Abstract
In recent years, the proliferation of coronavirus disease has profoundly affected the world. The vitality of urban space is difficult to recover in the short term. Therefore, in the early stage of human-to-human transmission of the epidemic, we need to determine the potential urban agglomeration space as soon as possible, the timely find of hidden danger areas, and carry out spatial optimization to prevent the further spread of the epidemic. This becomes the urgent problem at the moment. Jinan is the capital city of Shandong Province, and the mega-city of China. The study is focused on the main urban area within the bypass. This study used spatial data methods such as spatial grammar and GIS technology. First, we analyzed the spatial topological properties of urban road network during the epidemic. Then, we carried out spatial autocorrelation analysis on the topological attributes to get the shape of urban spatial clustering layout during the epidemic. Finally, the thesis crawled through various types of infrastructure points-of-interest and conducted nuclear density analysis to get the dynamic trend of urban space in Jinan. The research results showed that there is significant space for agglomeration in the main urban area of Jinan. The areas with strong agglomeration are basically located in tourism areas, school areas, business areas, living circle areas of residential communities in Licheng and Lixia districts, transportation hub areas in Tianqiao District, and high-tech industrial areas in Lixia District. Topography, water body, greening, and parks could effectively reduce the concentration of human flow, and are important areas to relieve the potential abnormal epidemic. This study provided a new method for detecting epidemic prevention and control areas, optimizing urban space layout and formulating prevention and control strategies in the early stage of human-to-human epidemic transmission and lack of case surveillance data and control measures.
1 Introduction
Since the outbreak of coronavirus disease (COVID-19) in the early 2020, China’s urban economic and social orders have suffered a major impact. The long-term potential spread poses a threat to people’s lives and health. For human-to-human diseases such as COVID-19, it is more likely to cause outbreaks and spread in crowded areas. In the early stage of the epidemic (epidemic disease refers to all kinds of diseases similar to COVID-19 that can be transmitted from person to person), it is an urgent need to determine the potential areas of abnormal agglomeration as soon as possible and carry out spatial optimization to timely prevent and control the epidemic. Spatial layout will affect people’s cognition and behavior activities, guide pedestrian flow lines, and locate the crowd gathering place [1]. Among them, the developed urban road network system provides great convenience for the regional movement of people [2], and the perfect public service facilities attract people to gather in some areas, which enhances the urban vitality of this area. This situation promotes the outbreak and spread of the epidemic in local areas. Therefore, this study explored the occurrence of human-to-human transmitted diseases from the perspective of spatial layout [3]. The use of spatial big data approach to detect the spatial areas of urban agglomeration in the early stage of the epidemic could help us to accurately capture and locate the potential hidden space for epidemic and optimize the spatial layout to maintain urban vitality. Therefore, this method could assist the urban planners and government departments to take appropriate measures for emergency prevention and control of epidemic.
Scholars in the related fields have taken a series of studies on the spatial distribution of epidemic diseases [4]. Ma et al. [5] have passed the 314 Chinese cities to detect urban energy recovery mode and its impact factors after the epidemic. They divided the restoration patterns of urban vitality into six categories. Jinan city in this study belongs to Mode III. In this pattern, the impact of the epidemic was small in the early stage, and the recovery rate was slow in the later stage. In the middle and later stages, the vitality of the city was improved, but still lower than the level in the same period last year [6]. Jinan city is located in Shandong Province with a population of 100 million. As a second-tier city in China, it does not have the particularity of rapid economic development of Beijing city, Shanghai city, and Shenzhen city, nor does it have the particularity of Wuhan city as the national transportation hub. It is typical among the big cities in China. Therefore, the author selected Jinan city as a case to study the abnormal detection of urban agglomeration space under epidemic.
In the past, the following three methods were used to detect the geographical distribution anomalies of epidemic diseases: (1) Based on the analysis of traditional data statistics [7]. Through statistical analysis of the incidence of diseases, the number of confirmed cases, the number of deaths, and other attributes within the study area, researchers could identify abnormal areas with high epidemic transmission rates and susceptibility to outbreaks. (2) Based on the analysis of spatial–temporal distribution visualization model [8]. Traditional data statistics could not reflect the spatial and temporal distribution characteristics of epidemic diseases. According to this data, the researchers combined maps to build visual models of spatial and temporal distribution and they used visualizable images to convey the spatial and temporal distribution of epidemics. (3) Based on the analysis of spatial clustering correlation. According to the spatial correlation of the first law of geography and the spatial heterogeneity of the second law of geography, the authors further proposed a method of spatial clustering analysis to detect the abnormal distribution of epidemic diseases. For example, they used spatial autocorrelation method to analyze the spatial correlation of global and local epidemic distribution [9], used Getis G* hotspot analysis method to detect hot and cold spots of epidemic case distribution, and used Ant colony clustering algorithm and Bayesian gamma–Poisson model to detect the abnormal clustering areas of epidemics [10]. These methods analyze the distribution of case surveillance data obtained after the outbreak of an epidemic. They lack inferential predictions of potential abnormal areas in the absence of data at the beginning of the disease. They also lack research on how to optimize urban spatial layout to prevent further spread of the epidemic and maintain urban vitality.
With the coming of the network era of big data, research data acquisition approaches have gradually developed from traditional methods such as literature review, questionnaire survey, in-depth interview, and construction of evaluation index system to Internet channels such as mobile phone signaling data, social network data, LBS data, points-of-interest (POI) data, and Baidu thermal map data [11]. The research methods gradually developed from qualitative analysis to quantitative analysis and statistical analysis. And then, Research and analysis appeared to use ArcGIS, Depthmap, SPSS, R language, and other software for spatial visualization analysis.
From spatial big data visualization perspective, this study took urban roads in Jinan city as the main research object. This research selected the data of LOI (the topological axis of urban road network), and this data have often been ignored in past studies [12]. Then by exploring the spatial autocorrelation Moran index of total depth and integration, we further analyzed the agglomeration distribution of urban space. Urban topological attributes reflect the ease of reaching a space, spatial accessibility, the potential of a space to attract people and traffic, and spatial agglomeration. Based on this spatial autocorrelation analysis of total depth and integration, we further corroborated the distribution of road spatial agglomeration and dispersion. Finally, this study overlaid POI data to estimate the kernel density and studied the distribution of urban vitality (Figure 1).
