Dynamic Behavior Analysis And Prediction Of The Novel Coronavirus Pneumonia Syste

In this paper,two kinds of infectious disease models with latent period(SEIR1and SEIR2)are established.Then,the stability theory of differential equation and functional differential equation theory are used to conduct qualitative analysis on the above two kinds of infectious disease models,mainly discussing the existence and stability of equilibrium point.Finally,SEIR2 model is simulated and predicted by MATLAB software.The specific work is as follows:Firstly,a model of SEIR1 infection with bilinear incidence was studied.The basic regeneration number,which is the key parameter to determine whether the disease is transmitted or not,was calculated.The conditional thresholds of the existence of equilibrium points are analyzed and discussed.By constructing Lyapunov function and applying Routh-Hurwitz criterion and La Salle theorem,it is proved that the disease-free equilibrium point is globally asymptotically stable.By using the second additive matrix and the correlation theorem of competitive systems,we obtain the sufficient condition that the positive equilibrium point is global asymptotic stability.Secondly,the SEIR2 infectious disease model with time delay and saturation incidence is studied.The basic regeneration number is obtained by using regeneration matrix,which determines the complete extinction or continuous survival of the disease.The expressions of disease-free equilibrium points and positive equilibrium points are obtained,and the conditional thresholds of all kinds of equilibrium points under different conditions are discussed.By constructing Lyapunov function and applying Routh-Hurwitz criterion and La Salle theorem,we can obtain the sufficient condition that both disease-free equilibrium points and positive equilibrium points have global asymptotic stability.Finally,based on the SEIR2 infectious disease model,the relevant data of the COVID-19 outbreak in Wuhan,Hubei province from January 28,2020 to July 23,2020 were selected.MATLAB software was used to predict the number of infected persons and the epidemic trend of COVID-19 in Wuhan,and the influence of isolation measures on the trend of the number of infected persons was further analyzed.The results showed that the short-term prediction effect of SEIR2 model was better than the long-term prediction effect of SEIR2 model.Moreover,the adoption of isolation measures has reduced the peak number of infected people to a certain extent,which can restrain the spread of infectious diseases to a certain extent.