Spatial Transmission Network Analysis of the COVID-19 Outbreak in a Megacity: A Study Based on 2994 Affected Locations in Xi'an in 2021

Spatial Transmission Network Analysis of the COVID-19 Outbreak in a Megacity: A Study Based on 2994 Affected Locations in Xi'an in 2021 | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Spatial Transmission Network Analysis of the COVID-19 Outbreak in a Megacity: A Study Based on 2994 Affected Locations in Xi'an in 2021 Zheng Chen, Zhangbo Yang, Qin Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3436409/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Utilizing patient trajectory data from 2050 case text documents, we constructed a location-contact network to analyze the spatial transmission of the late 2021 COVID-19 outbreak in a megacity of China. Employing complex network analysis, we had several significant findings. The network exhibited 266 components, indicating a relatively sparse network density. Notably, locations with a higher risk of transmission encompassed universities, convenience stores, agricultural markets, and restaurants. Moreover, we applied a network immunization strategy to simulate the impact of lockdowns at various location types on virus spread. Our results show that lock down "shops" and "restaurants" can significantly diminish network connectivity. COVID-19 Complex network analysis Policy simulation Figures Figure 1 Figure 2 Figure 3 1 Introduction Urban areas with dense populations, extensive commerce, industry, and well-developed transportation systems are more susceptible to infectious disease transmission [ 1 ]. The COVID-19 outbreak that began in December 2019 has repeatedly challenged the resilience of modern cities to epidemiological threats. Researchers have primarily used the SIS and modified SEIR models in epidemiology to simulate viral transmission networks. They discovered that a few "super-spreaders" caused the vast majority of infections, emphasizing the importance of government social lockdowns and mass vaccinations [ 2 – 7 ]. Social isolation policies, initiated in 2020, have become central to many nations' vaccination strategies, notably prolonging home confinement [ 5 ]. Nevertheless, these mandatory lockdowns have profoundly affected urban economic growth [ 1 ]. COVID-19, as a unique global pandemic, exhibits social attributes not found in conventional epidemics, necessitating a departure from traditional epidemiological models. Complex network analysis has been used to map the transmission network of confirmed COVID-19 cases, shedding light on its spread trends [ 8 – 10 ]. Migration and tourism, especially in the case of male return travelers, have significantly contributed to the worldwide dissemination of the epidemic [ 9 , 10 ]. The social attributes of COVID-19 lead to varying exposure risks among different socioeconomic groups [ 11 ], with vulnerable populations at a higher risk of infection due to frequent grocery shopping and increased mobility [ 2 ]. Existing research has primarily focused on macro-level analysis, such as global, national, and inter-provincial perspectives, with limited research on micro-level transmission within cities. Data collection primarily relies on confirmed cases in diverse regions, frequently overlooking the epidemic's transmission to specific localities. With the evolution of the new Coronavirus, it becomes increasingly contagious, and confirmed patients may leave a risk of spreading the virus in any location they visited prior to quarantine. Although most pneumonia studies stress the importance of urban containment and contact tracing for patients, there is a scarcity of research that delves into the detailed dynamics of urban outbreak transmission. Research suggests that restricting the maximum occupancy at places frequently visited by ‘super spreaders’ is more effective than uniformly reducing mobility [ 2 ]. Therefore, the identification of 'star nodes' in epidemic transmission holds significant relevance for guiding future epidemic prevention and control measures. To address these gaps, we conducted a case study on the December 2021 outbreak in Xi'an. Utilizing a complex urban location network, we analyzed the outbreak's propagation pathways, pinpointing nodes with significant viral transmission potential. Additionally, we categorized these locations and explored how specific location categories could reduce network connectivity through policy simulations. 2 Data and methods 2.1 Data source and background of the epidemic The data for this study were derived from official case reports released during the 2021 Delta variant of the COVID-19 epidemic in Xi'an City, China. Xi'an is the capital and megacity of Shaanxi Province, China, as well as the most important central city in western China. There were 13,163,000 residents in Xi'an at the end of 2021, with a 79.49% urbanization rate. In December 2021, an outbreak of the Delta variant imported by flight PK854, which entered the city from Pakistan, occurred in Xi'an. The Delta variant strain has a short incubation period, rapid transmission, a high viral load, a long core acid conversion time, and a greater risk of developing a critical illness [ 12 ]. The pathogenicity and critical illness rate of this variant is higher compared to that of Omicron. In contrast to two previous outbreaks in Guangdong province, this outbreak affected more than 2,000 people and was the largest outbreak of a new strain of Delta variant in China to date. By August 2023, four large outbreaks have been reported in China as a result of the Delta variant strain. In order to prevent and control the outbreak, the local government closed the city completely to prevent and control it. By the end of January 2022, there were no new confirmed cases of Delta in Xi'an. The dataset for this study was constructed from two data sources. The case contact network data were derived from the daily case reports published by the Shaanxi Provincial Health and Wellness Commission on its official website, and the case activity trajectory text data were derived from daily activity trajectories of new cases published by the Xi'an Municipal Government. The daily case reports from the Shaanxi Provincial Health Commission reported information on the age, sex, area of residence, date of diagnosis, date of isolation, and relationship to other confirmed cases for each new daily case from 9 December 2021 onwards. For each of the daily new cases from 9 December to the time of isolation and treatment, the Xi'an Municipal Government published the activity trajectory and the location name for each day. Both data sources start on 9 December 2021 and end on 18 January 2022 and are very informative. 2.2 Methods We first collated the case information report and the daily case activity trajectory report into two databases by text coding. As each diagnosed case has a unique ID code, we merged the two databases using this unique key variable and synthesized a two-mode network matrix containing all the diagnosed cases as well as the locations they visited. The rows of the matrix represent the diagnosed cases and the columns represent the locations visited. Any lattice value ( m, n ) in the matrix represents the number of times case m has been visited to location n . We binarize this matrix and transform the two-mode network into a one-mode network (1-mode network) containing only locations based on confirmed case nodes. In this network, any node i represents a location that is included in the activity trajectory of at least one case. If there exists at least one patient whose activity trajectory contains both different locations on a given day, i.e., at least one case has visited both places on a given day, then an edge is created between these two nodes in the network graph. The edge between the two points indicates that there is an outbreak transmission link between the two locations, reflecting patient movement between them. After forming the network, we visualized the network of locations. We used Complex Network Analysis to analyze this location network. Its basic analysis steps are as follows: 2.2.1 Whole Network Structure Analysis We used the following whole network metrics to analyze the structure of the location network: Network Density . Network density is used to measure the denseness of the relationship between pairs of nodes in the network [ 13 ]. It is mathematically expressed as: $$\begin{array}{c}\rho =\frac{2L}{n\left(n-1\right)}\#\left(1\right)\end{array}$$ where ρ denotes the network density, L denotes the total number of edges in the network, and n denotes the network size, i.e., the number of nodes in the network. For a given number of nodes, the greater the number of edges in the network, the greater the network density, the denser that network is, and the greater the risk of an epidemic spreading through the network. Average network path length . The average network path length is used to measure the length of the average network path between nodes [ 14 ]. It is reflected in this network as the