Investigating the Relationship between the Built Environment and Relative Risk of COVID-19 in Hong Kong

Understanding the relationship between the built environment and the risk of COVID-19 transmission is essential to respond to the pandemic. This study explores the relationship between the built environment and COVID-19 risk using the confirmed cases data collected in Hong Kong. Using the information on the residential buildings and places visited for each case from the dataset, we assess the risk of COVID-19 and explore their geographic patterns at the level of Tertiary Planning Unit (TPU) based on incidence rate (R1) and venue density (R2). We then investigate the associations between several built-environment variables (e.g., nodal accessibility and green space density) and COVID-19 risk using global Poisson regression (GPR) and geographically weighted Poisson regression (GWPR) models. The results indicate that COVID-19 risk tends to be concentrated in particular areas of Hong Kong. Using the incidence rate as an indicator to assess COVID-19 risk may underestimate the risk of COVID-19 transmission in some suburban areas. The GPR and GWPR models suggest a close and spatially heterogeneous relationship between the selected built-environment variables and the risk of COVID-19 transmission. The study provides useful insights that support policymakers in responding to the COVID-19 pandemic and future epidemics.


Introduction
Three coronaviruses have emerged in the past two decades (i.e., SARS-CoV, MERS-CoV, and SARS-CoV-2) [1]. Among them, the novel coronavirus (SARS-CoV-2) and the COVID-19 pandemic it causes pose a particularly serious threat to global health, as the numbers of new COVID-19 cases and deaths continue to increase at alarming rates in some countries. COVID-19 was designated as a pandemic by the World Health Organization (WHO) on 11 March 2020 [2]. To mitigate the pandemic and control its spread in human populations, most governments have implemented drastic intervention measures, which include travel restrictions, stay-at-home orders, school closings, and restrictions of The location, density, and accessibility of different built-environment features (e.g., subway stations) may affect the density of people moving through certain spaces and thus may have a significant impact on disease transmission (e.g., higher built-environment densities tend to increase people's interactions) [17]. Different types of housing and the amount of green space in an area (which facilitates social distancing and the avoidance of crowdedness) may also be important factors. Specific types of venues and areas where superspreading events and cluster outbreaks tend to occur (e.g., pubs, restaurants, and karaoke venues) are also high-risk built-environment features for disease transmission.
Our knowledge about the influences of the built and social environments on the spread of highly contagious infectious diseases like COVID-19 is still highly limited to date, and some apparently useful findings from recent studies may be unreliable. For instance, in a recent study of 913 metropolitan counties in the U.S., Hamidi et al. [18] found that metropolitan size is more important than density in influencing the spread of the COVID-19 pandemic in the U.S., based on county-based COVID-19 infection and mortality rates. But this finding is contrary to the results we obtained using much smaller areal units on the COVID-19 pandemic in Hong Kong; urban density seems to be an important factor affecting the incidence rate and transmission risk of COVID-19. An important methodological issue ignored in Hamidi et al. [18] is that whether density matters may depend on the spatial scale of the analytical units or geographic areas (e.g., counties, census tracts, or census block groups) used in the analysis. This is the well-known modifiable areal unit problem (MAUP), which means that research findings may vary due to the use of different spatial scales or zonal schemes of the geographic areas for deriving the area-based variables (e.g., urban density and infection rates).
Further, studies have found that the coronavirus can survive on various specific environmental surfaces for a long time outside of its host organism [19]. For instance, Casanova et al. [20] observed that the coronavirus can remain infectious in water and sewage for days to weeks. In 2003, a clustered outbreak of SARS-CoV happened in a high-rise residential building in Hong Kong through the faulty and contaminated sewage system of the building [21]. Van et al. [22] reported that the SARS-CoV-2 virus can remain in aerosols after 3 hours and on plastic and stainless-steel surfaces after 72 hours. The various built-environment surfaces on which the coronavirus can survive are distributed among various venues (e.g., pubs and restaurants) across urban spaces, and infected individuals may leave the virus on certain surfaces (e.g., door handles, elevator buttons, and tableware) in the venues they visited or stayed (e.g., restaurants or hotels). Hence, many built-environment features that allow people to carry out their daily activities may become potential sources of infection transmission [23,24].
Many studies have investigated the relationship between the built environment, human behavior, and health [25][26][27][28]. For instance, researchers have observed that neighborhoods with healthy and diverse food environments can reduce the incidence of obesity [29,30]. Dense green spaces, lower building height, and a good sky view may encourage people to undertake more outdoor activities (e.g., running, walking, cycling, picnicking, and hiking) and may lead to better health [31,32]. People's immunity may improve as a result of more physical activities and exposures to green spaces, which in turn may reduce stress, obesity, and vulnerability to infectious disease [33,34]. These findings are relevant to studies on COVID-19 risk because people with poor health are more vulnerable and more easily infected, which often manifest in certain patterns of comorbidities (e.g., people with chronic diseases like diabetes and hypertension are far more likely to die from . On the other hand, studies have found that people tend to visit areas with high accessibility and high-density commercial areas for social activities with their friends (e.g., drinking in bars, watching movies, and dining in restaurants) to reduce their stress [35,36]. Further, areas with high-density transport facilities and diverse land-use types may encourage people to conduct more short-distance travel activities due to the convenience of activity opportunities [37].
On the whole, these studies highlight that the spatial distribution of built-environment features influences the geographic patterns of not only human contacts and social interactions but also people's health and immunity (by increasing certain health-promoting activities, which in turn may modify people's COVID-19 risk). This suggests that the risk of contracting COVID-19 may be reduced by modifying risky human behaviors through modifying their interaction patterns (e.g., stay-at-home orders) and certain features of the built environment [38]. For instance, the nodal accessibility of an area, which represents how well the area is connected with other areas via the transport network, can be dynamically modified (e.g., travel restrictions) to help control the spread of a pandemic [39,40]. In the long run, improving urban designs and restructuring urban spaces (e.g., including more green spaces in high-density areas) may modify pedestrian flows and the concentrations of activities in certain areas, which may help mitigate the spread of future pandemics [41]. Hence, the geographic patterns of human behaviors and interactions can be modified using built-environment-related non-pharmaceutical intervention measures to control the spread of COVID-19 [42]. It is thus important to first understand the transmission dynamics of COVID-19 by examining the relationships among built-environment features and COVID-19 risk.

