A Study Of Epidemic Model With Time-variant Parameter And Noise

Since the beginning of the 21st century,the process of globalization has accelerated and population movement has intensified.In terms of intuitive experience,infectious dis-eases occurring in a certain area may spread to the whole world if not controlled.There-fore,for different types of infectious diseases,building an appropriate infectious disease model is of great practical significance for understanding its dynamic process and how to prevent and control its spread.This article intercepts data on cumulatively infected individuals from the initial out-break of H1N1 influenza in the United States and Mexico from April 27 to June 28,2009.The SIR model and the SEIR model with time-varying parameters are proposed,and the experimental data is compared with the real data.The results show that the SIR model and SEIR model with time-varying parameters can simulate the real situation better.The former is in the overall trend while the latter is in better agreement with the real situation in the initial data.Then,the individual noise factor and the environmental noise factor are introduced.The experiment shows that the introduction of individual noise factor slightly increases the number of infected individuals predicted by the experiment;after the in-troduction of the environmental noise factor,even if the flow of individuals is slightly reduced,there will be a significant number of infected individuals reduce.Finally,the individual data of cumulative infections of COVID-19 pneumonia outside Hubei,China from June 2020 to March 2020 were intercepted and fitted with a time-varying parameter SIR model.The experimental data showed a good agreement with the real situation.In the case of population mobility,the differences in the results of the two models were discussed in the three cases of undirected flow,directed flow to the United States and directed flow to Mexico.Both models show that in the case of undirected and directed flow,when infected individuals move to areas with a large population,the number of infected individuals will eventually increase,while when they move to areas with a small population,the number of infected individuals will decrease.Among them,in the case of the SEIR model with time-varying parameters,when infected individuals flow to areas with a small population,the experimental data shows that there will be a obviously bistable point.