Research methodology framework of this project (Source: drawn by the author. Year: 2022).
By analyzing the layout of urban road network and interest points of infrastructure, we could infer the travel behavior of people. Thus, we could detect and identify abnormal potential areas of urban agglomeration in the early stages of the outbreak without case surveillance data, propose feasible prevention and control measures, and carry out regional optimization at the level of prevention and control to contain the further spread of the epidemic (Figure 2).
Research objectives and ideas (Source: drawn by the author. Year: 2022).
2 Methodology
2.1 Spatial grammatical topology analysis
Spatial grammar originated in the late 1970s and was proposed by Bill Hillier and others in the United Kingdom. It divided large-scale space into a large number of small-scale basic convex space units [13], and then realized the quantitative analysis of space. It transformed the connection relation of space into a more abstract topological relation diagram and built corresponding visual model for study. The commonly used analysis methods include convex space analysis, axis analysis, view area analysis, agent robot method, and line segment analysis [14,15]. The axis analysis method is the measurement method of road spatial topology network accessibility analysis. It is widely used in the urban space research.
In space syntax, if two adjacent spatial depths are recorded as one topological step, the shortest topological step from one space to another is the depth value between the two spaces [16]. And the sum of the depth values from one space to other spaces in the system is the total Depth. Since asymmetric line elements will interfere with road network calculation, it is necessary to eliminate the influence of absolutely symmetric spatial structure model on the calculation results of urban road space model. Considering the symmetry of spatial structure, some scholars proposed real relative asymmetry [17]. They regarded its reciprocal as integration [18]. The calculation formula is as follows:
where n is the total number of elements; MD i is the average depth value of element i; and TD i is the global depth value of element i. Total depth is proportional to RRA i , and integration is proportional to accessibility and potential for space attraction or transportation. It could be seen that the total depth is negatively correlated with the integration, and the integration is the reciprocal of the total depth [19].
2.2 Spatial autocorrelation analysis
Spatial autocorrelation analysis was proposed by Patrick Alfred Pierce Moran in 1950. It is an analytical method used to determine whether a variable has a spatial correlation of clustering, discrete or random uncorrelated, and to test whether the degree of spatial correlation is significant. At the same time, it could be used to determine the location of spatial agglomeration area and abnormal area. If the value of a variable is moderately similar to the decrease in distance, there is a spatial agglomeration phenomenon. It indicates that the variable shows a positive correlation among the factor data in its region. On the contrary, if the measured variable is more different from the decrease in distance, there is a discrete phenomenon in space. It indicates that the variable shows a negative correlation between the factor data in its region [20].
Spatial autocorrelation analysis could be divided into global and local analysis methods according to different spatial scales. Global autocorrelation is used to analyze the spatial correlation between factor data and neighboring factor data within the whole research scope, including agglomeration, discrete, and random distribution of three spatial distribution characteristics. It is represented by Moran’s I. Local autocorrelation is used to analyze the spatial correlation between a single variable of factor data in a local region and neighboring factor data variables. It could detect the spatial range of high value and outlier value of spatial variables [21].
2.2.1 Moran’s I coefficient of global spatial autocorrelation
The calculation formula of global autocorrelation is
where S 2 can be calculated as follows:
where n is the total number of elements; x i and x j are the attribute values of factor i and factor j, respectively. w ij is the spatial weight between element i and element j. If the area of element i and j is adjacent, w ij = 1; otherwise, w ij = 0.
Usually, Z test is required after calculation, and the calculation formula of Z I is:
where the calculation formula of the mean value and variance is as follows:
The molecular cross product of the global spatial autocorrelation Moran’s I is to compare the product of the observed values in adjacent regions with the mean deviation. Its value range is [−1, 1]. When the Moran index is greater than 0, it indicates that all regional spatial element attributes show spatial positive correlation. That is, the closer the element attribute values are, the more inclined they are to cluster. When Moran index is less than 0, it indicates that all regional spatial element attributes are spatially negatively correlated. That is, the closer the element attribute values are, the more likely they are discrete. When Moran index is equal to 0, it means that the regional spatial element attributes are randomly distributed without spatial correlation. After the global spatial autocorrelation is calculated, the results need to be tested to determine whether it is significant [22]. The commonly used Z test method is normal distribution 90% confidence test. When Z > 1.65, it shows significant positive spatial correlation; when Z < −1.65, it shows significant negative spatial correlation; when −1.65 ≤ Z ≤ 1.65, there is significant spatial irrelevance, and the observed values present independent random distribution [23].
2.2.2 Moran’s I coefficient of local spatial autocorrelation
The calculation formula of local autocorrelation is as follows:
where
where n is the total number of elements; w ij is the spatial weight between factor i and factor j. I i is the local Moran index of factor region i.
Local spatial autocorrelation Moran’s I is to further determine the clustering regions of spatial element attributes and the regions with outliers. Through analysis, five cluster distributions could be obtained: High–high clustering (H–H), low–low clustering (L–L), high–low clustering (H–L), low–high clustering (L–H), and random distribution. Among them, H–H clustering and L–L clustering represent spatial clustering distribution characteristics, H–L clustering and L–H clustering represent spatial discrete distribution characteristics, and random distribution means that spatial distribution has no correlation [24].
2.3 POI nuclear density analysis
Kernel density estimation (KDE) is an analysis method used to estimate the distribution state of simulated attribute variable data [25]. It is used to calculate the density of POI elements in the surrounding area and estimate the point or line density in a moving cell. The results could reveal detailed features, and they are gradual and almost not affected by subjective factors [26]. KDE method is derived from the first law of geography. That is, the closer the distance is, the closer the object is; the closer it is to the nuclear density element, the greater the density expansion value. It could be concluded that the center intensity decreases with the increase in the distance [27,28,29]. First, the sample points are set as x 1, x 2, x 3…, x n , and we need to analyze the distribution of attribute element variables by density core estimation [30].
The calculation formula of kernel density function used in this study is:
where k is the kernel function; (x − x i )2 + (y − y i )2 is the distance between the point (x i , y i ) and the point (x, y); n is the number of points within the research range; d is the data dimension [31]. In this study, d = 2 and h is the bandwidth. That is, it is a free parameter that defines the value of the smoothing quantity. In general studies, the common methods for selecting bandwidth include rule-of-thumb, plug-in, and cross-validation. In this study, the “rule-of-thumb” is selected to calculate the optimal bandwidth h, and the calculation formula is as follows:
where n is the total number of elements; D m is the median distance; SD is the standard distance.
