A Novel Predictor for Micro-Scale COVID-19 Risk Modeling: An Empirical Study from a Spatiotemporal Perspective

Abstract

Risk assessments for COVID-19 are the basis for formulating prevention and control strategies, especially at the micro scale. In a previous risk assessment model, various “densities” were regarded as the decisive driving factors of COVID-19 in the spatial dimension (population density, facility density, trajectory density, etc.). However, this conclusion ignored the fact that the “densities” were actually an abstract reflection of the “contact” frequency, which is a more essential determinant of epidemic transmission and lacked any means of corresponding quantitative correction. In this study, based on the facility density (FD), which has often been used in traditional research, a novel micro-scale COVID-19 risk predictor, facility attractiveness (FA, which has a better ability to reflect “contact” frequency), was proposed for improving the gravity model in combination with the differences in regional population density and mobility levels of an age-hierarchical population. An empirical analysis based on spatiotemporal modeling was carried out using geographically and temporally weighted regression (GTWR) in the Qingdao metropolitan area during the first wave of the pandemic. The spatiotemporally nonstationary relationships between facility density (attractiveness) and micro-risk of COVID-19 were revealed in the modeling results. The new predictors showed that residential areas and health-care facilities had more reasonable impacts than traditional “densities”. Compared with the model constructed using FDs (0.5159), the global prediction ability (adjusted R2) of the FA model (0.5694) was increased by 10.4%. The improvement in the local-scale prediction ability was more significant, especially in high-risk areas (rate: 107.2%) and densely populated areas (rate in Shinan District: 64.4%; rate in Shibei District: 57.8%) during the outset period. It was proven that the optimized predictors were more suitable for use in spatiotemporal infection risk modeling in the initial stage of regional epidemics than traditional predictors. These findings can provide methodological references and model-optimized ideas for future micro-scale spatiotemporal infection modeling.

Full text

International Journal of
Environmental Research
and Public Health
Article
A Novel Predictor for Micro-Scale COVID-19 Risk Modeling:
An Empirical Study from a Spatiotemporal Perspective
Sui Zhang , Minghao Wang, Zhao Yang and Baolei Zhang *


Citation: Zhang, S.; Wang, M.; Yang,
Z.; Zhang, B. A Novel Predictor for
Micro-Scale COVID-19 Risk
Modeling: An Empirical Study from a
Spatiotemporal Perspective. Int. J.
Environ. Res. Public Health 2021,18,
13294. https://doi.org/10.3390/
ijerph182413294
Academic Editor: Abolfazl Mollalo
Received: 26 October 2021
Accepted: 13 December 2021
Published: 16 December 2021
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
College of Geography and Environment, Shandong Normal University, Jinan 250014, China;
201814010401@stu.sdnu.edu.cn (S.Z.); 201814010418@stu.sdnu.edu.cn (M.W.);
201814010402@stu.sdnu.edu.cn (Z.Y.)
*Correspondence: blzhangsd01@sdnu.edu.cn
Abstract:
Risk assessments for COVID-19 are the basis for formulating prevention and control
strategies, especially at the micro scale. In a previous risk assessment model, various “densities”
were regarded as the decisive driving factors of COVID-19 in the spatial dimension (population
density, facility density, trajectory density, etc.). However, this conclusion ignored the fact that the
“densities” were actually an abstract reflection of the “contact” frequency, which is a more essential
determinant of epidemic transmission and lacked any means of corresponding quantitative correction.
In this study, based on the facility density (FD), which has often been used in traditional research, a
novel micro-scale COVID-19 risk predictor, facility attractiveness (FA, which has a better ability to
reflect “contact” frequency), was proposed for improving the gravity model in combination with
the differences in regional population density and mobility levels of an age-hierarchical population.
An empirical analysis based on spatiotemporal modeling was carried out using geographically and
temporally weighted regression (GTWR) in the Qingdao metropolitan area during the first wave of the
pandemic. The spatiotemporally nonstationary relationships between facility density (attractiveness)
and micro-risk of COVID-19 were revealed in the modeling results. The new predictors showed that
residential areas and health-care facilities had more reasonable impacts than traditional “densities”.
Compared with the model constructed using FDs (0.5159), the global prediction ability (adjusted
R
2
) of the FA model (0.5694) was increased by 10.4%. The improvement in the local-scale prediction
ability was more significant, especially in high-risk areas (rate: 107.2%) and densely populated
areas (rate in Shinan District: 64.4%; rate in Shibei District: 57.8%) during the outset period. It was
proven that the optimized predictors were more suitable for use in spatiotemporal infection risk
modeling in the initial stage of regional epidemics than traditional predictors. These findings can
provide methodological references and model-optimized ideas for future micro-scale spatiotemporal
infection modeling.
Keywords:
COVID-19; gravity model; geographically and temporally weighted regression (GTWR);
spatiotemporal risk modeling; Qingdao
1. Introduction
The COVID-19 pandemic is the most serious global public health event that has
occurred in the 21st century thus far and has become a hot topic in many different disci-
plines [
1
]. The global pandemic has severely damaged the global economy, society, finance,
and even the ecosystem and environment [
2
–
5
], highlighting the importance of recognizing
the “risks” of regional epidemics [
6
,
7
]. The level of risk not only shows the current situation
of epidemic infection and the probability of new cases occurring in a region, but, more
essentially, determines what level of prevention and control measures should be taken in
this region to reduce the risk of a pandemic as far as possible [
8
,
9
]. At the same time, the
rapid transmission of COVID-19 and its complexity mean that the time and space in which
both human–human and human–place interactions take place are particularly important
Int. J. Environ. Res. Public Health 2021,18, 13294. https://doi.org/10.3390/ijerph182413294 https://www.mdpi.com/journal/ijerph

