Analysis on early spatiotemporal transmission characteristics of COVID-19

Wang Cong; Yan Jie; Wang Xu; Li Min

doi:10.7498/aps.69.20200285

Abstract

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:

Authors and contacts

1.
Department of Computer Science & Technology, Sichuan Police College, Luzhou 646000, China
2.
Institute of Sichuan Police Science, Sichuan Police College, Chengdu 610200, China
3.
Department of Road Traffic Management, Sichuan Police College, Luzhou 646000, China
4.
School of Movie and Media, Sichuan Normal University, Chengdu 610068, China
5.
School of Computer Science, Sichuan Normal University, Chengdu 610068, China

Corresponding author: Yan Jie, yan_jie@foxmail.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61602331)

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References

[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)Google Scholar
[22]	Sina.com. https://news.sina.com.cn/c/2020-02-21/doc-iimxxstf 3200725.shtml [2020-2-21]
[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
[28]	Cnchu.com. http://www.cnchu.com/jingxuan/guoji/345.html [2020-3-10]
[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]

Cited By

图 1 不同的$\beta $取值下实际累积发病人数与预测发病人数的对比　(a) 2019年; (b) 2020年

Figure 1. Comparing the actual cumulative number of cases and its estimations according to different$\beta $: (a) Year 2019; (b) year 2020.

DownLoad: Full-Size Img PowerPoint

图 2 武汉“封城”前夕迁徙指数与2019年的对比　(a)迁入规模指数; (b) 迁出规模指数

Figure 2. Comparing the migration index of Wuhan before the spring festival with the same period of 2019: (a) Inner migration index; (b) outer migration index.

DownLoad: Full-Size Img PowerPoint

图 3 各省区首达病例时间预测误差

Figure 3. The estimation errors of the first arrival times for each provinces.

DownLoad: Full-Size Img PowerPoint

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

DownLoad: CSV

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
截至时点	软件抓取法	蒙特卡罗法	实际发病人数	上报CCDC人数
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

DownLoad: CSV

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

DownLoad: CSV

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 $
截至时点	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

DownLoad: CSV

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

DownLoad: CSV

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
省份	0.2213	0.2159	0.2070	实际日期	省份	0.2213	0.2159	0.2070	实际日期
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

DownLoad: CSV

[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)Google Scholar
[22]	Sina.com. https://news.sina.com.cn/c/2020-02-21/doc-iimxxstf 3200725.shtml [2020-2-21]
[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
[28]	Cnchu.com. http://www.cnchu.com/jingxuan/guoji/345.html [2020-3-10]
[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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[18]	Tian Hui-Li, Liu Mu-Ren, Kong Ling-Jiang. A study on an improved Nagel-Schreckenberg traffic flow -model with open boundary conditions. Acta Physica Sinica, 2002, 51(12): 2713-2718. doi: 10.7498/aps.51.2713
[19]	Lü XIAO-YANG, KONG LING-JIANG, LIU MU-REN. ANALYSIS ON MACROSCOPIC EQUATION TO ONE-DIMENSIONAL RANDOM TRAFFIC FLOW MODELS. Acta Physica Sinica, 2001, 50(7): 1255-1259. doi: 10.7498/aps.50.1255
[20]	WANG BING-HONG, WANG LEI, HUI PAK-MING, HU BAMBI. THE GRADUAL ACCELERATING TRAFFIC FLOW GELLULAR AUTOMATON MODEL IN WHICH ONLY HIG H SPEED CAR CAN BE DELAYED. Acta Physica Sinica, 2000, 49(10): 1926-1932. doi: 10.7498/aps.49.1926

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Vol. 69, Issue 8 - 2020-04-20

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