Study Area and Data
As the study area of this research, Hong Kong is a special administrative region of China in the eastern Pearl River Delta ( Figure 1). It is one of the most densely populated cities in the world. It has an estimated population of about 7.4 million (by the end of 2019) of various nationalities in a 1104 km 2 territory. This study seeks to shed light on the relationships between COVID-19 risk and built-environment features that may differ from other previous studies or other study areas [43,44]. It examines the spatially heterogeneous influences of various built-environment features on COVID-19 transmission risk in Hong Kong. orders) and certain features of the built environment [38]. For instance, the nodal accessibility of an area, which represents how well the area is connected with other areas via the transport network, can be dynamically modified (e.g., travel restrictions) to help control the spread of a pandemic [39,40]. In the long run, improving urban designs and restructuring urban spaces (e.g., including more green spaces in high-density areas) may modify pedestrian flows and the concentrations of activities in certain areas, which may help mitigate the spread of future pandemics [41]. Hence, the geographic patterns of human behaviors and interactions can be modified using built-environment-related nonpharmaceutical intervention measures to control the spread of COVID-19 [42]. It is thus important to first understand the transmission dynamics of COVID-19 by examining the relationships among built-environment features and COVID-19 risk.

Study Area and Data
As the study area of this research, Hong Kong is a special administrative region of China in the eastern Pearl River Delta ( Figure 1). It is one of the most densely populated cities in the world. It has an estimated population of about 7.4 million (by the end of 2019) of various nationalities in a 1104 km 2 territory. This study seeks to shed light on the relationships between COVID-19 risk and builtenvironment features that may differ from other previous studies or other study areas [43,44]. It examines the spatially heterogeneous influences of various built-environment features on COVID-19 transmission risk in Hong Kong. The study uses the COVID-19 data provided by the Hong Kong Department of Health that are freely available via the government's open-data website (https://data.gov.hk). These data provide the following information about the COVID-19 cases in Hong Kong: the number of confirmed cases, a brief history and some demographic data for each case, and the countries, buildings, or venues visited by the cases during the incubation period for both imported and local cases. The confirmed cases are classified into two groups according to the geographic origin of infection: (1) imported cases (individuals who were infected in a foreign country or city) and (2) local cases, which include cases with clearly local sources (e.g., infected by a family member or a colleague at work), and cases involving infection by local or imported cases or by possible close contact with local or imported cases (see Figure 1). The Hong Kong Government started releasing the COVID-19 data from 27 January 2020, and the data have been updated daily after that. Furthermore, the first wave (i.e., most of the cases are imported cases) and the second wave (i.e., most of the cases are local cases) of the The study uses the COVID-19 data provided by the Hong Kong Department of Health that are freely available via the government's open-data website (https://data.gov.hk). These data provide the following information about the COVID-19 cases in Hong Kong: the number of confirmed cases, a brief history and some demographic data for each case, and the countries, buildings, or venues visited by the cases during the incubation period for both imported and local cases. The confirmed cases are classified into two groups according to the geographic origin of infection: (1) imported cases (individuals who were infected in a foreign country or city) and (2) local cases, which include cases with clearly local sources (e.g., infected by a family member or a colleague at work), and cases involving infection by local or imported cases or by possible close contact with local or imported cases (see Figure 1). The Hong Kong Government started releasing the COVID-19 data from 27 January 2020, and the data have been updated daily after that. Furthermore, the first wave (i.e., most of the cases are imported cases) and the second wave (i.e., most of the cases are local cases) of the pandemic in Hong Kong had been under control by 14 April 2020 (i.e., no more local cases were found for several weeks after 14 April 2020). Hence, our analysis uses the data between 27 January 2020, and 14 April 2020 (which demarcate a period with two clear and complete waves of the pandemic) and is based on the 291 Tertiary Planning Units (TPUs) of Hong Kong and the specific buildings or venues visited by the confirmed cases (note that Hong Kong is divided into 291 TPUs for the purpose of town planning and census).