3 Research scope and data
3.1 Research scope
Jinan is also known as “Spring City”. Jinan is located in east China and the southeastern edge of North China Plain. It is a prefecture-level city, provincial capital, sub-provincial city, megacity, and the core city of Jinan metropolitan circle in Shandong Province. With a total area of 10,244.45 km2 and a built-up area of 760.6 km2, it has a jurisdiction of over 10 districts and 2 counties. It has a total resident population of 9,202,432, and it is one of the 14 megacities in China. Jinan is located in the middle and west of Shandong Province, bordering Mountain Tai in the south, the Yellow River in the north and the mountains and rivers. It borders Binzhou city and Dezhou city in the north, Tai’an city in the south, Liaocheng city in the southwest, and Zibo city in the east, respectively. It is located at 36°40′ north latitude and 117°00′ east longitude, with the terrain high in the south and low in the north. The development strategy of Jinan City Planning (2018–2050) defined Jinan as a spatial pattern of “one body, two wings, and multiple points.” The scope of “one body” includes the downtown area of Jinan, consisting of the main city, Zhangqiu group, Changqing group, high-tech group, and Airport group. The body is the main area of the central urban area of Jinan, and it gathers the commerce, culture, tourism, and leisure functions of Jinan city (Figure 3).
Location of main urban area of Jinan City (Source: drawn by the author. Year: 2022). Note: Jinan is located in east China and the southeastern edge of North China Plain. It is located in the middle and west of Shandong Province. It borders Binzhou city and Dezhou city in the north, Tai’an city in the south, Liaocheng city in the southwest, and Zibo city in the east, respectively. The main urban area is the central urban area of Jinan.
In addition to urban areas, Jinan city also includes large southern mountainous areas, water bodies, and rural areas. This area has low-density population and underdeveloped road network. So, it is not representative. Therefore, this study only selected the main urban area of Jinan city as the object. This article research scope is enclosed by Jinan Ring Expressway, Jinan–Guangzhou Expressway, and Beijing–Taiwan Expressway (partially overlapped with the area within the second ring road). The total research area is 535.66 km2, covering only 5.2% of the city’s total area, including all Lixia District and parts of Downtown District, Licheng District, Huaiyin District, and Tianqiao District. The perimeter road loop is 97.10 km in length. There are three horizontal (ten roads, north park viaduct, and second ring south expressway) and three vertical (Jiluo Road, shun river viaduct, and second ring east viaduct) trunk roads (Figure 4). By studying the spatial structure of road network in Jinan’s main urban area, we could analyze the potential abnormal areas of urban agglomeration in the early stage of the epidemic and optimize the urban spatial layout.
Scope of study on the main urban area of Jinan City (Source: drawn by the author. Year: 2022). Note: This article’s research scope defined for the main city area. It encloses Jinan Ring expressway, Jinan–Guangzhou Expressway, and Beijing–Taiwan Expressway (partially overlapped with the area within the second ring road). The total area of the research area is 535.66 km2, including all Lixia District and parts of Downtown District, Licheng District, Huaiyin District, and Tianqiao District. There are three horizontal and three vertical trunk roads.
3.2 Research data
Through field research, traditional data collection, and large data acquisition based on Internet space, the data of this study could be divided into two categories: Jinan urban road data (LOI axis network data) and infrastructure data (POI point data).
3.2.1 Jinan urban road data (LOI)
After field research and combined with OpenStreetMap, we have drawn the road network axis model within the research scope of Jinan city main area [32]. We have drawn the road axis according to the principle of “longest and least,” and selected the most economical and convenient travel route from the axis [33] (Figure 5).
Axis model of road network within the research scope of Jinan main urban area (Source: drawn by the author. Year: 2022). Note: Through field research and combined with OpenStreetMap, we have drawn the road network axis model within the research scope of Jinan city main area. We have drawn the road axis according to the principle of “longest and least.”
3.2.2 Infrastructure point data
By crawling through the Baidu map and Autonavi map databases of China in 2021, we could obtain data on 15 categories of infrastructure in the main urban area of Jinan, including food service, shopping service, medical service, accommodation service, living service, finance and insurance, automobile service, sports and leisure, government agencies, transportation facilities, business housing, companies and enterprises, education and culture, scenic spots, and natural features [34] (Table 1).
POI data of 15 types of infrastructure in main urban area of Jinan City
| Category of POI facilities | Number of points | Category |
|---|---|---|
| Food service | 946 | Business |
| Shopping service | 4,892 | Business |
| Medical service | 4,001 | Business |
| Accommodation service | 1,900 | Business |
| Living service | 4,676 | Business |
| Finance and insurance | 3,080 | Business |
| Automobile service | 3,140 | Business |
| Sports and leisure | 2,756 | Business |
| Government agencies | 7,888 | Government agencies |
| Transportation facilities | 10,310 | Transportation |
| Business housing | 5,760 | Residence |
| Companies and enterprises | 783 | Companies |
| Education and culture | 13,536 | Education |
| Scenic spots | 742 | Green space |
| Natural features | — | Others (excluding) |
Source: drawn by the author. Year: 2022.
Various types of infrastructure POI data contained information such as name, address, latitude, and longitude coordinates, and type [35]. Through data cleaning, filtering, and pre-processing [36], we removed some duplicate, incomplete, or incorrect location data. A total of 64,410 data were available from the final study. Then, we uniformly transformed them into WPS-1984 coordinate system. Finally, we classified the filtered data into 8 categories: commercial class (39.4%), government agency class (12.2%), transportation class (16%), residential class (8.9%), corporate class (1.2%), educational class (21%), green class (1.3%), and others (This refers to natural surface fixed objects such as rivers, lakes, seas, forests and grasslands, which are not included in the scope of study) [37] (Table 2).
Data classification of POI for eight kinds of infrastructure
| POI facility classification | Number of points | Proportion (%) |
|---|---|---|
| Commercial class | 25,391 | 39.4 |
| Government agency class | 7,888 | 12.2 |
| Transportation class | 10,310 | 16 |
| Residential class | 5,760 | 8.9 |
| Corporate class | 783 | 1.2 |
| Educational class | 13,536 | 21 |
| Green class | 742 | 1.3 |
| Others (excluding) | — | — |
Source: drawn by the author. Year: 2022.