average distance travelled from a location visited by a confirmed case to another location in the total graph. A shorter average path through the network indicates a higher level of accessibility between any two locations. This is expressed in a mathematical formula: $$\begin{array}{c}{C}_{B}\left(j\right)=\frac{2}{n\left(n+1\right)}\sum _{i\ge j}^{n}{d}_{ij}\#\left(2\right)\end{array}$$ where d ij represents the distance between node i and node j and n is the network size, i.e., the total number of nodes in the network. The shorter the average path length of the network, the higher the accessibility of the network, and a node needs only a few steps to connect to any other node in that network. Components . Components are the most straightforward criterion for partitioning cohesive subgroups [ 15 ]. A component is a subgraph in the network where every pair of nodes is connected by an edge, while there are no edges connecting any two connected components. Modularity . Modularity is a network clustering method proposed by the American statistical physicist Newman through community detection algorithms [ 16 ]. This method provides a clear evaluation metric for the quality of network community divisions. The Modularity algorithm is widely used for partitioning undirected graph networks. The formula for calculating modularity in undirected graphs is as follows [ 9 ]: where 'm' corresponds to the number of edges in the graph, 'k i ' denotes the degree of node 'i,' and 'A ij ' signifies the adjacency matrix. The study utilized Gephi software to partition the network according to modularity metrics. During the network visualization process, distinct color-coding was applied to different network partitions, culminating in the creation of the location network graph depicting the spread of the Xi'an city epidemic. 2.2.2 Analysis of nodes of high propagation capacity network In a network, the distribution of degrees is not even across nodes. A node with a high center in a network of locations indicates that the location is the core or key bridging point for disease dispersal, and enhanced crowd control at such locations can effectively prevent the spread of the epidemic. Network analysts measure the centrality of nodes by calculating a variety of network centrality metrics inductively. In this study, we introduce two network centrality metrics to parse the location network as follows: Degree centrality. If a node has a higher degree centrality, it means that the more locations the node is directly connected to, the more transmissible that location is for a new crown outbreak. In the context of patient contact networks, this metric demonstrates a robust correlation with the fundamental reproductive number of viral agents, making it a valuable indicator for assessing the rate of disease propagation [ 9 ]. The formula for its calculation is as follows: $$\begin{array}{c}{C}_{D}\left(i\right)=\sum _{j=1}^{n}{a}_{ij}\#\left(4\right)\end{array}$$ In this equation, i is a location visited by a confirmed case of an outbreak, j is a point connected to that location, and n is the network size. Degree centrality is the most intuitive measure of node power and importance. Eigenvector centrality. Eigenvector centrality (Eigencentrality), as defined by Jia et al. [ 17 ], serves as a measure of a node's significance within the network. However, it distinguishes itself by considering not only the node's inherent importance but also the significance of its neighboring nodes. The fundamental principle underlying its calculation posits that a node's centrality is intricately linked to the centrality of its neighboring nodes. Nodes with high eigenvector centrality in a network are usually those connected to nodes with a high degree centrality. The eigenvector centrality of l location i in the network is ECi, which is calculated as follows: $$\begin{array}{c}{\text{E}\text{C}}_{i}=c\sum _{j=1}{a}_{ij}{\text{X}}_{j}\#\left(5\right)\end{array}$$ where X j denotes the eigenvector centrality of node j, c is a constant of proportionality, and a ij is the number of links between location i and location j. When the steady state is reached after many iterations, it can be written in the following matrix form: $$\begin{array}{c}X=cAx\#\left(6\right)\end{array}$$ where x represents the eigenvector corresponding to the eigenvalue c-1 of matrix A. The higher the centrality of the eigenvector of a node, the higher its correlation with other nodes with high centrality, the more it resides in the center of the epidemic spreading network, the higher the risk of the epidemic spreading, and the more it needs to be prevented and controlled. Each of the above network indicators is calculated by Ucinet software and the Gephi network visualization tool. 2.2.3 Changes in network connectivity after removing different categories of nodes We would like to categorize locations within a real network to identify key categories influencing the outbreak spread. Instead of a city-wide blockade, we aim to pinpoint which categories, such as universities, convenience stores, and restaurants, can be selectively targeted for containment measures. We draw on prior studies [ 18 ] to model and analyze the impact of removing nodes from these specific categories on the network's connectivity. We classified the 2994 nodes into 14 categories based on the Foursquare place taxonomy. Foursquare, a cloud-based location technology platform and geographic information service network classifies global locations into over 1,200 categories, including 12 main top-level categories [ 19 , 20 ]. Based on the specific situation in China, we classify the following 13 categories (see it in Appendix A ): 3 Result 3.1 Statistics results of whole network indicators The Xi'an COVID-19 outbreak location network comprises 2,994 nodes, with 129 of them representing isolated nodes, accounting for 4.31% of the total node count. Isolated nodes indicate that a confirmed patient's trajectory includes only a single location. The network is characterized by 12,570 edges and a network density of 0.003, rendering it a sparse network. The average path length is 4.102, signifying that, on average, it takes approximately 4.1 steps to travel from one point on the graph to another. Figure 1 provides an overview of the network's structural distribution. Notably, there is a prominent large connectivity component surrounded by numerous smaller, more fragmented connectivity components, alongside multiple isolated nodes. The main component represents the largest connected segment of the network, encompassing the highest percentage of nodes within the total network graph. In this network, there are a total of 266 components, with the second largest connected component comprising merely 19 nodes, significantly smaller than the main component. Figure 2 visually depicts the primary component within the outbreak location network. This main component comprises 2,319 nodes, including all nodes with high degree centrality in this outbreak, and it is connected by a total of 11,466 edges. The network density within this main component is 0.004, and the average degree stands at 9.889, both exceeding the corresponding metrics for the entire network. Any node within this principal component that has been exposed to an infected individual is likely to disperse the disease across the entire network through connected trajectories. Furthermore, we've labeled nodes with the highest degree in each partition, which also indicates locations with a higher risk of transmitting the outbreak. 3.2 Network centrality indicators Table 1 shows the results of the measurement and calculation of each network centrality indicator. Table 1 Descriptive statistics results of network centrality indicators Variables Number Mean standard deviation Min Max degree 2,994 8.397 11.09 0 310 eigencentrality 2,994 0.0301 0.0543 0 1 Table 1 reveals that the average degree centrality is 8.397, suggesting that, on average, each location is connected to approximately 8.4 other locations. We normalized the eigenvector centrality results and ranked the centrality of each location in the network based on these metrics. The top ten locations in terms of both degree centrality and eigenvector centrality are displayed in Fig. 3 . In Fig. 3 , the top ten locations ranked by both centrality indicators are: Everyday Convenience Store, Mixue Ice City, Cainiao Pickup Point, Lanzhou Noodles, Changan University Main Campus, and Weishui Campus. This highlights these locations as crucial transmission nodes in the outbreak network. Among the top ten locations for degree centrality, there are three convenience stores, two food and beverage establishments. Mixue Ice City is the cheap drink shop with the most shops in mainland China. Keji 2nd Road Xi'an Optics Valley represents a residential area for Xi'an employees located next to a high-tech industrial park, while Cainiao Pickup Point serves as a major hub for one of China's largest express delivery companies. It's worth noting that Chinese residents frequently utilize offline platforms for sending and receiving parcels. 