| Novel coronavirus pneumonia is a new type of infectious disease,human infection with the coronavirus can cause fever,cough,fatigue and even pneumonia,kidney failure,death.As of March 2022,COVID-19 is raging in almost every country on the planet,posing a huge threat to people’s lives and safety.Therefore,it is urgent to use the knowledge of infectious disease dynamics to establish a mathematical model to study the new crown pneumonia virus.This dissertation constructs a reasonable mathematical model for COVID-19.The first chapter introduces the main characteristics of COVID-19,the research results in existing papers,and the research content and related preliminary results of this dissertation.Chapter 2 establishes an SEIARV model with the asymptomatic infected person and saturation incidence.Firstly,the equilibrium of the model is given,and the non-negative and bounded property of the model solution is proved according to the theory of differential equations.Secondly,by constructing the Lyapunov function combined with La Salle invariant principle,the global stability of the equilibrium point is analyzed.Finally,taking Wuhan as an example,the data published by the National Health Commission were fitted to validate the model,and the parameters were modified to simulate the changes in the development of the epidemic under the intervention of the Chinese government.Chapter 3 establishes a stochastic SCEIAR model with asymptomatic infected people and continuous vaccination.On the basis of the existence of a global unique positive solution of the model,the stochastic analysis theories such as the It?o formula,the law of powerful numbers,and the Lyapunov function are applied to obtain the traversal stationary distribution of the model and the sufficient conditions for extinction,respectively.The analytical results show that the interference of environmental noise indeed affects the propagation of COVID-19.Chapter 4 summarizes this thesis and briefly discusses the future work. |
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