As could be seen from Table 2, POI data of commercial class account for the highest proportion. The agglomeration development of inter-regional industries represents the economic development of the region and the core competitiveness of the city. The commercial agglomeration center of the city could generally represent the dynamic central space of the city. The research scope of this study is the main urban area of Jinan city. It belongs to the vitality center of Jinan city, so this area gathers most of the commercial POI infrastructure of Jinan city. The aim of studying POI infrastructure data in this study was to analyze the urban vitality areas. These zones are the areas where people tend to gather, and these are the places with abnormal potential risks of epidemic concentration in the city. Therefore, after data cleaning, screening, and pretreatment, this research obtained eight kinds of POI data of infrastructure.
Since this study analyzed the distribution of clustering abnormal hidden dangers in the early stage of human-to-human infectious diseases, we made the following assumptions for the convenience of subsequent analysis [38]:
This study applies to all human-to-human infectious diseases (excluding animal-to-human transmission or animal-to-animal transmission), and is not limited to COVID-19.
The drawn road network axis is only limited to all urban public roads without closure and control, excluding roads inside buildings and leading to buildings.
This study is applicable to the analysis of the early stage of the epidemic with loose control and lack of case surveillance data.
4 Model construction and analysis
4.1 Spatial topological model construction
This study constructed a topology model of road network in the main urban area of Jinan in the early stage of the epidemic, namely, the road network space under the state of full openness, no closure, and lack of control. We could find that the urban districts within the scope of the study show obvious central agglomeration along the main roads. The clustering space is the abnormal area of potential epidemic risks, and the clustering axis is the main distribution and development axis of epidemic risks. This study analyzed the topological model of urban road network, and illustrated the importance of urban roads and the important influence of roads on urban layout.
In the abnormal detection and analysis of road agglomeration space in Jinan main urban area, the Integration topological model obtained by depthmap mainly analyzed the agglomeration degree of road network space. It is the potential of attracting people and traffic [39]. It breaks the symmetry property of urban network structure. Areas with higher integration are represented by red roads, and conversely, areas with lower integration are represented by blue roads [40,41,42]. It could be seen from Figure 6a that the integration in the urban central area is the highest, so the road axis in the central area is red. The total depth topology model obtained by depthmap mainly analyzes the accessibility of the urban road network space. Contrary to the integration, areas with higher total depth are more difficult to reach, and roads are represented in blue; conversely, areas with lower total depth are represented in red [43]. As could be seen from Figure 6b, the total depth is the highest in the urban central area, so the road axis in the central area is blue. Through the relevant mathematical model and visual analysis in this study, it could be seen that the integration is the inversion of the total depth, and there is a negative correlation between the two. It could be concluded that the total depth is proportional to the road accessibility and the integration is proportional to the road’s potential to attract traffic. So it conforms to a certain linear relationship [44] (Figure 7).
Integration (a) and total depth (b) axis topological model of road network in the early stage of the epidemic in Jinan main urban area (Source: drawn by the author. Year: 2022). Note: Through the analysis of the axis topological model, it could be seen that the urban areas within the study area of Jinan main urban area show obvious central agglomeration and cluster along the main roads. The clustering space is the abnormal area of potential epidemic risks, and the clustering axis is the main distribution and development axis of epidemic risks.
Scatter diagram of integration and total depth correlation of road network in the main urban area of Jinan in the early stage of the epidemic (Source: drawn by the author. Year: 2022). Note: The integration is the inversion of the total depth, and there is a negative correlation between the two. It could be concluded that the total depth is proportional to the road accessibility and the integration is proportional to the road’s potential to attract traffic. So, it conforms to a certain linear relationship.
As could be seen from Figures 8 and 9, clear axis distribution and development trend of potential epidemic hazards could be obtained through the integration and total depth axis model analysis of road network in Jinan main urban area during the epidemic period. From the integration analysis diagram, it could be seen that the ten roads with the highest integration mainly include Qingyuan Road – Jiqi Road – Weishier Road – Yangguang New Road – Langmao Mountain Road; Jiluo Road – Tiancheng Road – Weier road – Hero Mountain road, and along the north extension of Jiluo Road; Lishan North Road – Lishan Road; Industrial South Road – Jiefang Road – Quancheng Road – Communist Youth League Road – Jingsi road, and along the Industrial South Road to the northeast extension; Heping Road – Luo Source Avenue – Jingqi road; Along the main road of the city through Jingshi Road to the east and west direction extension; Mountain Road – West Yanzi Mountain Road; Shunhe Viaduct Road – Wenhua West Road – Wenhua East Road – Yaotou Road; Minghu West Road – Minghu North Road – Minghu East Road – Huayuan Road; Zhangzhuang Road – Tikou Road. These are roads with high concentration of potential epidemic risks (Figure 10). It could be seen from the total depth analysis chart, there are Wuyingshan Middle Road – Beiyuan Street and Ji’an Street – Youth Road – Daming Lake Road – Dongguan Street are also easy to generate clustering abnormal risks. These are the roads with the highest total depth.
Integration axis analysis diagram of potential epidemic hazards of road network in the main urban area of Jinan in the early stage of the epidemic (Source: drawn by the author. Year: 2022). Note: The roads with the greatest epidemic risk mainly include: (1) Qingyuan Road – Jiqi Road – Weishier Road – Yangguang New Road – Langmaoshan Road; (2) Jiluo Road – Tiancheng Road – Weier Road – Hero Mountain Road, and extending north along Jiluo Road; (3) Lishan North Road – Lishan Road; (4) Industrial South Road – Jiefang Road – Quancheng Road – Communist Youth League Road – Jingsi Road, and extending northeast along Industrial South Road; (5) Heping Road – Luo Source Avenue – Jingqi Road; (6) extends east-west along the main road of the city through Jingshi Road; (7) Mountain Road – West Yanzi Mountain Road; (8) Shunhe Viaduct Road – Wenhua West Road – Wenhua East Road – Yaotou Road; (9) Minghu West Road – Minghu North Road – Minghu East Road – Huayuan Road; (10) Zhangzhuang Road – Tikou Road. These are the main roads.
Total depth axis analysis diagram of potential epidemic hazards of road network in the main urban area of Jinan in the early stage of the epidemic (Source: drawn by the author. Year: 2022). Note: On the basis of the analysis of integration, the roads with the greatest risk of epidemic hidden dangers are as follows: (1) Wuyingshan Middle Road – Beiyuan Street and (2) Ji’an Street – Youth Road – Daming Lake Road – Dongguan Street.