Using the building location information in the COVID-19 data, we first aggregate the case locations into the TPUs. Data on the relevant built-environment features of Hong Kong are then assembled from the same government open-data website (https://data.gov.hk) provided by various government departments (e.g., the Planning Department and the Transport Department). These data cover land use, population, building footprints, the multimodal transportation network, green spaces, transport facility density, and other features. The land-use dataset was compiled by the Planning Department in 2018 using multiple data sources (e.g., satellite images, in-house survey data, and other relevant information from various government departments), which is a 10 × 10 m raster dataset with 27 land-use types. Figure 2 shows an example of the data that includes various types of land use. The 2020 estimated population distribution was released by the Working Group on Population Distribution Projections (WGPD), which adopted the latest Census and Statistics Department's population projections released in September 2017 as the control. The building polygons are available as a 3D spatial dataset with building geometry and height. The multimodal transportation network dataset (as of 9 March 2020) includes data on the public transit routes and the location of public transit stations and stops (i.e., buses, the Mass Transit Railway, and ferries). Further, a sky-view factor (SVF) distribution dataset generated in a previous study is obtained from the authors [45]. This SVF dataset is a 10 × 10 m raster dataset retrieved from airborne LiDAR data. The SVF is the ratio of the visible sky with obstructions to that without obstruction, which ranges from zero to one to indicate a totally obstructed sky and open sky [46]. It has been found that the SVF is influenced by building height and density, which may in turn influence the health risk of an urban area [47]. Figure 3 shows the building polygons with height information and the spatial distribution of the sky-view factor. pandemic in Hong Kong had been under control by 14 April 2020 (i.e., no more local cases were found for several weeks after 14 April 2020). Hence, our analysis uses the data between 27 January 2020, and 14 April 2020 (which demarcate a period with two clear and complete waves of the pandemic) and is based on the 291 Tertiary Planning Units (TPUs) of Hong Kong and the specific buildings or venues visited by the confirmed cases (note that Hong Kong is divided into 291 TPUs for the purpose of town planning and census).
Using the building location information in the COVID-19 data, we first aggregate the case locations into the TPUs. Data on the relevant built-environment features of Hong Kong are then assembled from the same government open-data website (https://data.gov.hk) provided by various government departments (e.g., the Planning Department and the Transport Department). These data cover land use, population, building footprints, the multimodal transportation network, green spaces, transport facility density, and other features. The land-use dataset was compiled by the Planning Department in 2018 using multiple data sources (e.g., satellite images, in-house survey data, and other relevant information from various government departments), which is a 10 × 10 m raster dataset with 27 land-use types. Figure 2 shows an example of the data that includes various types of land use. The 2020 estimated population distribution was released by the Working Group on Population Distribution Projections (WGPD), which adopted the latest Census and Statistics Department's population projections released in September 2017 as the control. The building polygons are available as a 3D spatial dataset with building geometry and height. The multimodal transportation network dataset (as of 9 March 2020) includes data on the public transit routes and the location of public transit stations and stops (i.e., buses, the Mass Transit Railway, and ferries). Further, a sky-view factor (SVF) distribution dataset generated in a previous study is obtained from the authors [45]. This SVF dataset is a 10 × 10 m raster dataset retrieved from airborne LiDAR data. The SVF is the ratio of the visible sky with obstructions to that without obstruction, which ranges from zero to one to indicate a totally obstructed sky and open sky [46]. It has been found that the SVF is influenced by building height and density, which may in turn influence the health risk of an urban area [47]. Figure 3 shows the building polygons with height information and the spatial distribution of the sky-view factor.

Assessing COVID-19 risk.
We use two different measures to assess the COVID-19 risk in Hong Kong. The first measure is the incidence rate or prevalence (R1: case density), which is the number of confirmed cases per 1000 people in each of the 291 Tertiary Planning Units (TPUs) over a specified time period. Note that only "local" confirmed cases are included to calculate the incidence rate in this study because imported cases are the result of the risk factors in their source areas, not the built-environment risk factors of Hong Kong. The second measure is R2 (venue density), which is the number of venues or buildings visited by the confirmed cases in each TPU. As mentioned earlier, the coronavirus can survive on various built-environment surfaces, and certain built-environment features tend to attract more human activities and interactions and thus are more likely to become sources of COVID-19 transmission. Hence, the second measure COVID-19 risk (R2) is computed based on the number of places and venues visited by all confirmed cases (i.e., buildings or places visited by confirmed cases in the last 14 days). Note that both "local" and "imported" confirmed cases are included when calculating R2 because the measure identifies the high-risk places or venues (which have been visited by confirmed cases and as a result, other people who visited these places have a higher risk of contracting COVID-19). The formula for R2 is as follows: where 2 is the venue density of TPU , and is the number of buildings or places in TPU that have been visited by confirmed cases. TPUs with higher values of R1 and R2 have higher COVID-19 risk (i.e., their built-environment features and human activity patterns are more conducive to COVID-19 transmission).