3.3 Changes in connectivity of the network after removing different categories of nodes The t-test results for the change in network centrality metrics after removing different categories of nodes are given in Table 2 . Table 2 T-test results for mean centrality metrics before and after removing similar nodes. Removed Variables Before removing Mean2 After removing Mean1 Mean Difference Shops degree 2994 8.397 2503 7.026 -1.371*** eigencentrality 2994 0.0300 2503 0.0320 0.00200 Vegetable Markets degree 2994 8.397 2775 7.937 -0.459 eigencentrality 2994 0.0300 2775 0.0310 0.00100 Parks and outdoors degree 2994 8.397 2979 8.375 -0.022 eigencentrality 2994 0.0300 2979 0.0300 0.00100 Travel degree 2994 8.397 2981 8.302 -0.095 eigencentrality 2994 0.0300 2981 0.0290 0.00100 Sports degree 2994 8.397 2979 8.379 -0.017 eigencentrality 2994 0.0300 2979 0.0300 0 Art and Entertaining degree 2994 8.397 2962 8.352 -0.0450 eigencentrality 2994 0.0300 2962 0.0300 0 Restaurants degree 2994 8.397 2229 5.887 -2.510*** eigencentrality 2994 0.0300 2229 0.0320 0.002 Educational Institutions degree 2994 8.397 2933 8.371 -0.0260 eigencentrality 2994 0.0300 2933 0.0310 0.00100 Universities degree 2994 8.397 2939 8.097 -0.300 eigencentrality 2994 0.0300 2939 0.0270 -0.003*** Workplace degree 2994 8.397 2762 7.794 -0.602*** eigencentrality 2994 0.0300 2762 0.0320 0.00100 Home degree 2994 8.397 2397 7.577 -0.820*** eigencentrality 2994 0.0300 2397 0.0290 -0.00100 Transport sites degree 2994 8.397 2950 8.113 -0.284 eigencentrality 2994 0.0300 2950 0.0280 -0.003* In Table 2 , 'Before removing' represents the sample size prior to the removal of nodes from individual categories, while 'After removing' reflects the sample size after removing nodes from these categories separately. The results in Table 2 demonstrate that the removal of nodes in the 'Shops,' 'Restaurants,' 'Workplace,' and 'Home' categories significantly reduces the mean degree of the entire network (p < 0.001). Furthermore, deleting nodes from the 'Universities' and 'Transport sites' categories results in a substantial decrease in network Eigenvector centrality (p < 0.001, p < 0.05). A high Eigenvector centrality suggests that nodes in these categories are closely connected to nodes with the highest or second-highest transmission capacity in the network, which suggests that venues in the 'Universities' and 'Transport sites' categories connected to more locations with equally high transmission capacity. 4 Discussion The primary objective of this study was to examine high-transmission capacity nodes within Chinese cities during the COVID-19 pandemic. Initially, the network analysis revealed 266 separate sub-networks within the city of Xi'an, with 129 isolated nodes. The existence of these isolated nodes implies that certain patients were diagnosed without any prior travel history. However, it is important to note that outbreaks do not materialize spontaneously. Thus, the presence of numerous isolated nodes and numerous small components is theoretically implausible, suggesting the presence of concealed transmission chains within this outbreak. Chang's (2021) study suggests that individuals with lower income may face a heightened risk of viral exposure [ 2 ]. In our research, we aimed to investigate this hypothesis further by refining node categories. We segmented the 'Restaurants' category into two subcategories: 'Small Restaurants' and 'High-end Restaurants', based on per capita consumption prices obtained from Baidu Maps, using a threshold of 50 RMB per person. We conducted another round of simulations involving the removal of nodes, revealing that deleting nodes from the 'Small Restaurants' category significantly reduced the average degree centrality of the entire network (p < 0.001). While removing nodes from the 'High-end Restaurants' category also led to a decrease in average degree centrality, the significance was somewhat lower (p < 0.05), and the difference in means is smaller (-0.502 virus − 1.970). However, the removal of 'High-end Restaurants' nodes resulted in a significant decrease in network Eigenvector centrality (p < 0.01). These findings suggest that Small eateries often possess a notably high capacity for viral transmission. In contrast, high-end restaurants, while having a lower direct viral transmission capability than the former, are linked to locations with comparable high transmission potential. Table 3 T-test results for mean centrality metrics before and after removing different ‘Restaurants’ category nodes Removed Variables Before removing Mean2 After removing Mean1 Mean Difference Small Restaurants degree 2994 8.397 2361 6.427 -1.970*** eigencentrality 2994 0.0300 2361 0.0300 0 High-end Restaurants degree 2994 8.397 2862 7.895 -0.502* eigencentrality 2994 0.0300 2862 0.0270 -0.003** Based on the aforementioned simulations and our previous analyses, we have identified the significant roles played by shops and small dining establishments in the overall network connectivity. Shops, encompassing convenience stores and supermarkets, serve as critical points for both the inflow and outflow of goods. They are susceptible to the introduction of virus-carrying frozen food, potentially leading to infections. Moreover, shops are frequented by a large number of people, and the intricate movement of individuals within these premises is a key factor facilitating the spread of outbreaks. Small dining establishments are more likely to contribute to outbreak transmission compared to medium to high-end restaurants. Small restaurants typically offer food without a high price threshold, catering to a broader consumer base compared to medium and high-end counterparts. These establishments feature compact spaces, high customer turnover, and offer dine-in, takeout, or delivery services, leading to a diverse clientele. We believe that implementing targeted enhancements in epidemic prevention measures at these nodes will yield a more substantial impact on the network's overall connectivity. Our findings further develop those of Eubank (2004), who investigated how many nodes batch deletions in smallpox propagation can lead to a substantial decrease in network connectivity through a simulation modelling approach [ 21 ]. We have refined this conclusion to pinpoint specific node categories. Our findings diverge from the simulation results reported by Martin (2020), which indicated that school closures do not significantly affect Hong Kong's urban containment policies [ 4 ]. In contrast, our research highlights the pivotal role of universities. Li et al.'s study (2023) investigates the impact of the pandemic on grocery shopping habits at the county level in the United States [ 22 ]. Designing specific strategies for safer grocery shopping is essential. Our study reveals that shops pose a high risk of viral transmission, emphasizing the importance of bolstering control measures at such locations. Examples include new food retail models such as centralized government food transport and community gardens. 5 Conclusion In this study, we utilized case data and trajectory text data from the December 2021 Delta variant outbreak in Xi'an to construct a complex network perspective of urban locations within the outbreak. Our analysis revealed valuable insights through the assessment of network metrics, ranking of centrality metrics. The whole location network is comprised of 266 connectivity components, with the largest containing 2,319 nodes. By examining centrality rankings, we identified locations at a heightened risk of contributing to outbreak spread, which encompass universities, convenience stores, agricultural markets, and small food establishments. Notably, each of Chang'an University's three campuses plays a central role in the outbreak's sub-center. Moreover, our study included a policy simulation focusing on the containment and control of specific network nodes. This simulation highlighted convenience stores and restaurants as the nodes with the greatest potential for propagating the outbreak, emphasizing their significance in outbreak transmission dynamics. However, this paper also acknowledges several limitations while offering insights for future research directions. During data collection, unclear node names, like 'convenience store,' hindered precise identification. In addition, the endogenous construction process of the location network can be further investigated by adopting models such as exponential random graphs. Finally, for greater external validity, future studies should explore urban epidemics across various contexts. Busse KR, Logendran R, Owuor M, Omala H, NandoyaE, Ammerman AS, Martin SL. Food vendors and the obesogenic food environment of an informal settlement in Nairobi, Kenya: a descriptive and spatial analysis. JUrban Health . 2023;100(1):76–87 References Florida R, Rodríguez-Pose A, Storper M. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3436409","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":240940108,"identity":"b03912c6-76a5-4781-8a56-b96e3c6ab670","order_by":0,"name":"Zheng Chen","email":"","orcid":"","institution":"Xi'an Jiaotong University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Zheng","middleName":"","lastName":"Chen","suffix":""},{"id":240940109,"identity":"f779b87f-9ff3-499a-9165-e2056afbee8d","order_by":1,"name":"Zhangbo Yang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3klEQVRIiWNgGAWjYPCCA3JADGIwE6/FmIHhMIlaEhsgqonQYnD87OEXDH/upG84eP6YBEOFdWID+9kD+LWcyUuzYOB5ljuz4TCbBMOZ9MQGnrwE/FoO5JgZMEgczu1nAGphbDuc2CDBY4Bfy/k3QC0Gh9PZwFr+EaPlRo7xA4aEwwn8YC0NRGiRvPHGDBhgzwyBfjG2SDiWbtzGk4NfC9/5HOMPwBCTN7hx8OGNDzXWsv3sZ/BrUTjAwCb9B8SSOMDAkACk2fCqBwJ5YBR+ALP4GwipHQWjYBSMgpEKAJijSPCVoYoSAAAAAElFTkSuQmCC","orcid":"","institution":"Xi'an Jiaotong University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Zhangbo","middleName":"","lastName":"Yang","suffix":""},{"id":240940110,"identity":"d554eabe-fa9d-4f63-bfb7-b3ea91c3d6e2","order_by":2,"name":"Qin Wang","email":"","orcid":"","institution":"Nanjing Audit University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Qin","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2023-10-12 09:12:04","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3436409/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3436409/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":44940917,"identity":"d8893172-01b8-4c4b-bd92-aeef70d89151","added_by":"auto","created_at":"2023-10-19 17:51:58","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1583333,"visible":true,"origin":"","legend":"\u003cp\u003eNetwork of delta outbreak locations in Xi'an city\u003c/p\u003e\n\u003cp\u003e(nodes: locations; edges: patients passing through two locations)\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-3436409/v1/d6d14340413049d1b69827e8.png"},{"id":44941856,"identity":"025c216e-cd61-4099-9632-4e030190c796","added_by":"auto","created_at":"2023-10-19 17:59:57","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1482270,"visible":true,"origin":"","legend":"\u003cp\u003eMain Component Subgraph of Xi'an Epidemic Location Network (n=2319)\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-3436409/v1/4435eb011f1ed4bc76fb645d.png"},{"id":44940915,"identity":"a7859f4e-1c10-4ff0-8121-682beeb12339","added_by":"auto","created_at":"2023-10-19 17:51:57","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":542825,"visible":true,"origin":"","legend":"\u003cp\u003eTop 10 locations for each centrality indicator\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3436409/v1/ea2257bc56d3714179e2c0ad.jpeg"},{"id":51836001,"identity":"f030e3c3-2eff-4530-ab8c-d0dab301063d","added_by":"auto","created_at":"2024-02-29 21:28:12","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3201111,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3436409/v1/62634f46-11d8-41ae-b7b2-ddf3dee80a52.pdf"},{"id":44940914,"identity":"f54d1547-bf71-480d-929d-ec6e79b51780","added_by":"auto","created_at":"2023-10-19 17:51:57","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":15090,"visible":true,"origin":"","legend":"","description":"","filename":"AppendixA.docx","url":"https://assets-eu.researchsquare.com/files/rs-3436409/v1/44260a4fefe31c9bf796eb50.docx"}],"financialInterests":"","formattedTitle":"Spatial Transmission Network Analysis of the COVID-19 Outbreak in a Megacity: A Study Based on 2994 Affected Locations in Xi'an in 2021","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eUrban areas with dense populations, extensive commerce, industry, and well-developed transportation systems are more susceptible to infectious disease transmission [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. The COVID-19 outbreak that began in December 2019 has repeatedly challenged the resilience of modern cities to epidemiological threats. Researchers have primarily used the SIS and modified SEIR models in epidemiology to simulate viral transmission networks. They discovered that a few \"super-spreaders\" caused the vast majority of infections, emphasizing the importance of government social lockdowns and mass vaccinations [\u003cspan additionalcitationids=\"CR3 CR4 CR5 CR6\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Social isolation policies, initiated in 2020, have become central to many nations' vaccination strategies, notably prolonging home confinement [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Nevertheless, these mandatory lockdowns have profoundly affected urban economic growth [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eCOVID-19, as a unique global pandemic, exhibits social attributes not found in conventional epidemics, necessitating a departure from traditional epidemiological models. Complex network analysis has been used to map the transmission network of confirmed COVID-19 cases, shedding light on its spread trends [\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Migration and tourism, especially in the case of male return travelers, have significantly contributed to the worldwide dissemination of the epidemic [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. The social attributes of COVID-19 lead to varying exposure risks among different socioeconomic groups [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], with vulnerable populations at a higher risk of infection due to frequent grocery shopping and increased mobility [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eExisting research has primarily focused on macro-level analysis, such as global, national, and inter-provincial perspectives, with limited research on micro-level transmission within cities. Data collection primarily relies on confirmed cases in diverse regions, frequently overlooking the epidemic's transmission to specific localities. With the evolution of the new Coronavirus, it becomes increasingly contagious, and confirmed patients may leave a risk of spreading the virus in any location they visited prior to quarantine. Although most pneumonia studies stress the importance of urban containment and contact tracing for patients, there is a scarcity of research that delves into the detailed dynamics of urban outbreak transmission. Research suggests that restricting the maximum occupancy at places frequently visited by \u0026lsquo;super spreaders\u0026rsquo; is more effective than uniformly reducing mobility [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Therefore, the identification of 'star nodes' in epidemic transmission holds significant relevance for guiding future epidemic prevention and control measures.\u003c/p\u003e \u003cp\u003eTo address these gaps, we conducted a case study on the December 2021 outbreak in Xi'an. Utilizing a complex urban location network, we analyzed the outbreak's propagation pathways, pinpointing nodes with significant viral transmission potential. Additionally, we categorized these locations and explored how specific location categories could reduce network connectivity through policy simulations.\u003c/p\u003e"},{"header":"2 Data and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e2.1 Data source and background of the epidemic\u003c/h2\u003e\n \u003cp\u003eThe data for this study were derived from official case reports released during the 2021 Delta variant of the COVID-19 epidemic in Xi\u0026apos;an City, China. Xi\u0026apos;an is the capital and megacity of Shaanxi Province, China, as well as the most important central city in western China. There were 13,163,000 residents in Xi\u0026apos;an at the end of 2021, with a 79.49% urbanization rate. In December 2021, an outbreak of the Delta variant imported by flight PK854, which entered the city from Pakistan, occurred in Xi\u0026apos;an. The Delta variant strain has a short incubation period, rapid transmission, a high viral load, a long core acid conversion time, and a greater risk of developing a critical illness [\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e]. The pathogenicity and critical illness rate of this variant is higher compared to that of Omicron. In contrast to two previous outbreaks in Guangdong province, this outbreak affected more than 2,000 people and was the largest outbreak of a new strain of Delta variant in China to date. By August 2023, four large outbreaks have been reported in China as a result of the Delta variant strain. In order to prevent and control the outbreak, the local government closed the city completely to prevent and control it. By the end of January 2022, there were no new confirmed cases of Delta in Xi\u0026apos;an.\u003c/p\u003e\n \u003cp\u003eThe dataset for this study was constructed from two data sources. The case contact network data were derived from the daily case reports published by the Shaanxi Provincial Health and Wellness Commission on its official website, and the case activity trajectory text data were derived from daily activity trajectories of new cases published by the Xi\u0026apos;an Municipal Government. The daily case reports from the Shaanxi Provincial Health Commission reported information on the age, sex, area of residence, date of diagnosis, date of isolation, and relationship to other confirmed cases for each new daily case from 9 December 2021 onwards. For each of the daily new cases from 9 December to the time of isolation and treatment, the Xi\u0026apos;an Municipal Government published the activity trajectory and the location name for each day. Both data sources start on 9 December 2021 and end on 18 January 2022 and are very informative.