Perspective of main cluster roads in Jinan (Source: drawn by the author. Year: 2022). (a) Partial section of Lishan Road and (b) Partial section of Quancheng Road.
From the above analysis, it could be seen that the roads with the highest risk of epidemic hidden dangers and the highest concentration are basically the main development axis in the city, and the sections with the highest pedestrian and vehicle flow. These sections are mainly distributed around the scenic spots, passing through the commercial complex center area, the school area, the transportation hub area, the main roads leading to residential communities, and extending to the periphery along the external urban roads connecting the surrounding areas. The less concentrated road space is the secondary road of the city. The road is not easy to attract pedestrians, and most of the space around the road are the old areas of the city. They are not highly developed and need to be further updated. All these indicated that the main roads in a city have an important impact on the layout of urban space function, the direction and trend of urban development, and the agglomeration and development of urban center.
4.2 Spatial autocorrelation analysis
On the basis of the topological models of integration and total depth of road network in Jinan city, the study carried out spatial autocorrelation analysis, respectively, and obtained the corresponding global Moran’s I index, Z and P values to judge its significance. By further analyzing the local spatial autocorrelation, we could obtain five clustering distributions: H–H clustering, L–L clustering, H–L clustering, L–H clustering, and random distribution.
4.2.1 Global spatial autocorrelation analysis
According to the spatial autocorrelation analysis report (Figure 11), the Moran’s I index of integration and total depth of road network in Jinan urban area during the epidemic is 0.5465 and 0.6067 > 0, respectively. The global Z(I) is 174.7870 and 193.6082 > 1.65. The global P value is 0.0000 (Table 3). All these indicated that the road network space in the main urban area of Jinan tends to be concentrated on the whole and the clustering effect is significant. Road network forms an obvious agglomeration space [45,46,47,48]. In addition, the road network spatial structure in the main urban area of Jinan presents a significant positive correlation with the urban spatial structure in terms of agglomeration. It could be concluded that there is obvious abnormal space of agglomeration in the main urban area of Jinan city in the early stage of the epidemic. Relevant departments should take certain measures to plan the space layout and carry out epidemic prevention and control.
Analysis report of road network global integration spatial autocorrelation and global total depth spatial autocorrelation in Jinan city (Source: drawn by the author. Year: 2022). Note: The Moran’s I index of integration and total depth of road network in Jinan urban area in the early stage of the epidemic is 0.5465 and 0.6067 > 0, respectively. The global Z(I) is 174.7870 and 193.6082 > 1.65. The global P value is 0.0000.
Attribute values of global spatial autocorrelation analysis of road network in Jinan City
| Analyze project | Global Moran’s I index | Global Z(I) | Global P | Spatial agglomeration |
|---|---|---|---|---|
| Integration | 0.5465 | 174.7870 | 0.0000 | yes |
| Total depth | 0.6067 | 193.6082 | 0.0000 | yes |
Source: drawn by the author. Year: 2022.
4.2.2 Local spatial autocorrelation analysis
Global spatial autocorrelation analysis could find that the potential epidemic areas within a region are clustered. Local spatial autocorrelation analysis could further locate the aggregation region. Clustering and anomaly analysis are carried out on the basis of global spatial autocorrelation analysis to obtain the results of local spatial autocorrelation analysis. This result is a visual sketch of the abnormal regional distribution of epidemic potential (Figure 12).
Analysis map of road network global integration (a) and total depth (b) local spatial autocorrelation in Jinan city in the early stage of the epidemic (Source: drawn by the author. Year: 2022). Note: Clustering and anomaly analysis were carried out on the road network integration and total depth in the early stage of the epidemic in the main urban area of Jinan City, so that we could get the results of local spatial autocorrelation analysis and locate the specific location of the agglomeration area. This area is a visualized area with abnormal epidemic potential.
According to the above analysis, the epidemic risk area could be divided into three circles: high-risk agglomeration area, buffer area, and low-risk area. Among them, the high-risk agglomeration area is basically located in the landscape area, commercial complex center area, residential neighborhood life circle area, University city area, transportation hub area, and high-tech industry area (Figure 13). Because of their unique leisure, business, residence, education, and transportation, the industrial functions of these areas are easy to attract people and produce clustering characteristics. It makes them a high-risk focus for the epidemic. The buffer area has no spatial correlation. The low-risk area is discrete because it is far away from the central area (Figure 14).
Perspective view of main agglomeration points and scene view of people gathering in Jinan City (Source: drawn by the author. Year: 2022). (A) Resident community area in Huaiyin District; (B) Commercial and school area in Licheng District.
Analysis map of potential epidemic risk circle in Jinan City in the early stage of the epidemic (Source: drawn by the author. Year: 2022). Note: The area with the highest potential risk and agglomeration of epidemic in the city is basically located in the scenic area with strong tourism and attractive flow, the central area of commercial complex, the community area with concentrated living circles of residents in the neighborhood, the University city area, the transportation hub area, and the high-tech industry area. It is the high-risk agglomeration area of epidemic. There is no spatial correlation in the periphery of the buffer area. The most periphery is the low-risk area of epidemic because it is far away from the central area and its spatial distribution is discrete.
From the autocorrelation analysis map of local space of integration, combining the administrative boundary and traditional functional zoning, it could be found that the agglomeration space could be divided into seven zones: 1. scenic areas mainly consist of Quancheng Square, Daming Lake Park, Baotu Spring Park, Furong Street, Kuanhouli, and Qianfo Mountain; 2. Jinan Ronghui old commercial port, Grand View Garden, Heroes Mountain culture market, Shandong Sports Center, and Shandong Book City as the main commercial and stylistic area in downtown area; 3. Greenbelt Xinli Louvre Mansion, New World Sunshine Garden, Oriental New Heaven and Earth, Pingli community, Gongxiang street community, Shunxiang street community, etc., in Huaiyin District of Jinan old town resident community; 4. Lixia District schools and residential community areas of central campus of Shandong University, Shandong Normal University and its affiliated secondary schools, Jinan No.7 Middle School of Shandong Province, Shandong University of Finance and Economics, Shandong Art College, Shandong University of Architecture and adjacent residential communities; 5. Licheng commercial and school districts mainly consisting of Impression City, Hongjialou Business Circle, and Hongjialou campus of Shandong University; 6. transportation hub area of Tianqiao District mainly including Jinan station, Jinan long-distance bus general station, Jinan north station, Daming Lake station, Tianqiao Interchange, and Jinan Square bus station; 7. New and high technology industry zones in Lixia District centered on Qilu industrial park and Jinan International Convention and Exhibition Center. From the local spatial autocorrelation analysis map of total depth, we could see that the clustering centers present basically coincide with the integration analysis, and the clustering spreads to the surrounding areas. It could still be seen that the potential anomaly centers are mainly concentrated in the above seven core zones (Figure 15). Most of the southern side is mountainous and hilly terrain, with more green water surface. These areas are not conducive to the concentration of people. Both the northern water system, large water bodies, and park areas of the central Daming Lake could reduce the risk of the outbreak.