Deriving the Built-Environment Features
As shown in Table 1, nine built-environment features are selected as the independent variables in our analysis: nodal accessibility (NA), population density (PD), private residential density (PR), commercial density (CD), green space density (GSD), building height (BH), transport facility density (TF), land-use diversity (LUD), and sky view (SV). They are computed for each of the 291 TUPs of Hong Kong based on the land-use data, population census data, building polygon data, multimodal transportation network data, and the SVF dataset described earlier. These nine built-environment features are described as follows.
The nodal accessibility of a TPU is derived based on the multimodal transport stations in each TPU. First, each public transit station (i.e., a metro, bus, or ferry station) is regarded as a node, where a link connects node and according to the route network. A specific recommendation from Alexander et al. [48] is that the distance between two stations for a transfer trip should not exceed 183 m (e.g., Lee et al. [49] connected bus stops for internode transfers within a distance of shorter than 120 m in Seoul). Hence, we add a transfer link that connects nearby nodes and of different

Assessing COVID-19 Risk
We use two different measures to assess the COVID-19 risk in Hong Kong. The first measure is the incidence rate or prevalence (R1: case density), which is the number of confirmed cases per 1000 people in each of the 291 Tertiary Planning Units (TPUs) over a specified time period. Note that only "local" confirmed cases are included to calculate the incidence rate in this study because imported cases are the result of the risk factors in their source areas, not the built-environment risk factors of Hong Kong. The second measure is R2 (venue density), which is the number of venues or buildings visited by the confirmed cases in each TPU. As mentioned earlier, the coronavirus can survive on various built-environment surfaces, and certain built-environment features tend to attract more human activities and interactions and thus are more likely to become sources of COVID-19 transmission. Hence, the second measure COVID-19 risk (R2) is computed based on the number of places and venues visited by all confirmed cases (i.e., buildings or places visited by confirmed cases in the last 14 days). Note that both "local" and "imported" confirmed cases are included when calculating R2 because the measure identifies the high-risk places or venues (which have been visited by confirmed cases and as a result, other people who visited these places have a higher risk of contracting COVID-19). The formula for R2 is as follows: where R2 s is the venue density of TPU T s , and w i is the number of buildings or places in TPU T s that have been visited by confirmed cases. TPUs with higher values of R1 and R2 have higher COVID-19 risk (i.e., their built-environment features and human activity patterns are more conducive to COVID-19 transmission).

Deriving the Built-Environment Features
As shown in Table 1, nine built-environment features are selected as the independent variables in our analysis: nodal accessibility (NA), population density (PD), private residential density (PR), commercial density (CD), green space density (GSD), building height (BH), transport facility density (TF), land-use diversity (LUD), and sky view (SV). They are computed for each of the 291 TUPs of Hong Kong based on the land-use data, population census data, building polygon data, multimodal transportation network data, and the SVF dataset described earlier. These nine built-environment features are described as follows.
The nodal accessibility of a TPU is derived based on the multimodal transport stations in each TPU. First, each public transit station (i.e., a metro, bus, or ferry station) is regarded as a node, where a link connects node n and m according to the route network. A specific recommendation from Alexander et al. [48] is that the distance between two stations for a transfer trip should not exceed 183 m (e.g., Lee et al. [49] connected bus stops for internode transfers within a distance of shorter than 120 m in Seoul). Hence, we add a transfer link that connects nearby nodes n and m of different transport modes if the distance between these two stations is not more than 100 m. Second, we create a connectivity matrix C, where C mn presents all the links between nodes n and m (i.e., C mn = 1 if node n and m are connected or 0 if node n and m are not connected). Note that there may be l shortest paths between nodes n and m. Assume that a path connects l i stations via k − 1 nodes with p modal transfers, then the connectivity between nodes n and m is estimated as follows: where t (0 < t < 1) is the scalar measure of the ineffectiveness of transfer, and S (0 < S < 1) represents the scalar of the distance-decay effect. In this study, t is 0.7 and S is 0.8 based on the results of a previous study [50]. After estimating the connectivity between each pair of nodes, the nodal accessibility of node m is obtained by summing the total connectivity C mn over all n: Finally, the nodal accessibility of a TPU is derived by summing up the nodal accessibility of all the public transit stations in that TPU. Population density (PD) is the number of people per kilometer in each TPU. Private residential density (PR), commercial density (CD), transport facility density (TF), and green space density (GSD) are computed based on the area of each of these land-use types in each TPU divided by the area of that TPU. Note that green space density (GSD) in each TPU is estimated based on the sum of the area of grassland, shrubland, and woodland, which cover about 65.4% of the total land-use area of Hong Kong. This area is calculated based on the land-use data mentioned earlier, which classify a cell's land use as green space (i.e., grass, woodland, and shrubland) if the cell is covered dominantly by vegetation. Land-use diversity (LUD) is estimated using the following widely used entropy model: where p i represents the proportion of the ith land-use type, and n is the total number of land-use types.
Building height (BH) is estimated using the building polygon data and digital topographic information.
In this analysis, building height refers to the average building height for each TPU. Sky view (SV) refers to the average SVF per km 2 in each TPU, which is the total SVF in each TPU divided by the area of that TPU.

