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In this paper, a simple susceptible-infected (SI) model is build for simulating the early phase of COVID-19 transmission process. By using the data collected from the newest epidemiological investigation, the parameters of SI model is estimated and compared with those from some other studies. The population migration data during Spring festival in China are collected from Baidu.com and also extracted from different news sources, the migration characteristic of Wuhan city in the early phase of the epidemic situation is captured, and substituted into a simple difference equation model which is modified from the SI model for supporting migrations. Then several simulations are performed for the spatiotemporal transmission process of COVID-19 in China. Some conclusions are drawn from simulations and experiments below. 1) With 95% confidence, the infection rate of COVID-19 is estimated to be in a range of 0.2068–0.2073 in general situation, and the corresponding basic reproduction number R0 is estimated to be in a range of 2.5510–2.6555. A case study shows that under an extreme condition, the infection rate and R0 are estimated to be 0.2862 and 3.1465, respectively. 2) The Pearson correlation coefficient between Baidu migration index and the number of travelers sent by railway is 0.9108, which indicates a strong linear correlation between them, thus it can be deduced that Baidu migration index is an efficient tool for estimating the migration situation. 3) The epidemic arrival times for different provinces in China are estimated via simulations, specifically, no more than 1 day within an estimation error of 41.38%; no more than 3 days within an error of 79.31%, and no more than 5 days with an error of 95.55%. An average estimation error is 2.14 days. -
Keywords:
- COVID-19 /
- epidemic model /
- traffic flow /
- migration
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表 1 2019年累积发病人数
Table 1. The cumulative number of confirmed cases in 2019.
日期 人数 日期 人数 日期 人数 日期 人数 日期 人数 12/09 1 12/17 12 12/21 29 12/25 47 12/29 78 12/11 2 12/18 14 12/22 37 12/26 49 12/30 90 12/12 5 12/19 16 12/23 40 12/27 59 12/31 102 12/15 8 12/20 25 12/24 45 12/28 68 表 2 2020年各时间段累积发病人数
Table 2. The cumulative number of confirmed cases in each time slots in 2020.
截至时点 估计发病人数 实际发病人数 上报CCDC人数 软件抓取法 蒙特卡罗法 2019/12/31 102 49 102 0 2020/01/10 738 459 738—781 41 2020/01/20 6162 5800 6143—6187 291 2020/01/31 32661 29654 32633—32677 11821 2020/02/11 44692 69163 44672 44730 表 3 传染率
$\beta $ 可能的取值Table 3. Possible values of the infection rate.
截止日期 $\beta $ 置信区间 R2 截止日期 $\beta $ 置信区间 R2 2019/12/31 0.2213 [0.2152, 0.2274] 0.868 2020/01/11 0.2066 [0.2056, 0.2274] 0.990 2020/01/01 0.2171 [0.2116, 0.2225] 0.878 2020/01/12 0.2063 [0.2056, 0.2071] 0.993 2020/01/02 0.2168 [0.2127, 0.2209] 0.923 20200/1/13 0.2060 [0.2054, 0.2067] 0.995 2020/01/03 0.2159 [0.2127, 0.2191] 0.949 2020/01/14 0.2059 [0.2054, 0.2064] 0.997 2020/01/04 0.2155 [0.2130, 0.2179] 0.967 2020/01/15 0.2056 [0.2052, 0.2060] 0.998 2020/01/05 0.2138 [0.2118, 0.2159] 0.973 2020/10/16 0.2058 [0.2054, 0.2061] 0.998 2020/01/06 0.2127 [0.2109, 0.2144] 0.980 2020/01/17 0.2060 [0.2057, 0.2063] 0.999 2020/01/07 0.2109 [0.2093, 0.2126] 0.980 2020/01/18 0.2064 [0.2061, 0.2066] 0.999 2020/01/08 0.2091 [0.2075, 0.2107] 0.979 2020/01/19 0.2065 [0.2063, 0.2067] 0.999 2020/01/09 0.2080 [0.2067, 0.2094] 0.984 2020/01/20 0.2066 [0.2064, 0.2068] 0.999 2020/01/10 0.2067 [0.2054, 0.2080] 0.985 2020/01/21 0.2070 [0.2068, 0.2073] 0.999 表 4 重要时间节点的累积发病人数
Table 4. Cumulative confirmed cases in key time nodes.