Analysis map of epidemic potential area in the early stage of the epidemic in Jinan City (Source: drawn by the author. Year: 2022). Note: It could be seen from the local spatial autocorrelation analysis map of integration that the high-risk agglomeration areas are mainly concentrated in seven core areas: (1) scenic area in calendar lower area; (2) commercial and stylistic areas in the city center; (3) resident community area in Huaiyin District; (4) is Lixia District school and residential community zone; (5) commercial and school districts in Licheng District; (6) transportation hub area of Tianqiao District; (7) Lixia District high-tech industrial zone.
4.3 Infrastructure nuclear density estimation analysis
The analysis of road network topological structure in Jinan city could clearly show the aggregation of road space and reflect the potential aggregation abnormal space of the city. In this section, we introduced nuclear density estimation analysis of POI data of infrastructure within the scope of study [49]. The scope of agglomeration anomaly area of potential epidemic outbreak in main urban area of Jinan City was further confirmed by the visualization performance of urban space vigor.
According to “Silverman empirical rule,” the kernel density bandwidth of this analysis was determined to be 793.62 m [50]. It was divided into 5 grades by Jenks natural fracture method: key risk area, high risk area, medium risk area [51], low risk area, and no risk area [52] (Figure 16). Through the density distribution plane of POI data generated by kernel density analysis tool in ArcGIS spatial analysis, it could be reflected that the area with higher kernel density is the agglomeration area of urban vitality [53], namely, the potential abnormal area of epidemic. By the kernel density analysis of all infrastructures, the density distribution of POI is close to that of urban spatial vitality. The analysis result was a smooth grid surface, and the kernel density ranged from 1 to 1501.28 [54]. Based on the analysis, there are 3 areas with the highest risk of hidden dangers in the city. They are located in Quancheng Square, Baotu Spring, Furong Street, and Kuanhouli Block on the south side of Daming Lake, commercial complex areas such as Jinan Ronghui old commercial port, Grand View Garden and Wanda Square, and Impression City and Hongjialou commercial area. The medium-risk and high-risk areas radiate outwards around the key risk areas, and are basically located in the core areas of the main urban area of Jinan near commercial blocks, University towns, important transportation hubs, and scenic areas. And the radiation area obviously extends to the north along Jiluo Road, extends to the south along the Shunhe viaduct road, extends to the east along the North Park viaduct road, and extends to the west along the industrial north viaduct road. In the most periphery, there are low-risk areas and no risk areas, with relatively low urban vitality and temporary risk-free [55].
Kernel density analysis of POI of all infrastructures and risk circle layer of abnormal urban agglomeration area (Source: drawn by the author. Year: 2022). Note: The abnormal urban agglomeration area could be divided into five levels: key risk area, high risk area, medium risk area, low risk area, and no risk area. There are three key risk areas: (1) Baotu Spring Square, Baotu Spring, Furong Street, and Kuanhouli Block in the south of Daming Lake; (2) Jinan Ronghui old commercial port, Grand View Garden, Wanda Plaza, and other commercial complex areas; (3) Impression City and Hongjialou commercial area.
Kernel density analysis of POI was conducted for commercial, educational, residential, transportation, government institution, and green space infrastructure, respectively [56] (Figure 17). Commercial distribution area is the area with high incidence of crowd activities [57] and it has become a key gathering area; education area is the area with key activities of student groups; residential area is the area with population gathering at night; transportation area is the area with key activities of external floating population; and green space area is the area with key activities of tourist population [58]. These areas are the key detection abnormal areas of potential epidemic dangers. Government sector is the sub-key area where people gather and could be used as an auxiliary reference.
Kernel density analysis of POI of various infrastructures (Source: drawn by the author. Year: 2022). Note: Commercial distribution area is the area with high incidence of crowd activities, and it has become a key gathering area; education area is the area with key activities of student groups; residential area is the area with population gathering at night; transportation area is the area with key activities of external floating population; and green space area is the area with key activities of tourist population.
5 Discussion on spatial layout and structure optimization
5.1 Spatial analysis results
The following conclusions could be drawn from this study:
There are 12 roads with the greatest potential risk of epidemic. They mainly concentrate on the main development axis of the city and the outer urban roads connecting the surrounding areas, and the roads passing through the commercial complex central area, scenic area, school area, transportation hub area, and residential neighboring community area. This is the result of an analysis of the topological attributes of spatial grammar. This method could be used to analyze the urban roads. These roads are most likely to attract pedestrians and cause spatial agglomeration, and they are the ones that have been detected to have abnormal clustering potential.
Combining the administrative boundary and traditional functional zoning, we can divide seven districts with high road network accessibility and agglomeration in the main urban area of Jinan. They are in the scenic tourism areas centered on Quancheng Square, Baotu Spring, Daming Lake, Furong Street, and Kuanhouli. These areas are easy to attract people. The agglomeration area is also in the commercial, cultural, and sports areas of the downtown area; Huaiyin District of Jinan old town community area; Schools and residential communities in Lixia District, high-tech industrial areas, commercial, and school areas in Licheng District, and transportation hub areas in Tianqiao District. This is the result of the spatial autocorrelation analysis based on the axle topological model. This analysis method could roughly get the agglomeration centers. These areas are easy to attract people in the city, and they are the abnormal hidden danger areas of agglomeration detected.