Exploring the Relationship between Built-Environment Features and COVID-19 Risk
Given that the risk of COVID-19 (i.e., R1 and R2) mentioned in Section 3.2 are count data and that the Poisson regression model is a suitable technique for modeling count data [51], we thus use both global Poisson regression (GPR) and geographically weighted Poisson regression (GWPR) to investigate the relationship between built-environment features and COVID-19 risk. In this analysis, R1 and R2 are the dependent variables, and the independent variables are the nine built-environment features. The GPR and GWPR models are estimated based on the TPUs as the units of analysis. The GPR model is formulated as follows: where Ri represents the COVID-19 risk of TUP i, β i denotes the regression coefficients for the intercept term and the independent variables, and ε denotes the random error. The GWPR model was developed to take into account the issues that the relationships between variables may vary over space, which is referred to as spatial nonstationarity [52], and to reduce estimation error due to spatial autocorrelation. The GWPR model is a localized model that captures the spatial variations in the relationships between variables by fitting parameters that vary over space, weighting relevant neighboring observations (which are TPUs in this study) by using a spatial weight matrix. In this study, the GWPR model is formulated as follows: where i represents the ith TPU, R i stands for the COVID-19 risk of the ith TPU, β i is the estimated regression coefficients of the ith TPU, and ε i is the error term for TPUi. Note that β j is now a function of location ui = (uxi, uyi) , which denotes the two-dimensional coordinates of the ith point (the centroid of the ith TPU) in space. Thus, spatial nonstationarity is addressed in the GWPR modeling framework. In this modeling effort, spatially adaptive bandwidth values are obtained by using the method that minimizes the Akaike information criterion (AIC) of regression models. The variance inflation factor (VIF) is used to test the multicollinearity of the variables. The Akaike information criterion (AIC) approach is used to evaluate the tradeoff between the goodness of fit and the simplicity of the models (i.e., to assess the risk of overfitting or underfitting).

Assessing the COVID-19 Risk in Each TPU
In this subsection, we explore the characteristics of COVID-19 risk in Hong Kong based on the two measures described in Section 3.2. Recall that the first measure is the incidence rate or prevalence (R1: case density), which is the number of confirmed cases per 1000 people in each of the 291 Tertiary Planning Units (TPUs) over a specified time period. The second measure is R2 (venue density), which is the number of venues or buildings visited by the confirmed cases in each TPU. Figure 4 presents the frequency distribution of COVID-19 risk at the TPU level. Both the frequency distributions of R1 and R2 among the 291 TPUs in Hong Kong declines dramatically, indicating that COVID-19 risk is concentrated in the top few TPUs. In order to understand the decay effects in the frequency distributions of R1 and R2, we fit two probability distribution curves using the exponential function p(x) ∼ e bx and the power-law function p(x) ∼ x b to the distributions. The results indicate that both R1 and R2 have a better fit to the exponential function (i.e., R 2 = 0.97 for R1 and R 2 = 0.98 for R2) than to the power-law function (i.e., R 2 = 0.88 for R1 and R 2 = 0.91 for R2). Further, the rate of decay for R1 is higher than that for R2, reflecting that the number of TPUs with high R1 is smaller than R2.  Figure 5 shows the spatial distribution of COVID-19 risk in Hong Kong at the TPU level. As indicated by the results of the frequency distribution analysis of R1 and R2, areas with a high COVID-19 risk are concentrated in a few TPUs in Hong Kong. With respect to the spatial distribution of R1 (Figure 5a), there are three areas (marked as A, B, and C) with high R1. Specifically, Area A is the downtown area with a high density of population and commercial buildings. Areas B and C are suburban areas with low population density and large amounts of public spaces (e.g., country parks and beaches). Figure 5b displays the spatial distribution of R2, where six areas (marked as A, B, C, D, E, and F) with high R2 are identified. Specifically, Areas A and B have high-density commercial and residential buildings, while Areas C, D, E, and F are suburban areas with large amounts of open space (e.g., country parks and beaches). These results suggest that both the downtown and certain suburban areas in the city are high COVID-19 risk areas. Moreover, the incidence rate indicator (R1) may underestimate the COVID-19 risk in some suburban areas with a considerable amount of public spaces.

The Relationship between Built-Environment Features and COVID-19 Risk: Results of the GPR Analysis
In this subsection, we explore the relationships between selected built-environment variables and COVID-19 risk in the study area. The nine built-environment variables described in Section 3.3 are used as the independent variables in the following global Poisson regression (GPR) and  Figure 5 shows the spatial distribution of COVID-19 risk in Hong Kong at the TPU level. As indicated by the results of the frequency distribution analysis of R1 and R2, areas with a high COVID-19 risk are concentrated in a few TPUs in Hong Kong. With respect to the spatial distribution of R1 (Figure 5a), there are three areas (marked as A, B, and C) with high R1. Specifically, Area A is the downtown area with a high density of population and commercial buildings. Areas B and C are suburban areas with low population density and large amounts of public spaces (e.g., country parks and beaches). Figure 5b displays the spatial distribution of R2, where six areas (marked as A, B, C, D, E, and F) with high R2 are identified. Specifically, Areas A and B have high-density commercial and residential buildings, while Areas C, D, E, and F are suburban areas with large amounts of open space (e.g., country parks and beaches). These results suggest that both the downtown and certain suburban areas in the city are high COVID-19 risk areas. Moreover, the incidence rate indicator (R1) may underestimate the COVID-19 risk in some suburban areas with a considerable amount of public spaces.  Figure 5 shows the spatial distribution of COVID-19 risk in Hong Kong at the TPU level. As indicated by the results of the frequency distribution analysis of R1 and R2, areas with a high COVID-19 risk are concentrated in a few TPUs in Hong Kong. With respect to the spatial distribution of R1 (Figure 5a), there are three areas (marked as A, B, and C) with high R1. Specifically, Area A is the downtown area with a high density of population and commercial buildings. Areas B and C are suburban areas with low population density and large amounts of public spaces (e.g., country parks and beaches). Figure 5b displays the spatial distribution of R2, where six areas (marked as A, B, C, D, E, and F) with high R2 are identified. Specifically, Areas A and B have high-density commercial and residential buildings, while Areas C, D, E, and F are suburban areas with large amounts of open space (e.g., country parks and beaches). These results suggest that both the downtown and certain suburban areas in the city are high COVID-19 risk areas. Moreover, the incidence rate indicator (R1) may underestimate the COVID-19 risk in some suburban areas with a considerable amount of public spaces.