截至时点 $\beta $ 0.2213 0.2159 0.2080 0.2066 2019/12/31 130 116 97 95 2020/01/10 1190 1001 777 753 2020/01/20 10870 8666 6220 5964 表 5 武汉市三大火车站发送旅客人数与迁出指数
Table 5. The Baidu inner migration index and the number of the travelers sent from Wuhan`s major railway stations.
日期 迁徙指数 人数/万 日期 迁徙指数 人数/万 日期 迁徙指数 人数/万 2020/01/10 6.6232 27 2020/01/22 11.8403 29.96 2019/01/29 7.0282 27.2 2020/01/11 7.5612 29.8 2019/01/21 4.5718 21.6 2019/01/30 7.1072 27.7 2020/01/12 6.2165 27 2019/01/22 4.6892 21.4 2019/01/31 7.4800 28.1 2020/01/13 5.7620 24.8 2019/01/23 4.8062 23 2019/02/01 8.7140 29.8 2020/01/15 5.9087 26.5 2019/01/24 4.8605 21.7 2019/02/02 9.6043 31.5 2020/01/16 6.0028 27.7 2019/01/26 7.0436 27 2019/02/03 9.2247 29.1 2020/01/19 7.4060 30 2019/01/28 6.7706 26.8 表 6 省级区域的首例到达时间
Table 6. The arrival times of each provinces.
省份 $\beta $ 实际日期 省份 $\beta $ 实际日期 0.2213 0.2159 0.2070 0.2213 0.2159 0.2070 安徽 01/06 01/06 01/07 01/07 辽宁 01/11 01/12 01/13 01/09 北京 01/07 01/07 01/08 01/08* 内蒙古 01/13 01/14 01/16 01/16 福建 01/09 01/09 01/10 01/06 宁夏 01/17 01/18 01/20 01/17 甘肃 01/10 01/11 01/12 01/04 青海 01/19 01/21 01/23 01/21 广东 01/05 01/05 01/06 01/04 山东 01/08 01/08 01/09 01/08 广西 01/08 01/09 01/09 01/13 山西 01/09 01/10 01/10 01/14 贵州 01/08 01/08 01/09 01/06 陕西 01/09 01/09 01/10 01/12 海南 01/10 01/11 01/12 01/13 上海 01/08 01/08 01/09 01/10 河北 01/08 01/09 01/09 01/13 四川 01/08 01/08 01/09 01/07 河南 01/04 01/04 01/05 01/03 天津 01/14 01/15 01/16 01/11 黑龙江 01/12 01/13 01/14 01/12 西藏 > 01/23 > 01/23 > 01/23 01/30 湖南 01/05 01/05 01/06 01/05 新疆 01/12 01/12 01/14 01/17 吉林 01/15 01/15 01/17 01/14 云南 01/09 01/11 01/10 01/07 江苏 01/06 01/07 01/07 01/10 浙江 01/07 01/07 01/08 01/04 江西 01/06 01/07 01/07 01/07 重庆 01/08 01/08 01/09 01/06 -
[1] Li Q, Guan X H, Wu P, Wang X Y, Zhou L, Tong Y Q, Ren R Q, Leung S, Lau E, Wong J, Xing X S, Xiang N J, Wu Y, Li C, Chen Q, Li D, Liu T, Zhao J, Li M, Tu W X, Chen C D, Jin L M, Yang R, Wang Q, Zhou S H, Wang R, Liu H, Luo Y B, Liu Y, Shao G, Li H, Tao Z F, Yang Y, Deng Z Q, Liu B X, Ma Z T, Zhang Y P, Shi G Q, Lam T, Wu J, Gao G, Cowling B, Yang B, Leung G, Feng Z J 2020 N. Engl. J. Med. 382 1199
Google Scholar
[2] Zhou T, Liu Q H, Yang Z M, Liao J Y, Yang K X, Bai W, Lv X, Zhang W 2020 J. Evid.-based Med. 20 3
[3] Zhang S, Diao M Y, Yu W B, Pei L, Lin Z F, Chen D C 2020 Int. J. Infect. Dis. 93 201
Google Scholar
[4] 曹盛力, 冯沛华, 时朋朋 2020 浙江大学学报 49 1
Google Scholar
Cao S L, Feng P H, Shi P P 2020 J. Zhejiang Univ. 49 1
Google Scholar
[5] 范如国, 王奕博, 罗明, 张应青, 朱超平 2020 电子科技大学学报 (in press)
Google Scholar
Fan R G, Wang Y B, Luo M, Zhang Y Q, Zhu C P 2020 J. Univ. Electron. Sci. & Tech. China (in press
Google Scholar
[6] Dirk B, Helbing D 2013 Science 342 1337
Google Scholar
[7] Wu J T, Leung K, Leung G M 2020 Lancet 395 e41
Google Scholar
[8] Wang J, Wang X, Wu J 2018 Proceedings of the 24th ACM SIGKDD Conference on Knowledge Discovery and Data Mining London, United Kingdom, Augest 19–23, 2018 p2830
