Establishment And Stability Analysis Of Infectious Disease Model Based On Dynamic Data

The 2019 outbreak of the COVID-19 infectious disease occurred suddenly,spread rapidly,and the number of infected patients and deaths increased sharply,causing extremely serious damage to public health and socioeconomics.Research on the COVID-19 infectious disease is extremely valuable.This paper firstly establishes a combined model of SIR-Poisson and SIR-ARIMA based on epidemic data to describe the evolution of COVID-19.Secondly,based on the transmission mechanism of COVID-19,multiple mathematical models are established and the dynamic behavior of COVID-19 is analyzed.The main contents of this study are as follows:1.based on the real-time data of COVID-19 in Ukraine,combined with the characteristics of the early spread of the COVID-19 disease,the SIR-Poisson combined model and the SIR-ARIMA combined model were established.evolutionary laws and transmission risks.2.considering more factors in the transmission mechanism of COVID-19:incubation period,follow-up isolation,hospitalization,vaccination,etc.,based on the SEIR model,establishes the SEIPHR model of the disease,and further analyzes the dynamics of this model learning behavior.The positive invariance of the system solution,the stability of the disease-free equilibrium point,and the consistent persistence of the endemic equilibrium point are proved.And based on real-time data in Indonesia,the spread of COVID-19 in the region was simulated.3.considering the periodicity of the spread of the new crown epidemic,a SEIPHR infectious disease model with periodic coefficients is established.The disease-free equilibrium point is globally asymptotically stable if R₀<1,and the system has the existence of periodic solutions if R₀>1.With the help of numerical analysis,the rationality of the conclusions obtained by the model is verified.