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003e2.2 Methods\u003c/h2\u003e\n \u003cp\u003eWe first collated the case information report and the daily case activity trajectory report into two databases by text coding. As each diagnosed case has a unique ID code, we merged the two databases using this unique key variable and synthesized a two-mode network matrix containing all the diagnosed cases as well as the locations they visited. The rows of the matrix represent the diagnosed cases and the columns represent the locations visited. Any lattice value (\u003cem\u003em, n\u003c/em\u003e) in the matrix represents the number of times case \u003cem\u003em\u003c/em\u003e has been visited to location \u003cem\u003en\u003c/em\u003e. We binarize this matrix and transform the two-mode network into a one-mode network (1-mode network) containing only locations based on confirmed case nodes. In this network, any node \u003cem\u003ei\u003c/em\u003e represents a location that is included in the activity trajectory of at least one case. If there exists at least one patient whose activity trajectory contains both different locations on a given day, i.e., at least one case has visited both places on a given day, then an edge is created between these two nodes in the network graph. The edge between the two points indicates that there is an outbreak transmission link between the two locations, reflecting patient movement between them. After forming the network, we visualized the network of locations.\u003c/p\u003e\n \u003cp\u003eWe used Complex Network Analysis to analyze this location network. Its basic analysis steps are as follows:\u003c/p\u003e\n \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.1 Whole Network Structure Analysis\u003c/h2\u003e\n \u003cp\u003eWe used the following whole network metrics to analyze the structure of the location network:\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eNetwork Density\u003c/strong\u003e. Network density is used to measure the denseness of the relationship between pairs of nodes in the network [\u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e]. It is mathematically expressed as:\u003c/p\u003e\n \u003cdiv id=\"Equa\" class=\"Equation\"\u003e\n \u003cdiv id=\"FileID_Equa\" class=\"mathdisplay\"\u003e$$\\begin{array}{c}\\rho =\\frac{2L}{n\\left(n-1\\right)}\\#\\left(1\\right)\\end{array}$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003ewhere \u0026rho; denotes the network density, L denotes the total number of edges in the network, and n denotes the network size, i.e., the number of nodes in the network. For a given number of nodes, the greater the number of edges in the network, the greater the network density, the denser that network is, and the greater the risk of an epidemic spreading through the network.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eAverage network path length\u003c/strong\u003e. The average network path length is used to measure the length of the average network path between nodes [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e]. It is reflected in this network as the average distance travelled from a location visited by a confirmed case to another location in the total graph. A shorter average path through the network indicates a higher level of accessibility between any two locations. This is expressed in a mathematical formula:\u003c/p\u003e\n \u003cdiv id=\"Equb\" class=\"Equation\"\u003e\n \u003cdiv id=\"FileID_Equb\" class=\"mathdisplay\"\u003e$$\\begin{array}{c}{C}_{B}\\left(j\\right)=\\frac{2}{n\\left(n+1\\right)}\\sum _{i\\ge j}^{n}{d}_{ij}\\#\\left(2\\right)\\end{array}$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003ewhere d\u003csub\u003eij\u003c/sub\u003e represents the distance between node i and node j and n is the network size, i.e., the total number of nodes in the network. The shorter the average path length of the network, the higher the accessibility of the network, and a node needs only a few steps to connect to any other node in that network.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eComponents\u003c/strong\u003e. Components are the most straightforward criterion for partitioning cohesive subgroups [\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e]. A component is a subgraph in the network where every pair of nodes is connected by an edge, while there are no edges connecting any two connected components.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eModularity\u003c/strong\u003e. Modularity is a network clustering method proposed by the American statistical physicist Newman through community detection algorithms [\u003cspan class=\"CitationRef\"\u003e16\u003c/span\u003e]. This method provides a clear evaluation metric for the quality of network community divisions. The Modularity algorithm is widely used for partitioning undirected graph networks. The formula for calculating modularity in undirected graphs is as follows [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e]:\u003c/p\u003e\n \u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"442\" height=\"76\"\u003e\u003c/p\u003e\n \u003cp\u003ewhere \u0026apos;m\u0026apos; corresponds to the number of edges in the graph, \u0026apos;k\u003csub\u003ei\u003c/sub\u003e\u0026apos; denotes the degree of node \u0026apos;i,\u0026apos; and \u0026apos;A\u003csub\u003eij\u003c/sub\u003e\u0026apos; signifies the adjacency matrix. The study utilized Gephi software to partition the network according to modularity metrics. During the network visualization process, distinct color-coding was applied to different network partitions, culminating in the creation of the location network graph depicting the spread of the Xi\u0026apos;an city epidemic.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.2 Analysis of nodes of high propagation capacity network\u003c/h2\u003e\n \u003cp\u003eIn a network, the distribution of degrees is not even across nodes. A node with a high center in a network of locations indicates that the location is the core or key bridging point for disease dispersal, and enhanced crowd control at such locations can effectively prevent the spread of the epidemic. Network analysts measure the centrality of nodes by calculating a variety of network centrality metrics inductively. In this study, we introduce two network centrality metrics to parse the location network as follows:\u003c/p\u003e\n \u003cp\u003eDegree centrality. If a node has a higher degree centrality, it means that the more locations the node is directly connected to, the more transmissible that location is for a new crown outbreak. In the context of patient contact networks, this metric demonstrates a robust correlation with the fundamental reproductive number of viral agents, making it a valuable indicator for assessing the rate of disease propagation [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e]. The formula for its calculation is as follows:\u003c/p\u003e\n \u003cdiv id=\"Equd\" class=\"Equation\"\u003e\n \u003cdiv id=\"FileID_Equd\" class=\"mathdisplay\"\u003e$$\\begin{array}{c}{C}_{D}\\left(i\\right)=\\sum _{j=1}^{n}{a}_{ij}\\#\\left(4\\right)\\end{array}$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eIn this equation, i is a location visited by a confirmed case of an outbreak, j is a point connected to that location, and n is the network size. Degree centrality is the most intuitive measure of node power and importance.\u003c/p\u003e\n \u003cp\u003eEigenvector centrality. Eigenvector centrality (Eigencentrality), as defined by Jia et al. [\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e], serves as a measure of a node\u0026apos;s significance within the network. However, it distinguishes itself by considering not only the node\u0026apos;s inherent importance but also the significance of its neighboring nodes. The fundamental principle underlying its calculation posits that a node\u0026apos;s centrality is intricately linked to the centrality of its neighboring nodes. Nodes with high eigenvector centrality in a network are usually those connected to nodes with a high degree centrality. The eigenvector centrality of l location i in the network is ECi, which is calculated as follows:\u003c/p\u003e\n \u003cdiv id=\"Eque\" class=\"Equation\"\u003e\n \u003cdiv id=\"FileID_Eque\" class=\"mathdisplay\"\u003e$$\\begin{array}{c}{\\text{E}\\text{C}}_{i}=c\\sum _{j=1}{a}_{ij}{\\text{X}}_{j}\\#\\left(5\\right)\\end{array}$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003ewhere X\u003csub\u003ej\u003c/sub\u003e denotes the eigenvector centrality of node j, c is a constant of proportionality, and a\u003csub\u003eij\u003c/sub\u003e is the number of links between location i and location j. When the steady state is reached after many iterations, it can be written in the following matrix form:\u003c/p\u003e\n \u003cdiv id=\"Equf\" class=\"Equation\"\u003e\n \u003cdiv id=\"FileID_Equf\" class=\"mathdisplay\"\u003e$$\\begin{array}{c}X=cAx\\#\\left(6\\right)\\end{array}$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003ewhere x represents the eigenvector corresponding to the eigenvalue c-1 of matrix A. The higher the centrality of the eigenvector of a node, the higher its correlation with other nodes with high centrality, the more it resides in the center of the epidemic spreading network, the higher the risk of the epidemic spreading, and the more it needs to be prevented and controlled.