Study On Robustness Of TD-SIR Model For COVID-19 Epidemic

Since ancient times,human beings have been fighting against infectious diseases,such as pestis,smallpox,influenza,SARS and so on.Every time a virus strikes,people are caught off guard.It can be said that the history of human development is also a history of human struggle against infectious diseases.Now,with the development of human science and technology,human medicine has made great progress,and many of the previously difficult problems have been solved one by one,further opening the door to the micro world,improving human awareness of preventing and resolving unknown virus risks,and providing people with more means to respond to the epidemic.However,in December 2019,a sudden COVID-19 began to spread all over the world.Its infectious capacity and speed were unexpected,making it the largest "Black swan"incidents in 2020,which has brought great resistance to the development of the world economy.In the absence of effective vaccines,how to take precautions in advance is particularly important.Mathematical and statistical models have attracted much attention in the study of the COVID-19 due to their advantages of quantification,scientificity,accuracy and reliability.The rich research achievements of many scholars at home and abroad in this field also prove that mathematical and statistical models have broad application prospects in epidemic research.Based on the good characteristics of mathematical and statistical models,this article strives to establish models through research on the development of infectious disease models in the epidemic situation.In order to increase the accuracy and practicality of epidemic development prediction,the specific methods are as follows.First of all,considering that complex variants of the model require more parameters to be set,resulting in increased uncertainty in the model,this paper selects the SIR model as the basic model for research.This type of model is a coupled nonlinear ordinary differential equation,which is difficult to obtain analytical solutions.The Runge kutta algorithm is specifically selected to solve the numerical solution of the model,transforming the prediction problem into a simple parameter estimation problem.At the same time,in order to characterize the complex changes in the epidemic situation,a sliding time window is set in the parameter estimation to obtain a parameter sequence that continuously changes over time.Secondly,COVID-19 not only has a high degree of similarity to the symptoms of influenza virus infection,but also has situations such as asymptomatic infection.Data statistics may deviate from the actual situation,and the data has significant uncertainty.We have set parameter uncertainty intervals to measure data uncertainty through parameter uncertainty intervals,and increase prediction accuracy through interval prediction,making the prediction curve more realistic.Finally,an empirical study was conducted on the epidemic development in 14 provinces in China,such as Beijing and Shanghai,and 6 countries,such as the United States and France.In domestic prediction,under better epidemic prevention and control measures,each province can obtain better prediction results;In foreign prediction,due to the absence of epidemic prevention,there are many uncontrollable factors leading to the development of the epidemic,and there are small deviations in the prediction results.Therefore,we have improved the prediction effect of foreign epidemic situations by increasing the classification of dead people and improving the model.At the same time,in order to verify the impact of various parameters during the development of the epidemic,we have also added the re-infection rate to explore its impact on the development of the epidemic.The study found that during the actual infection process,multiple infected populations have a small impact on the development of the epidemic and will not cause large-scale transmission of the epidemic.In addition,this article also introduces the LSTM algorithm to extend the prediction days,which can be more effective in advance prevention.