key: cord-0940948-dxtbp4kd authors: Lin, S.; Qiao, Y.; Huang, J.; Yan, N. title: Research on the Influence of Effective Distance Between Cities on the Cross-regional Transmission of COVID-19 date: 2020-03-30 journal: nan DOI: 10.1101/2020.03.27.20044958 sha: f5aa1f504fab8faadb7b8da6b69cecc9665026c4 doc_id: 940948 cord_uid: dxtbp4kd The COVID-19 epidemic in China has been effectively controlled. It is of great significance to study the law of cross-regional spread of the epidemic, for the prevention and control of the COVID-19 in the future in China and other countries or regions. In this study, the cross-regional connection intensity between cities was characterized based on the probability and the effective distance of the shortest path tree, and the empirical analysis was carried out based on the high-frequency data such as the cases of COVID 19 outbreaks. It is concluded that the higher the intensity of inter-city connection, the larger scale the cross-regional spread of the epidemic. In December 2019, the novel coronavirus This study has several strengths. First, based on the theory of infectious diseases, the theory of complex network system and the characteristics of COVID-19, considering that the incubation period was still infectious, we propose an epidemic model which describes how people move between cities and spread disease; Second, the concept of "effective distance", which is not related to geographical distance, but related to transportation and population size, is introduced to analyze the effect of effective distance on epidemics and the transmission mechanism of the COVID-19; Third, big data and data mining technologies are used to retrieve the database of population migration data, Baidu Index and so on. Fourth, by applying the methods of descriptive statistics, multivariate analysis, econometrics, and the mathematical modeling methodology, we verified the effect of prevention and control efforts on reducing the transmission of COVID-19 among cities. The rest of the paper is organized as follows. Section 2 presents the literature review of the mathematical model of the epidemic transmission and how travel can contribute to the rapid spread of disease; Section 3 introduces a mathematical model of how COVID-9 flows and spreads disease between different cities; Research and assumption on model constructing and the meaning of each variable in the study and their sources are introduced in Section 4. Section 5 shows the empirical analysis result and combs the transmission mechanism of COVID-19; In the last section, we make a conclusion and discussion of the content and proposes the direction of future research. The epidemic of infectious diseases is a complex spreading process that occurs in population. There is a long history of modeling infectious disease epidemics (Anderson et al., 1992) , and various modeling paradigms have been developed. Kermark & Mckendrick (1927) proposed the classic SIR model, which is a compartmental model. Assuming that every individual is the same, the population is homogeneous mixing. The contact is instant and independent of history, infection rate and recovery rate are constant. All people in the same state form a compartment, and as the state changes, personnel move between the compartments. With the growth of urban population and the development of transportation networks, social mobility has increased, and the spatial expansion of infectious diseases has shown a new pattern. Especially when people move between different regions, the spread of infectious diseases is very common. Understanding the impact of human movement patterns on the prevalence of infectious diseases has attracted considerable attention (Gonzalez et al., 2008) , and a meta-population model derived from ecology has been applied in the field of infectious diseases. With the rise of complexity science, the micro-modeling specification has been developed and combined with social networks, a network-based micro-individual modeling method has been developed, which provides a new way to understand the spread of infectious diseases. These models enable epidemiologists and health authorities to understand the transmission process, predict its impact on healthy populations, and assess the After the outbreak of COVID-19 in Wuhan, most of the research focused on estimating the source, transmission characteristics and the estimation of the scale (Mizumoto et al., 2020; Zhou et al., 2020; Hébert-Dufresne et al., 2020; Fu et al., 2020; Yeo et al., 2020) . In particular, the basic reproduction ratio has been widely debated as a parameter that reflects the speed of virus transmission. Some literatures analyzed the spread of COVID-19 using population migration data, which are calculated based on the migration outflow from Wuhan (Zhan et al., 2020; Ding et al., 2020; Chen et al., 2020) , Little attention has been paid to the spread of the nationwide and even global cities caused by population migration. There is also a literature on how to intervene and control the spread of the COVID-19 virus (Qian et al., 2020; Heymann & Shindo, 2020) ; Gao et al., 2020) . Although there are many articles on the transmission mechanism of infectious diseases, the research on the law of transmission between regions is still insufficient. Especially with the development of modern transportation and the increasing scale of inter-regional and even All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10. 