\u003c/p\u003e\n \u003cp\u003eEach of the above network indicators is calculated by Ucinet software and the Gephi network visualization tool.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.3 Changes in network connectivity after removing different categories of nodes\u003c/h2\u003e\n \u003cp\u003eWe would like to categorize locations within a real network to identify key categories influencing the outbreak spread. Instead of a city-wide blockade, we aim to pinpoint which categories, such as universities, convenience stores, and restaurants, can be selectively targeted for containment measures. We draw on prior studies [\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e] to model and analyze the impact of removing nodes from these specific categories on the network\u0026apos;s connectivity.\u003c/p\u003e\n \u003cp\u003eWe classified the 2994 nodes into 14 categories based on the Foursquare place taxonomy. Foursquare, a cloud-based location technology platform and geographic information service network classifies global locations into over 1,200 categories, including 12 main top-level categories [\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e]. Based on the specific situation in China, we classify the following 13 categories (see it in \u003cspan class=\"InternalRef\"\u003eAppendix A\u003c/span\u003e):\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"3 Result","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n\u003ch2\u003e3.1 Statistics results of whole network indicators\u003c/h2\u003e\n\u003cp\u003eThe Xi'an COVID-19 outbreak location network comprises 2,994 nodes, with 129 of them representing isolated nodes, accounting for 4.31% of the total node count. Isolated nodes indicate that a confirmed patient's trajectory includes only a single location. The network is characterized by 12,570 edges and a network density of 0.003, rendering it a sparse network. The average path length is 4.102, signifying that, on average, it takes approximately 4.1 steps to travel from one point on the graph to another.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e provides an overview of the network's structural distribution. Notably, there is a prominent large connectivity component surrounded by numerous smaller, more fragmented connectivity components, alongside multiple isolated nodes.\u003c/p\u003e\n\u003cp\u003eThe main component represents the largest connected segment of the network, encompassing the highest percentage of nodes within the total network graph. In this network, there are a total of 266 components, with the second largest connected component comprising merely 19 nodes, significantly smaller than the main component. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e visually depicts the primary component within the outbreak location network. This main component comprises 2,319 nodes, including all nodes with high degree centrality in this outbreak, and it is connected by a total of 11,466 edges. The network density within this main component is 0.004, and the average degree stands at 9.889, both exceeding the corresponding metrics for the entire network. Any node within this principal component that has been exposed to an infected individual is likely to disperse the disease across the entire network through connected trajectories. Furthermore, we've labeled nodes with the highest degree in each partition, which also indicates locations with a higher risk of transmitting the outbreak.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n\u003ch2\u003e3.2 Network centrality indicators\u003c/h2\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e shows the results of the measurement and calculation of each network centrality indicator.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eDescriptive statistics results of network centrality indicators\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eVariables\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eNumber\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMean\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003estandard deviation\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMin\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMax\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003edegree\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2,994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e11.09\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e310\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eeigencentrality\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2,994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0301\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0543\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e reveals that the average degree centrality is 8.397, suggesting that, on average, each location is connected to approximately 8.4 other locations. We normalized the eigenvector centrality results and ranked the centrality of each location in the network based on these metrics. The top ten locations in terms of both degree centrality and eigenvector centrality are displayed in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eIn Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e, the top ten locations ranked by both centrality indicators are: Everyday Convenience Store, Mixue Ice City, Cainiao Pickup Point, Lanzhou Noodles, Changan University Main Campus, and Weishui Campus. This highlights these locations as crucial transmission nodes in the outbreak network. Among the top ten locations for degree centrality, there are three convenience stores, two food and beverage establishments. Mixue Ice City is the cheap drink shop with the most shops in mainland China. Keji 2nd Road Xi'an Optics Valley represents a residential area for Xi'an employees located next to a high-tech industrial park, while Cainiao Pickup Point serves as a major hub for one of China's largest express delivery companies. It's worth noting that Chinese residents frequently utilize offline platforms for sending and receiving parcels.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n\u003ch2\u003e3.3 Changes in connectivity of the network after removing different categories of nodes\u003c/h2\u003e\n\u003cp\u003eThe t-test results for the change in network centrality metrics after removing different categories of nodes are given in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab2\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eT-test results for mean centrality metrics before and after removing similar nodes.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eRemoved\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eVariables\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eBefore removing\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMean2\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eAfter removing\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMean1\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMean Difference\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eShops\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003edegree\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2503\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e7.026\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1.371***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eeigencentrality\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2503\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0320\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00200\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eVegetable Markets\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003edegree\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2775\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e7.937\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.459\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eeigencentrality\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2775\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0310\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00100\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eParks and