.According to the transmission mechanism and the spread status of COVID-19 in South Korea,the third part builds an SEUIR infectious disease model incorporating vaccination and isolation measures.Firstly,the control reproduction number of the model is calculated and the sensitivity analysis are given,then the final scale of the model is inferred.Finally,numerical simulations are conducted on the coverage rate of vaccination and the effectiveness of the isolation measures.The numerical simulations indicate that increasing the coverage rate of vaccines and enhancing people’s awareness of prevention can effectively reduce the scale of outbreak.In the fourth part,comprehensively considering the impact of vaccination and environmental virus on the spread of COVID-19,an SEIARW infectious disease model is established.First,the control reproduction number of the model is calculated,and then by constructing Lyapunov function,the global stability of the disease-free equilibrium and the endemic equilibrium are proved,and then sensitivity analysis and numerical simulations are carried out.The numerical simulations indicate that effective elimination of viruses in the environment and continuous improvement of vaccine coverage are effective measures for controlling the outbreak of COVID-19.