Exploration on the evolutionary characteristics of COVID-19: a functional data view
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摘要:
目的 探索和分析COVID-19疫情发展以来各地COVID-19病例数随时间的演变特征，以发现疫情发展特点并比较不同的卫生防疫思路，为公共卫生管理积累经验。 方法 从函数型数据视角分析处理累计病例数据，采用函数型主成分分析刻画各地累计病例数据随时间变化的主要演变特征，并利用函数型主成分得分对各地累计病例数据曲线进行层次聚类，找出各地疫情演变发展的相似性。 结果 各地的累计确诊、治愈和死亡病例在各时段上分别保留了前3个主成分，反映了样本数据在不同时期的主要变异性。各时段上分别把各地聚成了5类，每类的国家随时间发展有所变动。 结论 全球疫情处于持续的起伏发展态势，分别在2020年6月底、9月底、11月底呈现反复的增长，表明目前尚未有有效办法遏制疫情，且聚类结果的变化也表明集中隔离和严格管控入境人员依然是目前较快速有效的防控措施。 Abstract:Objective We explored and analyzed the evolutionary characteristics of COVID-19 cases numbers in different regions over time since the outbreak of the epidemic, so as to compare kinds of prevention and control measures and gain experience for public health management. Methods From the perspective of functional data, we applied functional principal component analysis to catch the primary temporal characteristics in cases number data over several periods, and performed hierarchical clustering on daily cases curves from various countries based on functional principal component scores to find the similarities among states. Results The first 3 functional principal components were retained for cumulative confirmed, cured and death cases numbers of all countries over each time period, each reflecting certain variability pattern among data at different times. On each period, 5 clusters were obtained, and the countries in clusters has changed over time. Conclusions The global epidemic has been fluctuating that cases numbers repeatedly grew at the end of June, September and November in 2020, which shows that there has been no effective measures so far. Changes in the clustering results also indicated that centralized isolation and strict management of imported persons are still the relative fast and effective intervention measures. -
Key words:
- COVID-19 /
- Cases number /
- Functional data /
- Principal component analysis /
- Clustering
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图 1 第一、二时间段累计确诊、治愈、死亡病例数据的前3个主成分函数
Figure 1. The first 3 FPCs for accumulative confirmed, cured, death cases number on the first and second periods
图 2 第三、四时间段累计确诊、治愈及死亡病例数据的前3个主成分函数
Figure 2. The first 3 FPCs for accumulative confirmed, cured, death cases number on the third and fourth periods
图 3 第一、二时间段的国家聚类系谱图
Figure 3. Hierarchical clustering dendrograms of countries on the first and second periods
图 4 第三、四时间段的国家聚类系谱图
Figure 4. Hierarchical clustering dendrograms of countries on the third and fourth periods
表 1 各时段累计确诊、治愈、死亡病例数据各主成分的方差贡献率
Table 1. The percentage of variability of each FPC for accumulative confirmed, cured, death cases number on each time period
方差贡献率(%) 第一时间段 第二时间段 第三时间段 第四时间段 确诊 FPC1 53.87 45.72 29.17 54.47 FPC2 9.57 4.32 8.65 34.55 FPC3 36.53 49.91 62.18 10.95 治愈 FPC1 32.25 62.22 37.82 32.96 FPC2 26.24 34.37 3.74 39.34 FPC3 41.51 3.08 58.44 27.67 死亡 FPC1 50.34 32.99 23.07 54.68 FPC2 33.04 65.11 11.64 26.50 FPC3 16.61 1.88 65.29 18.81 
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表 2 各时段的国家聚类结果
Table 2. The clusters of countries on each time period
类别 第一时间段 第二时间段 第三时间段 第四时间段 第一类 中国(含港澳台地区) 美国 美国 印度 第二类 意大利 巴西 巴西 巴西 第三类 伊朗 印度、俄罗斯 印度 俄罗斯 第四类 韩国、英国、法国、西班牙、美国、德国 土耳其、伊朗、法国、西班牙、意大利、德国、秘鲁、智利 俄罗斯 意大利、德国、土耳其、哥伦比亚、阿根廷、西班牙、法国 第五类 比利时、奥地利、日本、泰国、智利、印度、埃及、俄罗斯、秘鲁、哥伦比亚、阿根廷、南非、土耳其、乌克兰、孟加拉国、新西兰、新加坡、希腊、巴西、加拿大、澳大利亚、马来西亚 中国(含港澳台地区)、加拿大、南非、孟加拉国、比利时、埃及、阿根廷、乌克兰、哥伦比亚、新加坡、日本、奥地利、韩国、新西兰、希腊、泰国、马来西亚、澳大利亚 法国、德国、意大利、伊朗、中国(含港澳台地区)、西班牙、韩国、比利时、奥地利、日本、泰国、智利、埃及、秘鲁、哥伦比亚、阿根廷、南非、土耳其、乌克兰、孟加拉国、新西兰、新加坡、希腊、加拿大、澳大利亚、马来西亚 加拿大、孟加拉国、智利、乌克兰、南非、伊朗、秘鲁、日本、奥地利、埃及、中国(含港澳台地区)、马来西亚、希腊、韩国、澳大利亚、新加坡、泰国、新西兰
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