The schematic diagram of risk grade of abnormal urban agglomeration area could be clearly divided into five risk grade circle structures: key risk area, high risk area, medium risk area, low risk area, and no risk area. This is the result of kernel density analysis on POI points of interest of various infrastructures in the main urban area of Jinan City. According to the diagram, we could see that there are three areas with the highest risk of hidden dangers in the city. They are located in Quancheng Square, Baotu Spring, Furong Street, and Kuanhouli Block on the south side of Daming Lake; Jinan Ronghui old commercial port, Grand View Garden, Wanda Plaza, and other commercial complex areas; Impression city and Hongjialou commercial area. These areas are the most dynamic spaces in the city. It could be found from the study that these three areas are basically located in the commercial center and are most affected by commerce, so they need to focus on prevention and control. At the same time, the analysis of POI kernel density also confirmed the conclusion of road network space analysis again.
The terrain, water body, afforestation, and park in the south could effectively reduce the concentration of people. It is an important area for relieving abnormal hidden dangers of the epidemic. Because the south side is affected by the mountain terrain, large urban parks and green space could be formed.
The water system in the north, the large water space of Daming Lake in the middle of the city, and large parks in the city could effectively prevent the hidden dangers of the epidemic.
5.2 Verification of analysis results
Taking the COVID-19 as an example, from March 28, 2022 to April 26, 2022, there was a recurrence of the epidemic in Jinan. According to the itinerary of positive infected persons in Jinan published by Jinan Health Commission, we could find 130 locations of positive infected persons in this period, and 81 of them are within the scope of this study (Figure 18). Only 49 sites were located in large areas outside the study area. Thus, it could be verified that the selected main urban area of Jinan is the main agglomeration center area within the scope of Jinan city.
Location distribution of epidemic cases in Jinan city during local time period (Source: drawn by the author. Year: 2022). Note: By superimposing and analyzing the case monitoring data in the scope of study with the 12 agglomeration abnormal hidden danger roads, 7 agglomeration abnormal hidden danger zones, and the risk level circles of urban aggregation hidden danger in this study, we could conclude that there are 67 trajectory locations in the interior of the dangerous road or area, and there are 9 trajectory locations within the 3 key risk circles, while only 14 are located in low or temporary risk areas.
By superimposing and analyzing the case monitoring data in the scope of study with the 12 agglomeration abnormal hidden danger roads, 7 agglomeration abnormal hidden danger zones and the risk level circles of urban aggregation hidden danger in this paper, we could conclude that there are 67 trajectory locations in the interior of the dangerous road or area, and there are 9 trajectory locations within the three key risk circles, while only 14 are located in low or temporary risk areas. Therefore, it could be verified that the abnormal potential roads and areas measured by the analysis of urban road network and infrastructure spatial layout are relatively accurate and could be used for the predictive analysis of the potential aggregation areas in the early stage of the epidemic.
In addition, the author also found that most of the potential epidemic outbreak locations are located in Baotu Spring, Black Tiger Spring, Kuanghouli, Furong Street, and other landscape tourism areas on the southern side of Daming Lake, as well as surrounding large commercial areas, transportation hub area centered on Jinan Station in Tianqiao District, community living areas with concentrated residents in Huaiyin District, and along the Jingshi road. It could be verified that the outbreak of the epidemic is mainly caused by the movement of foreign population, the increase in the number of people in scenic spots, the gathering of people in shopping malls, and the relative concentration of residents in the community life circles. Therefore, in the face of the outbreak of the epidemic, more emergency prevention and control should be carried out from these aspects.
5.3 Analysis of prevention and control measures
In view of the abnormal hidden danger areas gathered in the early stage of the epidemic and the reasons for the substantial increase in the risk of interpersonal communication, the author proposed the following solutions:
Set up epidemic potential prevention and control areas. We should set up more intensive hazard prevention and control points on the 12 roads with the greatest risk of epidemic and reduce the setting accordingly on the other roads. On this basis, we should set up potential hazard prevention and control points according to seven zones to ensure that the service radius could fully cover each zone.
Build centralized epidemic isolation areas. We should distribute centralized isolation points in low-risk areas and temporary non-risk areas which are the most peripheral areas in the circle of abnormal risk level of urban agglomeration. At the same time, we could also set up centralized epidemic isolation points in the southern mountain area.
Establish shelter rescue hospital in time. We should build shelter rescue hospitals and epidemic prevention and control command centers with the highest emergency level in the three key risk areas in the urban agglomeration abnormal risk hierarchy. This is to curb the large-scale outbreak and spread of the epidemic in the most efficient way.
Block local sections and areas. In the event of an outbreak of the epidemic, the 12 roads with the greatest risk of potential epidemic hazards should be urgently blocked or restricted, and the scenic area, commercial complex area, school area, residential community area, and transportation hub area should be strictly controlled. Close treatment shall be carried out according to the situation.
Carry out emergency control on some public places and service facilities. For shopping malls, scenic spots, restaurants, cinemas, hotels, postal logistics areas, and other public places with high vitality in the city, we should immediately carry out emergency control when the epidemic situation breaks out, and should also focus on the behavior of internal personnel and close contacts.
In the face of the sudden epidemic, the isolated traditional public health measures could still play a key role in containment. Wilder-Smith and Freedman [59] have carefully analyzed the successful application of traditional public health measures in isolation, social control, and community containment in view of the COVID-19 epidemic. On this basis, this study puts forward a more perfect scheme of prevention and control measures, and skillfully combines the implementation of prevention and control measures with the spatial layout analysis. This is an important progress in epidemic prevention and control. At present, China is in the stage of strict control of national epidemic prevention. According to the COVID-19 epidemic prevention and control announcement publicly released by the health commission of Jinan City, there are only four case track distribution locations since May 2022. They are respectively located in Huairen Village, Gucheng Village, Zhoujiaji Village, and Fujiamiao Village, Huairen Town, Shanghe County, and they are all located in non-main urban areas outside the scope of study. It could be seen that China’s strict control measures have achieved remarkable results. Under the human interference, the hidden danger points have shifted from the area with abnormal concentration to the place with relatively loose control.
5.4 Optimization of prevention and control measures
According to the analysis results of this study, the author proposed the following optimization strategies for timely relieving of the abnormal clustering space of epidemic hidden dangers, maintaining the vitality of the city and optimizing the spatial layout:
Optimization of scenic area. The current outbreak in Chinese cities is already in a stable situation, but Jinan city still could not relax vigilance. In the early stage of the epidemic, relevant personnel should pay attention to the restrictions on daily flow of people and the control of entrances and exits in Daming Lake, Quancheng Square, Baotu Spring, Furong Street, and Kuanhouli scenic spot. In Daming Lake road, Baotu Spring road, and other sections, there should be daily restrictions on vehicles, because these sections are easy to attract people, and cause crowded streets. This could not only maintain the vitality of normal streets, but also prevent a large number of people from gathering and causing abnormal risks of the epidemic.