1101 transnational population movements, it is becoming increasingly difficult to grasp the spread of infectious diseases across regions. The transmission factors of the disease are extremely complicated, and it is closely related to the physical conditions of the virus carrier, the environment around, the weather, and the conditions of the contacts. We focus on the influence of spatial connection between cities on the COVID-19 epidemic. The population flow between cities is a key factor affecting the scale of inter-city virus transmission. The population flow is related to urban density and transportation. Brockmann & Helbing (2013) proposed a new concept of distance, which believes that the spread of disease is not related to the geographical distance between cities, but is closely related to the "effective distance" between cities. What is the effective distance? The effective distance between cities is the length selected by a passenger in various selectable routes from city i to city j. A passenger can be regarded as a random walking particle, who randomly visits the surrounding cities according to the traffic flow. After arriving at the next city, it is converted into a probability to visit the neighboring cities of the next city according to the traffic flow... Finally, the path which the particle most likely to choose from city i to city j is namely the most likely path. The length of this most likely path is the effective distance. We argue that this probabilistic effective distance is related to the flow of population and the degree of transportation convenience, and can reflect the strength of the spatial connection between cities. The effective distance varies with the strength of the spatial connection. This concept is more accurate than traditional connection strength calculations based on the size and distance of the two cities, such as economic connection, market potential, and market access; it is also more accurate than simply using the population flow to characterize the connection, because it cannot express the strength of the connection between the two cities, not to mention the convenience of the connection between the two cities. With probabilistic effective distances instead of conventional geographic distances, complex spatiotemporal patterns can be simplified into uniform wave transmission patterns. The effective distance is defined as the best path of transportation in the two cities, which depends on the Probabilistic traffic flow. Assume that mn p is the conditional probability from node n to destination m is All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which was not peer-reviewed) is The shorter the effective distance, the greater the probability that the epidemic will spread to the area, then the greater the possibility of increasing the number of imported cases, and the earlier the large-scale epidemic will outbreak (Brockmann & Helbing, 2013) . Because healthy individuals are constantly exposed to possible sources of pollution, as long as the lack of protective equipment and effective isolation, they face a serious risk of cross-infection. The can lead to the outbreak of COVID -19 (Read et al., 2020) . Based on the classic transmission model and the effective distance of Brockmann & Helbing (2013) , the mechanism of epidemic spread and control is shown in Figure 2 . Based on such understanding of the transmission mechanism, the hypothesis is put forward as follows: the smaller the effective distance, the earlier the outbreak, and the more infectious cases there are in the region. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10.1101/2020.03.27.20044958 doi: medRxiv preprint According to the above mechanism, the empirical model is constructed as follows: There are five kinds of data sources: (2) Baidu Search Index. Baidu Search Index will reflect a keyword search volume, and with the keyword related to "pneumonia", "syndromes", "mask", "COVID-19" and "travel restriction" will also appear in our search index. The search index can be used to judge the self-consciousness of citizens and explore their behavior trends. Based on the official website of health commission of Hubei Province (wjw.hubei.gov.cn), we obtained the trend of pneumonia epidemic with novel coronavirus infection over time in Hubei Province. (3) The history epidemic date and the trend of pneumonia epidemic with COVID-19 infection are obtained from the official Health Commission. According to regional health policy and measures of disease control and prevention, we evaluate the prevention and control intensity of cities by scoring mechanism. The earlier the policy is issued, the more strict the policy is, the more extensive the monitoring is, and the higher the score is. Proportion of emigration from other cites: the ratio of emigration from one cites in the overall emigration form all the other cities. Proportion of immigration to other cites：the ratio of immigration to one cites in the overall emigration to all the other cites. According to the proportion of emigration from Wuhan since January 