[9] Yang Z F, Zeng Z Q, Wang K, Wong S S, Liang W H, Zanin M, Liu P, Cao X D, Gao Z Q, Mai Z T, Liang J Y, Liu X Q, Li S Y, Li Y M, Ye F, Guan W J, Yang Y F, Li F, Luo S M, Xie Y Q, Liu B, Wang Z L, Zhang S B, Wang Y N, Zhong N S, He J X 2020 J. Thorac. Dis. 12 2077
[10] Baidu.com. https://qianxi.baidu.com [2020-3-10]
[11] Chinese Center for Disease Control and Prevention. http://www.chinacdc.cn[2020-3-10]
[12] Cohen J 2020 https://www.sciencemag.org/news/2020/02/scientists-are-racing-model-next-moves-coronavirus-thats-still-hard-predict[2020-3-10]
[13] 中国疾病预防控制中心新型冠状病毒肺炎应急响应机制流行病学组 2020 中华流行病学杂志 41 145
Google Scholar
The Novel Coronavirus Pneumonia Emergency Response Epidemiology Team 2020 Chin. J. Epidemiol. 41 145
Google Scholar
[14] Chen X L, Zhou T S, Feng L, Liang J B, Lilgeros F, Havlin S, Hu Y Q 2019 Phys. Rev. E 100 032310
[15] Wang J, Wang L, Li X 2016 IEEE Trans. Cybernetics 46 2782
Google Scholar
[16] Chen L M, Holzer M, Shapiro A 2018 Chaos 28 013105
Google Scholar
[17] Chowell G, Viboud C, Hyman J, Simonsen L 2015 PLoS Currents 7 1
[18] Viboud C, Simonsen L, Chowell G 2016 Epidemics-Neth 15 27
Google Scholar
[19] Chen D B, Zhou T 2008 arXiv: 2003.00305 v1[Quantitative Biology]
[20] Wallinga J, Lipsitch M 2007 Proc. R. Soc. Lond, B 274 599
Google Scholar
[21] Guan W J, Ni Z Y, Hu Y, Liang W H, Ou C Q, He J X, Liu L, Shan S, Lei C L, Hui D, Du B, Li L J, Zeng G, Yuen K, Chen R C, Tang C L, Wang T, Chen P Y, Xiang J, Li S Y, Wang J L, Liang Z J, Peng Y X, Wei L, Liu L, Hu Y H, Peng P, Wang J M, Liu J Y, Chen Z, Li G, Zheng Z J, Qiu S Q, Luo J, Ye C J, Zhu S Y, Zhong N N 2020 N. Engl. J. Med. (in press)
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[23] Huanqiu.com https://china.huanqiu.com/article/9CaKrnKpveQ [2020-2-21]
[24] Lipsitch M, Cohen T, Cooper B, Robins J, Ma S, James L, Gopalakrishna G, Chew S K, Tan C C, Samore M, Fisman D, Murray M 2003 Science 300 1966
Google Scholar
[25] Ho H, Fraser C, Lam T, Ghani C, Leung G, Leung G, Chau Y K, Ho P L, Lo , Abu-Raddad L, Donnelly C, Anderson D, Chan K, Lee K, Lau E, Hedley A, RileyS, Tsang T, Ferguson N, Thach D T 2003 Science 300 1961
Google Scholar
[26] Wallinga J, Teunis P 2004 Am. J. Epidemiol. 160 509
Google Scholar
[27] 许小可, 文成, 张光耀, 孙皓宸, 刘波 2020 电子科技大学学报 (in press)
Google Scholar
Xu X K, Wen C, Zhang G Y, Sun H C, Liu B 2020 J. Univ. Electron. Sci. & Tech. China (in press
Google Scholar
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[29] Thepaper.cn. https://www.thepaper.cn/newsDetail_forward_5642450 [2020-3-10]
[30] Tenent.com. https://xw.qq.com/act/fytrace [2020-3-10]
[31] Tenent.com. https://new.qq.com/omn/BJC20200/BJC2020012401027800.html [2020-3-10]
[32] Sohu.com. https://www.sohu.com/a/371749528_100030926 [2020-3-10]
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