The Relationship between Built-Environment Features and COVID-19 Risk: Results of the GPR Analysis
In this subsection, we explore the relationships between selected built-environment variables and COVID-19 risk in the study area. The nine built-environment variables described in Section 3.3 are used as the independent variables in the following global Poisson regression (GPR) and

The Relationship between Built-Environment Features and COVID-19 Risk: Results of the GPR Analysis
In this subsection, we explore the relationships between selected built-environment variables and COVID-19 risk in the study area. The nine built-environment variables described in Section 3.3 are used as the independent variables in the following global Poisson regression (GPR) and geographically weighted Poisson regression (GWPR) analysis, and R1 and R2 are the dependent variables in separate models (see Table 2). Note that population density and building height are rescaled and standardized to a range from 0 to 1 in the GPR and GWPR models. Two GPR models with R1 or R2 as the dependent variable are estimated to examine the global relationships between the built-environment variables and COVID-19 risk, respectively, in Hong Kong. The regression results are presented in Table 3. As the results indicate, the values of the variance inflation factor (VIF) of the independent variable are less than 10, indicating that there is no multicollinearity among the variables. Transport facility density, population density, private residential density, land-use diversity, and building height are significantly associated with R1. Meanwhile, nodal accessibility, population density, private residential density, commercial density, green space density, and sky view are significantly associated with R2. The ratios of residual deviance to degrees of freedom are 1.01 and 1.03 for R1 and R2, suggesting that there is no significant overdispersion in the GPR models. The adjusted percent deviance explained is 0.44 for R1 and 0.58 for R2, which means that the selected built-environment variables can explain 44% and 58% of the variance in R1 and R2.
Further, the regression coefficients indicate that private residential density has a positive association with both R1 and R2, which means that areas with higher private residential density tend to have a higher COVID-19 risk. Population density, however, has a negative association with both R1 and R2. Transport facility density and building height have positive associations with R1, while land-use diversity has a negative association with R1. Green space density has a positive association with R2, which means that higher green space density tends to increase the visiting frequency of the confirmed cases. The reason is that green space is likely to attract people to undertake various outdoor activities and these people include some of the confirmed cases. Moreover, sky view has a negative association with R2, which suggests that areas with better sky view have lower risk assessed with R2. The result means that a higher possibility of seeing the sky tends to reduce the risk of COVID-19. Degrees of freedom = 181 AIC = 1513.14 Adjusted percent deviance explained = 0.58 * Represents statistically significant at the p < 0.1 level. ** Represents statistically significant at the p < 0.05 level. *** Represents statistically significant at the p < 0.01 level.