outdoors\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003edegree\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2979\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.375\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.022\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eeigencentrality\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2979\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00100\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eTravel\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003edegree\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2981\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.302\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.095\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eeigencentrality\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2981\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0290\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00100\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eSports\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003edegree\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2979\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.379\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.017\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eeigencentrality\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2979\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eArt and Entertaining\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003edegree\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2962\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.352\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.0450\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eeigencentrality\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2962\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eRestaurants\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003edegree\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2229\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e5.887\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2.510***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eeigencentrality\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2229\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0320\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.002\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eEducational Institutions\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003edegree\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2933\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.371\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.0260\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eeigencentrality\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2933\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0310\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00100\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eUniversities\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003edegree\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2939\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.097\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.300\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eeigencentrality\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2939\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0270\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.003***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eWorkplace\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003edegree\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2762\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e7.794\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.602***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eeigencentrality\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2762\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0320\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00100\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eHome\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003edegree\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e7.577\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.820***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eeigencentrality\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0290\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.00100\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eTransport sites\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003edegree\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2950\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.113\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.284\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eeigencentrality\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2950\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0280\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.003*\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eIn Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, 'Before removing' represents the sample size prior to the removal of nodes from individual categories, while 'After removing' reflects the sample size after removing nodes from these categories separately. The results in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e demonstrate that the removal of nodes in the 'Shops,' 'Restaurants,' 'Workplace,' and 'Home' categories significantly reduces the mean degree of the entire network (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Furthermore, deleting nodes from the 'Universities' and 'Transport sites' categories results in a substantial decrease in network Eigenvector centrality (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001, p\u0026thinsp;\u0026lt;\u0026thinsp;0.05). A high Eigenvector centrality suggests that nodes in these categories are closely connected to nodes with the highest or second-highest transmission capacity in the network, which suggests that venues in the 'Universities' and 'Transport sites' categories connected to more locations with equally high transmission capacity.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4 Discussion","content":"\u003cp\u003eThe primary objective of this study was to examine high-transmission capacity nodes within Chinese cities during the COVID-19 pandemic. Initially, the network analysis revealed 266 separate sub-networks within the city of Xi'an, with 129 isolated nodes. The existence of these isolated nodes implies that certain patients were diagnosed without any prior travel history. However, it is important to note that outbreaks do not materialize spontaneously. Thus, the presence of numerous isolated nodes and numerous small components is theoretically implausible, suggesting the presence of concealed transmission chains within this outbreak.\u003c/p\u003e\n\u003cp\u003eChang's (2021) study suggests that individuals with lower income may face a heightened risk of viral exposure [\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e]. In our research, we aimed to investigate this hypothesis further by refining node categories. We segmented the 'Restaurants' category into two subcategories: 'Small Restaurants' and 'High-end Restaurants', based on per capita consumption prices obtained from Baidu Maps, using a threshold of 50 RMB per person. We conducted another round of simulations involving the removal of nodes, revealing that deleting nodes from the 'Small Restaurants' category significantly reduced the average degree centrality of the entire network (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). While removing nodes from the 'High-end Restaurants' category also led to a decrease in average degree centrality, the significance was somewhat lower (p\u0026thinsp;\u0026lt;\u0026thinsp;0.05), and the difference in means is smaller (-0.502 virus \u0026minus;\u0026thinsp;1.970). However, the removal of 'High-end Restaurants' nodes resulted in a significant decrease in network Eigenvector centrality (p\u0026thinsp;\u0026lt;\u0026thinsp;0.01). These findings suggest that Small eateries often possess a notably high capacity for viral transmission. In contrast, high-end restaurants, while having a lower direct viral transmission capability than the former, are linked to locations with comparable high transmission potential.