关键词: 新冠肺炎疫情, 滚动灰色GM(1,1)模型, 传染病动力学模型, 情景重建

Abstract: In the past 20 years, a series of major public health emergencies such as SARS(2003),H1N1(2009), MERS(2012), Ebola(2014), Zika(2016), and COVID-19(2019) have broken out in the world. These major public health emergencies have not only severely threatened human health and life safety but also dealt heavy blows to the global economy. Taking the COVID-19 pandemic as an example,General Secretary Xi Jinping emphasized that the COVID-19 pandemic is “the most serious global public health emergency since the end of World War II”. This epidemic is not just a test for any one country, but a massive trial for the whole world. As of January 15, 2022, the total number of confirmed COVID-19 infections worldwide had reached 324 421 646, with a cumulative death toll of 5 543 545.
After the occurrence of a sudden public health event,it is vitally important to promptly grasp the epidemic's development pattern and accurately predict the spread of the epidemic, which is of significant reference value for emergency prevention and control of major epidemic outbreaks. Among them,infectious disease dynamics models, as the most effective means of epidemic spread evolution modeling,are significantly influenced by different prevention and control measures in their construction. However, this method requires high-quality parameter data, and any slight error may lead to a large discrepancy between the final prediction results and the actual data. On the other hand,the grey GM(1,1) model is an essential tool for modeling and predicting scenarios with minimal data and poor information. To fully utilize the advantages of both models and improve the fitting accuracy of the model, a combined optimization model is constructed by integrating them to predict the development trend of the epidemic.
This paper takes the scenario reconstruction of the COVID-19 epidemic in Wuhan as an example. Firstly,considering the priority of new and old information,a rolling mechanism is adopted to dynamically update the initial values of data series,and a rolling grey GM(1,1) model is constructed for predicting the trend of the epidemic changes. Then,the SEIH₁H₂RD infectious disease dynamics model is modified by integrating the prediction results of the rolling grey GM(1,1) model. Notably,this model takes into full account many realistic influencing factors such as city lockdowns and the construction of emergency hospitals. Lastly,to verify the fitting effect of the modified model,a posterior difference test is used to analyze the fitting accuracy between the model fitting results and actual epidemic data. We also examine the influence of different rolling decision cycle values in the rolling grey GM(1,1) model on the model's fitting accuracy. Moreover,to fully demonstrate the corrective effect of the rolling grey GM(1,1) model on the infectious disease dynamics model,we apply different preference coefficients for quantitative analysis.
The results of the numerical tests show that: 1)The infectious disease dynamics model,modified by the rolling grey GM(1,1) model proposed in this paper,performs well in both short-term and long-term modeling fitting. This model fully integrates the absolute advantage of the grey GM(1,1) model in short-term prediction and the astonishing effect of the infectious disease dynamics model in fitting the long-term development trend of the outbreak. It expands the application space of different models,promotes the cross-fusion of different models,and improves the fitting accuracy of a single model. 2)Although the rolling grey GM(1,1) model has some corrective effect on the infectious disease dynamics model,it is not the case that the larger the weight of the rolling grey GM(1,1) model,the better. There is a threshold effect in the weight distribution between the two.
To facilitate the calculation,this paper only uses the equivalent interval value method to study the impact of different preference coefficient values on model performance. In the future,we will research introducing intelligent algorithms to determine the optimal value of preference coefficients,thereby making the prediction model have better adaptive performance.

Key words: COVID-19, rolling grey GM(1,1) model, epidemic model, scenario reconstruction