Optimization of residential community areas. The residential community space with strong road concentration in Huaiyin District and Lixia District should be the focus of epidemic prevention and control. After field research, it could be found that most of the road networks in this area are equipped with one-way pavements. They are easy to cause road section blockage. A lot of parking is directly set in the narrow streets. In this case, we should widen the processing network, develop underground parking lot in residential community, and gradually replace above-ground parking.
Optimization of school area. Student groups tend to gather in school districts in Lixia District and Licheng District. Therefore, these areas should adopt semi-closed management to limit the opening of entrances and exits in the early stage of the epidemic. The entrances should be set in open roads and sections that are not easy to gather people, and open at staggered peak periods within the time limit.
Optimization of business area. Jinan Ronghui old commercial port, Grand View Garden, Hongjialou commercial circle, and other commercial agglomeration centers in the city center are easy to attract large numbers of people. These areas should widen the surrounding streets, add green isolation belts, and set green ring islands at the crossings. This is used to plan restrictions on popularity.
Optimization of transportation hub area. The transportation hub areas such as Jinan Station, Daming Lake Station, and Jinan long-distance bus terminal in Tianqiao District are most vulnerable to external epidemics. We should strictly regulate the access routes of inbound and outbound passengers, set up a large number of open parking lots around, broaden the main roads around, and ease the traffic. This could prevent people from gathering.
Optimization of urban main road. Driving restrictions should be imposed on roads with high radiation potential for epidemic. We could widen alternative roads in the same direction around the road. And we could increase the road density appropriately to evacuate the traffic and reduce the hidden danger of road aggregation.
Optimization of urban open space. Urban city makes full use of the favorable conditions of terrain, water body, greening, and parks. During an epidemic, we could use the existing resources of terrain, water, greening, and parks for emergency evacuation.
In the past, there has been a lot of research on the optimization of spatial layout, such as the research on the spatial layout of fire stations, medical service facilities, and other infrastructures within the scope of population use [60], the research on the spatial layout relationship between retail business or industry and road traffic network [61], and the research on the internal spatial layout of a certain area such as large parks or rural settlements [62]. However, there is a lack of research on the combination of prevention and control of epidemic risks and optimization of spatial layout. This study proposes different optimization strategies for scenic area, residential community area, school area, business area, transportation hub area, main urban roads, and urban natural space at the beginning of the outbreak of human-to-human epidemic. This has promoted new progress in the research field of spatial layout optimization.
6 Conclusion
The consequences of the outbreak of interpersonal transmission epidemic could not be ignored. Therefore, the study puts forward a new method to accurately infer the hidden danger space of abnormal gathering hidden dangers in the city in the absence of control and case data at the initial stage of the epidemic, to carry out emergency prevention and control and space optimization. In this way, the further spread of the epidemic could be curbed in time. This study takes urban road network space as the main research object for quantitative analysis, and combines new research methods of spatial big data. First of all, we built a road network topology model in the main urban area of Jinan City at the initial stage of the epidemic, and located 12 roads with hidden dangers. They are the main axis of the city and the external urban roads, as well as the roads passing through the central area of the commercial complex, the scenic area, the school area, the neighborhood community area, and the traffic hub area; On this basis, we carried out spatial autocorrelation analysis on the road topology model and divided it into seven risk areas of gathering hidden dangers. They are landscape tourism sites, commercial and sports areas in downtown district, residential communities in Huaiyin District, schools areas, residential communities, and high-tech industry areas in Lixia District, commercial and school areas in Licheng District, and transportation hub areas in Tianqiao District. Then, we analyzed the urban vitality space through the core density estimation method of interest-points, determined five risk level circles, and confirmed the analysis results again. The study also concluded that terrain, water surface, greening, and parks could effectively reduce the concentration of people flow, and this area is an important area for relieving the abnormal hidden dangers of the epidemic. Finally, the study verified and analyzed the obtained case monitoring data, and confirmed that it is feasible to analyze the epidemic hidden danger points by using the spatial layout of roads and infrastructure.
According to the analysis results, the author proposed five prevention and control measures, including setting up epidemic potential prevention and control points, setting up epidemic centralized isolation points, timely establishment of shelter rescue hospitals, blocking local roads and areas, and emergency control of some public places and service facilities. The author also divided the hidden danger area into scenic area, residential community area, school area, commercial area, traffic hub area, main urban roads, and urban natural space for zoning optimization.
This study introduced spatial big data to conduct quantitative research on urban road network space. The method breaks through the traditional qualitative research ideas. This has become a new method for monitoring epidemic outbreak points and hidden danger points by using city maps, and further proposing prevention and control and optimization measures. It is applicable to the initial stage of human-to-human transmission and the normalization period of epidemic with loose control. The method is accurate, simple, practical, and operable. The implementation of the new method provides valuable reference for relevant practitioners and scholars in urban protection, urban analysis, urban management, and urban construction. It has become a major breakthrough in the application of space syntax in the field of urban public security prevention and control. However, through analysis, we can only find out the areas with high potential epidemic risks. We also need to further study the influencing factors that cause the hidden danger of epidemic agglomeration in the region. We will continue to discuss how to maintain the urban vitality during the normalization of future epidemic and how to restore the urban vitality after the epidemic.
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Funding information: This work was supported by the 2021 Key Project of Education Science Planning, Heilongjiang, China (Project number: GJB1421230); The Opening Fund of Key Laboratory of Interactive Media Design and Equipment Service Innovation, Ministry of Culture and Tourism, China (Project number: 2020 + 11), and Teaching and Research Project of Northeast Forestry University in 2022 (Project number: DGY2022-32).
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Author contributions: M.S. and Q.R. contributed to the conception and design of the study. M.S. organized the database. Q.R. performed the statistical analysis. M.S. wrote the first draft of the manuscript. Q.R. wrote sections of the manuscript. All authors contributed to manuscript revision and read and approved the submitted version.
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Conflict of interest: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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Publisher’s note: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
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