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab3\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eT-test results for mean centrality metrics before and after removing different \u0026lsquo;Restaurants\u0026rsquo; category nodes\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eRemoved\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eVariables\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eBefore removing\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMean2\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eAfter removing\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMean1\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMean Difference\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eSmall Restaurants\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003edegree\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2361\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e6.427\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1.970***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eeigencentrality\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2361\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eHigh-end Restaurants\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003edegree\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.397\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2862\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e7.895\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.502*\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eeigencentrality\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2994\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0300\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2862\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0270\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.003**\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eBased on the aforementioned simulations and our previous analyses, we have identified the significant roles played by shops and small dining establishments in the overall network connectivity. Shops, encompassing convenience stores and supermarkets, serve as critical points for both the inflow and outflow of goods. They are susceptible to the introduction of virus-carrying frozen food, potentially leading to infections. Moreover, shops are frequented by a large number of people, and the intricate movement of individuals within these premises is a key factor facilitating the spread of outbreaks.\u003c/p\u003e\n\u003cp\u003eSmall dining establishments are more likely to contribute to outbreak transmission compared to medium to high-end restaurants. Small restaurants typically offer food without a high price threshold, catering to a broader consumer base compared to medium and high-end counterparts. These establishments feature compact spaces, high customer turnover, and offer dine-in, takeout, or delivery services, leading to a diverse clientele. We believe that implementing targeted enhancements in epidemic prevention measures at these nodes will yield a more substantial impact on the network's overall connectivity.\u003c/p\u003e\n\u003cp\u003eOur findings further develop those of Eubank (2004), who investigated how many nodes batch deletions in smallpox propagation can lead to a substantial decrease in network connectivity through a simulation modelling approach [\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e]. We have refined this conclusion to pinpoint specific node categories. Our findings diverge from the simulation results reported by Martin (2020), which indicated that school closures do not significantly affect Hong Kong's urban containment policies [\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e]. In contrast, our research highlights the pivotal role of universities. Li et al.'s study (2023) investigates the impact of the pandemic on grocery shopping habits at the county level in the United States [\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e]. Designing specific strategies for safer grocery shopping is essential. Our study reveals that shops pose a high risk of viral transmission, emphasizing the importance of bolstering control measures at such locations. Examples include new food retail models such as centralized government food transport and community gardens.\u003c/p\u003e"},{"header":"5 Conclusion","content":"\u003cp\u003eIn this study, we utilized case data and trajectory text data from the December 2021 Delta variant outbreak in Xi'an to construct a complex network perspective of urban locations within the outbreak. Our analysis revealed valuable insights through the assessment of network metrics, ranking of centrality metrics.\u003c/p\u003e \u003cp\u003eThe whole location network is comprised of 266 connectivity components, with the largest containing 2,319 nodes. By examining centrality rankings, we identified locations at a heightened risk of contributing to outbreak spread, which encompass universities, convenience stores, agricultural markets, and small food establishments. Notably, each of Chang'an University's three campuses plays a central role in the outbreak's sub-center.\u003c/p\u003e \u003cp\u003eMoreover, our study included a policy simulation focusing on the containment and control of specific network nodes. This simulation highlighted convenience stores and restaurants as the nodes with the greatest potential for propagating the outbreak, emphasizing their significance in outbreak transmission dynamics.\u003c/p\u003e \u003cp\u003eHowever, this paper also acknowledges several limitations while offering insights for future research directions. During data collection, unclear node names, like 'convenience store,' hindered precise identification. In addition, the endogenous construction process of the location network can be further investigated by adopting models such as exponential random graphs. Finally, for greater external validity, future studies should explore urban epidemics across various contexts.\u003c/p\u003e \u003cp\u003eBusse KR, Logendran R, Owuor M, Omala H, NandoyaE, Ammerman AS, Martin SL. Food vendors and the obesogenic food environment of an informal settlement in Nairobi, Kenya: a descriptive and spatial analysis. \u003cem\u003eJUrban Health\u003c/em\u003e. 2023;100(1):76\u0026ndash;87\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eFlorida R, Rodr\u0026iacute;guez-Pose A, Storper M. Critical Commentary: Cities in a post-COVID world. \u003cem\u003eUrban Stud. \u003c/em\u003e2023;60(8):1509-31.\u003c/li\u003e\n\u003cli\u003eChang S, Pierson E, Koh PW\u003cem\u003e, et al.\u003c/em\u003e. Mobility network models of COVID-19 explain inequities and inform reopening. \u003cem\u003eNature. \u003c/em\u003e2021;589(7840):82-87.\u003c/li\u003e\n\u003cli\u003eChang Y, Mayer S, Davis ES\u003cem\u003e, et al.\u003c/em\u003e. Transmission Dynamics of Large Coronavirus Disease Outbreak in Homeless Shelter, Chicago, Illinois, USA, 2020. \u003cem\u003eEmerg Infect Dis. \u003c/em\u003e2022;28(1):77-85.\u003c/li\u003e\n\u003cli\u003eMartín-Calvo D, Aleta A, Pentland A, Moreno Y, Moro S. Effectiveness of social distancing strategies for protecting a community from a pandemic with a data-driven contact network based on census and real-world mobility data. \u003cem\u003eMIT Connection Science. \u003c/em\u003e2020.\u003c/li\u003e\n\u003cli\u003ePines JM, Zocchi MS, Black BS\u003cem\u003e, et al.\u003c/em\u003e. Characterizing pediatric emergency department visits during the COVID-19 pandemic. \u003cem\u003eThe American Journal of Emergency Medicine. \u003c/em\u003e2021;41:201-04.\u003c/li\u003e\n\u003cli\u003ePrem K, Liu Y, Russell TW\u003cem\u003e, et al.\u003c/em\u003e. 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Changes of Grocery Shopping Frequencies and Associations with Food Deserts during the COVID-19 Pandemic in the United States. \u003cem\u003eJ Urban Health. \u003c/em\u003e2023.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"COVID-19, Complex network analysis, Policy simulation","lastPublishedDoi":"10.21203/rs.3.rs-3436409/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3436409/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eUtilizing patient trajectory data from 2050 case text documents, we constructed a location-contact network to analyze the spatial transmission of the late 2021 COVID-19 outbreak in a megacity of China. Employing complex network analysis, we had several significant findings. The network exhibited 266 components, indicating a relatively sparse network density. Notably, locations with a higher risk of transmission encompassed universities, convenience stores, agricultural markets, and restaurants. Moreover, we applied a network immunization strategy to simulate the impact of lockdowns at various location types on virus spread. Our results show that lock down \"shops\" and \"restaurants\" can significantly diminish network connectivity.\u003c/p\u003e","manuscriptTitle":"Spatial Transmission Network Analysis of the COVID-19 Outbreak in a Megacity: A Study Based on 2994 Affected Locations in Xi'an in 2021","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-10-19 17:51:53","doi":"10.21203/rs.3.rs-3436409/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"1e7b6b5e-4aad-4415-ba5f-276f7cc26474","owner":[],"postedDate":"October 19th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-04-17T15:01:48+00:00","versionOfRecord":[],"versionCreatedAt":"2023-10-19 17:51:53","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3436409","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3436409","identity":"rs-3436409","version":["v1"]},"buildId":"rHA-KDH7Qsr4HCuvH75dn","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}