1, 2020, it is found that most of the emigration population enters Hubei Province, Hunan Province, Jiangxi Province, Henan Province and Anhui Province. After cutting off the transmission of the virus, the proportion of moving out of Wuhan has decreased significantly. According to the migration big data of Baidu map, the cities with the largest emigration population before New Year's Eve in 2020 are the Pearl River Delta, Yangtze River Delta and Chengdu-Chongqing urban agglomerations. Shenzhen, Beijing, Shanghai, Guangzhou and Chengdu are the top five cities with the largest emigration population. In addition, Dongguan, Zhengzhou, Hangzhou, Xi'an and other cities are also cities with a large outflow of people before the Spring Festival. Recently, the work resumption was promoted orderly, and the number of people coming to the other places has increased gradually. The top five cities were Shanghai (4.58%), Shenzhen (3.73%), Chengdu (3.64%), Guangzhou (3.56%) and Beijing (3.06%). With the further migration return, central cities such as Shanghai, Shenzhen, Guangzhou, Chengdu, Chongqing and Beijing will face obvious pressure of prevention and control, and measures must be taken in advance to response to the large-scale migration. Let mn P is the fraction of travelers that leave node n and arrive at node m, the effective distance nm d from a node n to a connected node m is mn P log 1− , which is generally asymmetric nm mn d d  . High value All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which was not peer-reviewed) is High value All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10.1101/2020.03.27.20044958 doi: medRxiv preprint We assess the severity of COVID-19 by utilizing multisource datasets including cumulative and new cases of reported, death, cured and so on. Visualizing the Progression of the COVID-19 Outbreak see figure 6. Confirmed rate per million people: the number of confirmed cases for every million people. Cure rate for confirmed cases：how many people of the confirmed cases were cured and discharged，reflects the quality of medical treatment and cure condition. Mortality rate for confirmed cases: how many people of the confirmed cases have died， reflects the severity of the epidemic in this area. Diffusion index: the number of newly infirmed patients on that day / the cumulative number of infirmed on the previous day. Reduction index: (currently new cures + new deaths on the day) / cumulative confirmed cases on the previous day. We establish an evaluation system for the intensity of epidemic prevention and control, including: launching level 1 response, stop of inter-city passenger transportation, stop of ordinary public transportation in the city, stop of part of public places in the city, closed management of residential areas, centralized isolation of returnees from the key epidemic areas (Hubei) for 14 days, centralized isolation of returnees from non-key epidemic areas for 14 days, prohibition of local personnel to go out, centralized isolation of close contact of All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which was not peer-reviewed) is . https://doi. org/10.1101 org/10. /2020 confirmed patients for 14 days, isolation of suspected patients for medical observation and treatment. Each item is divided into full, partial, and no three items, with a score of 1, 0.5, and 0 respectively. The content and implementation time of the measures come from the information or announcements issued by epidemic prevention and control headquarters in prefectural-level districts. We will explore the relationship between effective distance from Wuhan and the number of COVID-19 cases confirmed in different cities. As shown in Figure 6 (b), the correlation between the proportion of the outflow of people from Wuhan and the number of cases is not significant on the whole. We analyze that there are two reasons cause the result: First, he incubation period of COVID-19 is long, the patients only have mild symptoms, such as fever, fatigue and cough. The paper titled " Time-varying transmission dynamics of Novel Coronavirus Pneumonia in China " published in the international medical authoritative journal "the New England Journal of Medicine" revealed that the average incubation period of new coronary pneumonia is 5.2 days ; Second is that the first cases reported in most cities are after January 20. Although the number of cases was not previously reported, the possibility of an earlier infection cannot be ruled out. It is estimated that the outbreak started much earlier, and both within China and international infectious exports occurred before January and in early January. Based on the analysis above, this paper considers the All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10. 