The Relationship between Built-Environment Features and COVID-19 Risk: Results of the GWPR Analysis
In this subsection, we examine the relationship between the built-environment variables and COVID-19 risk based on the results of the GWPR models. The values of the bandwidth estimated by the models are 66 and 55 for R1 and R2, respectively. Table 4 shows the results of the relative performance of the GPR and GWPR models. As the table indicates, the adjusted percent deviance explained by the GWPR models (0.63 for R1 and 0.74 for R2) are higher than those of the GPR models (i.e., 0.44 for R1 and 0.58 for R2). Moreover, the Akaike information criterion (AIC) of the GWPR models (i.e., 149.42 for R1 and 512.93 for R2) are remarkably lower than those of the GPR models (429.71 for R1 and 1513.14 for R2). The improvement in adjusted percent deviance explained and the reduction in the AIC values indicate that the GWPR models have better explanatory power than the GPR models for examining the influence of the built-environment features on COVID-19 risk in Hong Kong.  Figure 6 presents the spatial distributions of local percent deviance explained by the GPWR models for R1 and R2. The results show that the two GPWR models present similar spatial distributions of local percent deviance explained in the north and western parts of the study area. Meanwhile, it can be observed that the GPWR models have lower explanatory power for R1 and R2 in the TPUs of and around Kwun Tong (marked as A in Figure 6a) and Mong Kok (marked as A in Figure 6b), respectively. ISPRS Int. J. Geo-Inf. 2020, 9, x FOR PEER REVIEW 12 of 19 Figure 7 shows the spatial distributions of the standard residuals from the two GPWR models for R1 and R2; 95% and 96% of the standard residuals have values in the range of (-2.58, 2.58), respectively. We further examine the spatial autocorrelation of the standard residuals and obtain the global Moran's I for the standard residuals of the GPWR models, which are −0.03 and −0.02, respectively, revealing that the distributions of the standard residuals from the GPWR models are random at the 5% level of significance. Moreover, the low values of the global Moran's I also indicate that there is no systematic error in the models. The spatial distribution of the estimated coefficients of the built-environment variables is presented in Figures 8 and 9. The blue color signifies that the corresponding built-environment variable has a negative influence on COVID-19 risk, while the red color indicates a positive influence. The GWPR models reveal the spatially varying influence of each built-environment variable on COVID-19 risk. In Figure 8, it can be observed that the associations between transport facility density, population density, private residential density, land-use diversity, and building height, and COVID-19 risk fluctuate from negative to positive for R1. For variables such as transport facility density, private residential density, and building height, the proportions of TPUs with positive and negative coefficients are comparable to each other, which implies a complicated relationship between these variables and R1. For instance, the positive values for transport facility density, private residential density, and building height are mainly distributed in the downtown area and Tung Chung, while the negative values are found largely in the peripheral suburban areas (Figures 8a,c,e). Regarding population density, most TPUs in Hong Kong exhibit negative associations with R1, while the TPUs with positive associations only cover the village clusters in Ma On Shan (Figure 8b). Similarly, landuse diversity has a negative relationship with R1 for most TPUs (Figure 8d).  Figure 7 shows the spatial distributions of the standard residuals from the two GPWR models for R1 and R2; 95% and 96% of the standard residuals have values in the range of (−2.58, 2.58), respectively. We further examine the spatial autocorrelation of the standard residuals and obtain the global Moran's I for the standard residuals of the GPWR models, which are −0.03 and −0.02, respectively, revealing that the distributions of the standard residuals from the GPWR models are random at the 5% level of significance. Moreover, the low values of the global Moran's I also indicate that there is no systematic error in the models.
The spatial distribution of the estimated coefficients of the built-environment variables is presented in Figures 8 and 9. The blue color signifies that the corresponding built-environment variable has a negative influence on COVID-19 risk, while the red color indicates a positive influence. The GWPR models reveal the spatially varying influence of each built-environment variable on COVID-19 risk. In Figure 8, it can be observed that the associations between transport facility density, population density, private residential density, land-use diversity, and building height, and COVID-19 risk fluctuate from negative to positive for R1. For variables such as transport facility density, private residential density, and building height, the proportions of TPUs with positive and negative coefficients are comparable to each other, which implies a complicated relationship between these variables and R1. For instance, the positive values for transport facility density, private residential density, and building height are mainly distributed in the downtown area and Tung Chung, while the negative values are found largely in the peripheral suburban areas (Figure 8a,c,e). Regarding population density, most TPUs in Hong Kong exhibit negative associations with R1, while the TPUs with positive associations only cover the village clusters in Ma On Shan (Figure 8b). Similarly, land-use diversity has a negative relationship with R1 for most TPUs (Figure 8d). variables and R1. For instance, the positive values for transport facility density, private residential density, and building height are mainly distributed in the downtown area and Tung Chung, while the negative values are found largely in the peripheral suburban areas (Figures 8a,c,e). Regarding population density, most TPUs in Hong Kong exhibit negative associations with R1, while the TPUs with positive associations only cover the village clusters in Ma On Shan (Figure 8b). Similarly, landuse diversity has a negative relationship with R1 for most TPUs (Figure 8d).   In summary, the associations between the selected built-environment features and COVID-19 risk vary spatially across the study area. The GPR models provide the global relationship between the built-environment features and COVID-19 risk for the TPUs, and the GWPR models reveal some distinctive and complex differences among the TPUs by considering spatial autocorrelation and spatial nonstationarity. The model results shed light on the relationships between built-environment variables and COVID-19 risk at a more microscopic scale. ISPRS Int. J. Geo-Inf. 2020, 9, Figure 9a indicates that nodal accessibility has a positive association with R2 for the entire study area, and higher associations are located in Hong Kong Island, Lamma Island, and Tin Shui Wai. Private residential density has a positive association with R2 for most TPUs (Figure 9c). Further, the associations between population density (Figure 9b  In summary, the associations between the selected built-environment features and COVID-19 risk vary spatially across the study area. The GPR models provide the global relationship between the built-environment features and COVID-19 risk for the TPUs, and the GWPR models reveal some distinctive and complex differences among the TPUs by considering spatial autocorrelation and spatial nonstationarity. The model results shed light on the relationships between built-environment variables and COVID-19 risk at a more microscopic scale.

