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| 三种数学模型在新型冠状病毒肺炎预测中的应用 摘 要 2019 年 12 月，一种新型冠状病毒袭击了中国武汉，并且迅速蔓延到全国，对我国人民健康安全构成持续的威胁。疫情何时能被有效控制，成为全国乃至全世界人民关注的焦点。 本文针对病毒传播问题，使用系统动力学和统计学等方法，建立SEIR传染病模型、ARIMA模型和灰色新陈代谢预测模型，运用matlab和EViews等软件编程，对感染病毒的病例人数进行预测。 首先，对现阶段的武汉疫情发展进行分析，得出虽然新增确诊人数增速减缓，但形势依然不容乐观。 其次，针对病毒的传播，分析其特点，首先建立了具有多种影响因素且存在潜伏期的系统动力学SEIR传染病模型，通过已知数据拟合，确定参数，构建了一组的微分方程，最后运用matlab软件做出预测。 然后，针对疫情随时间的迅速发展，对数据进行处理，得到平稳的序列，建立了ARIMA模型。对模型进行识别、检验，对数据预测，效果较好。 最后，针对已经收集得到的病例数据，建立了灰色新陈代谢模型，根据过去的信息，经数据列的生成，建立可预测数学模型。将计算的结果替换最初的信息得到新序列，循环预测，得到的预测结果通过了相对残差和级比偏差的检验。 本文的运用多种方法，针对不同的影响因素对疫情进行预测，既对疫情走向和发展做出预测，又预测了患病人数。本文对模型进行了检验分析，还对模型的优点和缺点进行了评价，对模型进行了推广。 关键词：新型冠状病毒；SEIR模型；ARIMA模型；新陈代谢GM(1，1)模型；Matlab Abstract In December 2019, a new coronavirus attacked Wuhan, China, and quickly spread throughout the country, posing a constant threat to the health and safety of our people. When the outbreak can be effectively controlled, become the focus of the country and the world. In this paper, we use system dynamics and statistics to establish the SEIR infectious disease model, ARIMA model and gray metabolism prediction model for virus transmission, and use software programming such as matlab and EViews to predict the number of cases of virus infection. First, an analysis of the development of the epidemic situation in Wuhan at this stage shows that although the growth rate of the number of newly diagnosed people has slowed, the situation is still not optimistic. Secondly, to analyze the characteristics of the spread of the virus, the SEIR epidemic model of system dynamics with multiple influencing factors and incubation periods was first established. The known data was fitted to determine the parameters and a set of differential equations was constructed. Use matlab software to make predictions. Then, in response to the rapid development of the epidemic over time, the data was processed to obtain a stable sequence, and the ARIMA model was established. Identify and test the model and predict the data, the effect is better. Finally, based on the collected case data, a gray metabolism model was established. Based on past information, a predictable mathematical model was established through the generation of data series. Replace the calculated information with the original information to obtain a new sequence, and make a cyclic prediction. The obtained prediction result passes the test of relative residual error and order deviation. This article uses a variety of methods to predict the epidemic situation according to different influencing factors. It not only predicts the trend and development of the epidemic situation, but also predicts the number of patients. In this paper, the model is tested and analyzed, and the advantages and disadvantages of the model are evaluated, and the model is generalized. Key words: the novel coronavirus; SEIR model; ARIMA model; grey metabolism GM (1, 1) model; Matlab 目录 一、绪论4 1.1引言4 1.2 新冠肺炎的研究现状4 1.3 论文研究的主要内容5 二、模型假设与符号表示5 2.1 模型假设5 2.2 符号表示5 三、疫情发展的现状及其特点6 四、模型建立和求解7 4.1 SEIR模型的分析与建模7 4.1.1 SEIR模型的建立7 4.1.2 SEIR模型的求解并得出结果8 4.2 ARIMA模型的分析与建模9 4.2.1 ARIMA模型的建立9 4.2.2 ARIMA模型的求解并得出结果13 4.3 GM（1，1）模型的分析与建模14 4.3.1 GM（1，1）模型的建立14 4.3.2 GM（1，1）模型的求解并得出结果16 五、模型评价与改进18 5.1模型优点18 5.2 模型缺点18 5.3 模型改进19 六、模型推广19 七、参考文献19 |