1101 incubation period, and replaces the actual time of infection with the time of cases confirmed, and obtains the relationship between the flow of people out of the Wuhan and the number of pneumonia cases in the other cities, as shown in Figure 6 . From the data and figures above, we can see that if we take the incubation period into consideration, the cumulative confirmed cases are significantly related to the outflow of people from Wuhan, and the effect of effective distance on the new confirmed cases is significantly negative. regression results are shown in Table 2 . the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which was not peer-reviewed) is . https://doi. org/10.1101 org/10. /2020 In this paper, a variety of methods are used to test the robustness of the benchmark regression conclusion, shown in Table 3 . (1) Using multi-source datasets including cumulative number of reported, death, quarantined and suspected cases, cure rate for confirmed cases, mortality rate for confirmed cases as the explanatory variable, the result is also robust. (2) PPML method. Silva & tennero (2006) pointed out that if there is an option of heteroscedasticity or zero value (due to the fact that the number of initial case in many cities is zero), Poisson maximum likelihood model (PPML) should be used to test the robustness. (3) The effective distance is replaced by the absolute number of people moving out of Wuhan. the explained variable. After replacing explanatory variable, the regression result is also robust. (4)Different Sample time selection. The sample period of standard regression is from January 1st, 2020 to February 18th, 2020. However, there are still many events that may have a significant impact on the number of cases during the sample period, such as the Spring Festival and lockdown of the city. In order to test whether the choice of time period has an impact on the regression results, further regression is carried out according to the sub-samples before and after Wuhan has been locked down. In each sub-sample , the effect of effective distance on the number of new confirmed cases is always negative, which implies that results are robust. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which was not peer-reviewed) is The incubation period of the novel coronavirus is the main source of endogeneity. In this paper, we use the lag of effective distance as an instrument variable to address the endogeneity, which is shown in table 4. In this article, by introducing the effective distance to reflect the strength of the All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10. 1101 connection between cities and constructing an empirical model. it is concluded that: (1) the scale of local COVID-19 epidemic is closely related to the effective distance, that is, the strength of the connection between the two cities. The shorter the effective distance, the more newly confirmed cases and the more severe the local epidemic; (2) The greater the prevention and control efforts of urban epidemic, the more health institutions, the fewer cases there are; (3) The regions with higher per capita GDP have more population flow and more cases of epidemic cases; The more severe the outbreak, the higher the awareness of how to protect. According to the conclusions above, there are the following implications: First, strengthen cross-regional epidemic prevention and control linkages to achieve joint prevention and control between regions. The smaller the effective distance, the more convenient the connection between the two cities, the larger the scale of population flow, so the easier the epidemic will spread across regions, the more important it is for cross-regional cooperation to prevent and control the epidemic. In the future epidemic prevention and control, it's necessary to establish cross-region epidemic information sharing, prevention and control measures linkage, and medical resources collaboration. Second, strengthen comprehensive measures for comprehensive prevention and control of the epidemic. The large investment in prevention and control which has a large impact on the economy and society can control the epidemic in a short time and shorten the time of the impact of the epidemic on the economy and society. This requires comprehensive measures. On the one hand, the government, society, and residents should make concerted efforts to jointly control, accelerating the speed of epidemic control; on the other hand, we must strengthen the multi-faceted reserves of materials needed for epidemic prevention and control. the government, society, and residents jointly control and control, and work together to accelerate the speed of epidemic control; On the other hand, it is necessary to strengthen the multi-faceted stock of materials needed for epidemic prevention and control, so that comprehensive measures can be taken when the epidemic occurs Third, investment in public health resources should be strengthened. The more developed the city is, the easier it is for people to contact, and the larger the scale of population flow, the easier it is for the epidemic to spread. Therefore, the more developed the economy, the more it is necessary to increase investment in public health resources. All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10. 1101 Infectious diseases of humans: dynamics and control Is There a Case for Quarantine? Perspectives from SARS to Ebola The hidden geometry of complex, network-driven contagion phenomena Identify, isolate, inform: Background and considerations for Ebola virus disease preparedness in US ambulatory care settings Distribution of the COVID-19 epidemic and correlation with population emigration from wuhan, China. 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