Discussion and Conclusions
Understanding the relationship between the built environment and COVID-19 risk could support health authorities to respond to the pandemic. In this paper, we utilized GPR and GWPR

Discussion and Conclusions
Understanding the relationship between the built environment and COVID-19 risk could support health authorities to respond to the pandemic. In this paper, we utilized GPR and GWPR models to investigate the relationship between built-environment features and COVID-19 risk in Hong Kong at the TPU level. The risk of COVID-19 is assessed using the incidence rate (R1) and venue density (R2). The main findings of the study are summarized as follows.
First, both R1 and R2 have a remarkable decay effect over space. It implies that there are a few areas with a high COVID-19 risk. Similar results have been observed in the studies by Desjardins et al. [53] and Gatto et al. [54] in the U.S. and Italy in the early stage of the pandemic. Further, the rate of decay of R1 is higher than that of R2, reflecting that the number of TPUs with a high R1 is smaller than the number of TPUs with a high R2. This implies that the incidence rate indicator may underestimate the COVID-19 risk in some suburban areas with a large area of public space. Second, the GPR model results reveal a close relationship between selected built-environmental variables and COVID-19 risk. Note that Nguyen et al. [55] reported similar results by using large Google Street View image datasets on American neighborhoods (i.e., zip code area). They found that land-use diversity and higher accessibility have positive associations with higher COVID-19 cases without considering spatial nonstationarity. Meanwhile, our results show a negative association between population density and the risk of COVID-19. The result differs from those of the studies of Amram et al. [56] and Xiong et al. [57] in the U.S. and China (i.e., population density has a positive or nonsignificant association with COVID-19 risk). These conflicting results raise several hypotheses that are worth discussing. First of all, as we mentioned in Section 2, using different spatial scales of the analytical units or geographic areas (e.g., counties, census tracts, or census block groups) in the analysis may lead to different results (i.e., the modifiable areal unit problem). Then, several other variables could potentially prevent disease transmission over the neighborhoods in a dense and developed city. For instance, dense areas in a developed city may have better access to health care facilities and better adherence to social distancing by residents (e.g., more than 97.5% of the people in Hong Kong wore a mask when they went out and more than 85% of them avoided crowded places during February and March 2020 [58]).
Taking into account spatial nonstationarity, our results present that the GWPR models perform better than GPR models based on the value of adjusted percent deviance explained and AIC. The low global Moran's I values (R1: −0.03; R2: −0.02) in the residual maps indicate that there is no systematic error in the models. The results show that the relationships between selected built-environmental variables and COVID-19 risk (i.e., R1 and R2) vary spatially across the study area. For built-environment features such as transport facility density, private residential density, building height, population density, commercial density, green space density, and sky view, the relative proportions of TPUs with positive and negative coefficients indicate a complicated relationship between selected built-environment variables and COVID-19 risk.
Based on the results of the two sets of regression models, we observed the complex relationships between selected built-environment variables and COVID-19 risk. The results also suggest other interesting observations that are worth discussing. For instance, most of the confirmed cases who lived in Tung Chung were actually infected in their workplaces (i.e., Central). It implies that the strong spatial interactions between suburban areas (e.g., Tung Chung) and the downtown area (e.g., Central) may result in similar patterns in COVID-19 risk (e.g., transport facility density for R1 and nodal accessibility for R2). Moreover, green space density and sky view in the downtown area (e.g., Central and Tsim Sha Tsui) and some suburban areas (e.g., Tung Chung and Tuen Mun) have opposite effects on COVID-19 risk.
Our findings have several important implications for non-pharmaceutical intervention measures for the government during the pandemic. First, the results of the frequency and spatial distributions of COVID-19 risk indicate that a few TPUs have a higher COVID-19 risk. Health authorities should thus focus on these areas for follow-up interventions in order to control the COVID-19 pandemic. Second, the results suggest that the incidence rate may underestimate the risk of COVID-19 in some suburban areas with large areas of public recreational space (e.g., parks). On one hand, areas with dense transport facilities, higher nodal accessibility, more green space, and a good sky view tend to attract more visitors. On the other hand, people who live in suburban areas may have to go to work in the downtown area, which has a higher risk. Moreover, the GPR and GWPR models indicate that dynamic interventions of COVID-19 transmission risk should be considered during the pandemic. For instance, restricting people from going to the country parks and certain residential areas in the suburb or limiting group activities in these areas may help control the pandemic.
In this study, we found that the spatial patterns of built-environment features influence the spatial patterns of COVID-19 risk across the study area. The findings suggest that COVID-19 can be explained by pertinent built-environment features. The methods used in the study can be applied to other cities in the world to investigate the relationship between the built environment and COVID-19 risk. Comparative studies would be helpful in revealing the effects of different human behaviors and intervention measures in different sociocultural contexts. This is a fruitful possible direction for future research.
Meanwhile, there are several limitations in this study. First, the study used COVID-19 data from 27 January to 14 April 2020, during which the Hong Kong Government had implemented several non-pharmaceutical intervention measures in response to the COVID-19 pandemic. The results from our regression models thus captured the relationship between built-environment features and COVID-19 risk under these non-pharmaceutical interventions. It is unclear whether the relationship between the built environment and COVID-19 risk we identified will also hold under normal times (i.e., without intervention measures). In the future, we plan to explore this in the post-pandemic period. Second, this study used the incidence rate and venue density as measures of COVID-19 risk.
Other indicators, such as the decrease in survived coronavirus estimated based on the last visiting time by confirmed cases, could be considered in the future. As the decay effect of coronavirus survival over time is related to different environmental surfaces, incorporating this variable into the analysis may provide more insights into COVID-19 risk and its relationship with specific types of built environments. Third, this study did not consider the temporal dynamics of the spatial interaction among TPUs (e.g., the spatial interactions among TPUs may change between different times of a day or before and after the implementation of intervention policies), which may lead to different associations between the built environment and COVID-19 risk.