Dynamic Characteristics Analysis Of COVID-19 Random SEQIR Mode

At present,the spread of COVID-19 is inevitably affected by random factors such as isolation measures and environment,which directly affects the mortality rate,recovery rate and other related parameters in the infectious disease model,so that the basic infectious disease model can be used to analyze COVID-19 The results are not ideal.Therefore,based on the traditional SEIR compartment model,this paper introduces the isolation index,constructs a stochastic SEQIR model and a stochastic SEQIR model considering vaccination,and uses theoretical knowledge such as stochastic differential equations and stochastic processes to analyze the kinetic characteristics of the constructed models.The main work is as follows:（1）The research background and research status of the current COVID-19 and in-fectious disease models are sorted out.For the existing basic infectious disease models such as SIR and SEIR,the impact of random factors such as isolation measures,vac-cination and environment on COVID-19 is not analyzed.For the issue of the influence of the virus development trend,a random SEQIR model and a random SEQIR model considering vaccination were constructed by adding isolation indicators and vaccination probability coefficients.（2）Using the next generation matrix method,the basic reproduction number of the disease is solved,and the threshold theory of disease extinction and continuation is proved based on the random SEQIR model under vaccination.（3）Prove the stability of the disease-free equilibrium point and the asymptotic prop-erty of the endemic equilibrium point of the COVID-19 stochastic model,and finally carry out numerical experiments to show that when R₀<1,the random The solution of the model is asymptotically stable near the disease-free equilibrium point of the determined model,which indicates that the disease will perish;when R₀>1,the solution of the stochastic model is determined in the endemic equilibrium of the model.It is asymptot-ically stable near the point,and the result shows that the disease will prevail.At the same time,it is also shown in the experiment that the larger the random interference,the greater the degree of fluctuation of the solution.