Duan Huiming, Nie Weige
School of Science, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China.
Physica A. 2022 Sep 15;602:127622. doi: 10.1016/j.physa.2022.127622. Epub 2022 May 30.
The COVID-19 pandemic has lasted for nearly two years, and the global epidemic situation is still grim and growing. Therefore, it is necessary to make correct predictions about the epidemic to implement appropriate and effective epidemic prevention measures. This paper analyzes the classic Susceptible Infected Recovered Model (SIR) to understand the significance of model characteristics and parameters, and uses the differential and difference information of the grey system to put forward a grey prediction model based on SIR infectious disease model. The Laplace transform is used to calculate the model reduction formula, and finally obtain the modeling steps of the model. It is applied to large and small numerical cases to verify the validity of different orders of magnitude data. Meanwhile, data of different lengths are modeled and predicted to verify the robustness of model. Finally, the new model is compared with three classical grey prediction models. The results show that the model is significantly superior to the comparison model, indicating that the model can effectively predict the COVID-19 epidemic, and is applicable to countries with different population magnitude, can carry out stable and effective simulation and prediction for data of different lengths.
新冠疫情已持续近两年，全球疫情形势依然严峻且呈蔓延之势。因此，有必要对疫情做出正确预测，以便实施恰当有效的防疫措施。本文对经典的易感-感染-康复模型（SIR）进行分析，以了解模型特征及参数的意义，并利用灰色系统的微分和差分信息，提出一种基于SIR传染病模型的灰色预测模型。运用拉普拉斯变换计算模型简化公式，最终得出该模型的建模步骤。将其应用于大小数值案例，以验证不同数量级数据的有效性。同时，对不同长度的数据进行建模和预测，以验证模型的稳健性。最后，将新模型与三个经典灰色预测模型进行比较。结果表明，该模型显著优于对比模型，这表明该模型能够有效预测新冠疫情，适用于不同人口规模的国家，能够对不同长度的数据进行稳定有效的模拟和预测。