Int. J. Environ. Res. Public Health 2021,18, 13294 2 of 16
in the study of the spatial epidemiology of COVID-19 [
10
–
12
]. Therefore, it is self-evident
that the quantitative analysis and micro-modeling of COVID-19 from the spatiotemporal
perspective are necessary for epidemic risk measurement, especially in the initial stage
before the complete outbreak of a regional epidemic [13,14].
Based on the empirical evidence provided by previous studies, people’s mobility and
contact are considered as decisive factors in the transmission of COVID-19 [
11
,
15
]. Theoret-
ically, the compact development of cities will lead to closer contact between people and
more frequent interactions occurring among residents, which also makes these high-density
areas potential hot spots for the rapid spread of emerging epidemics [
16
,
17
]. Therefore,
“densities” are given priority in most cases when micro-modeling the spread and risk of
infectious diseases [
18
,
19
]. “Densities” can be divided into three categories: population
density, trajectory density, and facility density [
11
,
20
,
21
]. Population density has always
been regarded as the determinant of epidemic exposure and transmission risk, and many
studies have explored the complex relationship between population density and epidemic
spread in various spatiotemporal contexts [
22
,
23
]. However, because most population
density data are in the form of statistical data, corresponding high-resolution geospatial
data usually need to undergo complex spatial correction processing, and it is difficult to
carry out microscopic epidemiological modeling directly [
24
,
25
]. This has caused urban big
data, which are more accurate than population data, to generally receive more attention in
recent studies [
26
,
27
]. Density analyses based on trajectory data (smartphone data, traffic
trajectory) have been implemented in many studies, providing unique advantages for
the analysis of population dynamic characteristics and the initial modeling of epidemic
diseases [
11
,
28
]. However, due to the high cost of accessing the trajectory data, some
researchers use points of interest (POI) instead to combine and model specific or multiple
facility densities. Different from urban roads, another spatial element of cities that often
leads to people being more mobile is the closeness of different facilities. This causes more
people to gather in one location and thus plays a pivotal role in the transmission of highly
contagious epidemics. Complementing population density, which is commonly used in the
classical theory of infectious disease ecology and transmission, the use of various facility
densities can better simulate the people’s contact frequency. Due to these characteristics,
modeling studies that predict epidemic risk from the perspective of urban planning based
on facility density, the mapping of urban functions in gathering places, and calculating the
probability of people gathering and coming into contact in airtight places have attracted
great attention [
21
,
29
,
30
]. Although several empirical studies have highlighted the sig-
nificance of the local epidemic source of COVID-19 as a driving mechanism in the initial
stage of the pandemic, various density indicators play a dominant role in the modeling of
micro-scale spatiotemporal epidemiology [13,31].
However, the use of “densities” is obviously not perfect for the micro-scale spatiotem-
poral modeling of COVID-19 risk. Firstly, a considerable number of studies have found that
“densities” have limited effects in the initial stage of regional epidemics [
31
]. Secondly, no
matter what the simple population density is, trajectory density or facility density cannot
reflect the real mechanism of human interaction. Although they can simulate the static and
dynamic density of the population (population density, track density) and the possibility
of people gathering in one space (facility density), respectively, such one-sided modeling
usually leads to biased estimations of densely populated areas with low gathering possibil-
ities and sparsely populated areas with high possibilities of people gathering [
16
,
17
,
32
].
In addition, differences in the age structure of the population and resulting differences in
travel modes and capacities are usually not considered in the micro-modeling of COVID-
19 risk [
13
,
33
]. To sum up, although traditional “densities” models have been widely
used in previous studies and achieved excellent results, compared with non-compound
“densities” the deeper determinants of the intracity risks of epidemics are undoubtedly
more multi-levelled. When complex population structures and the spatial heterogeneity
of different types of facility density are considered, the result of comprehensive modeling
is not so much related to “densities” in the traditional meaning, but more related to “con-

Int. J. Environ. Res. Public Health 2021,18, 13294 3 of 16
tact”, which is similar to the word “interaction” (which is often mentioned in the field of
geographical analysis) [
34
,
35
]. Therefore, in this study we try to simulate the frequency of
human–human and human–place interactions occurring between different kinds of people
and gathering places based on low-cost and accessible data. Taking population distribution,
age structure, and gathering probability into account, a quantitative predictor, facility
attractiveness (FA), which can be widely applied instead of the predictor of traditional
facility density (FD), was used. We then built a spatiotemporal risk model in a small
area where there was an outbreak of COVID-19 and evaluated its prediction efficiency in
different application scenarios.
The main purposes of this study include: (1) improving the gravity model to build
facility attractiveness (FA); (2) modeling and visualizing the varying spatiotemporal impact
of the selected driving factors on the risk of COVID-19 in the Qingdao metropolitan area
using geographically and temporally weighted regression (GTWR); (3) comparing and
discussing the advantages and disadvantages of the traditional FD model and the novel FA
model in different application scenarios.
2. Data and Methodology
2.1. Empirical Area
Qingdao is located in the east of Shandong Province, China, facing Japan and South
Korea across the sea. It is the economic center of Shandong Province and an important
international port city in China. Based on its geographical location and important business
status, Qingdao is considered to be one of the regions with the highest risk of the occurrence
of a local epidemic in China. In this study, the Qingdao metropolitan area was selected as
our empirical area (120
◦
52
0
~120
◦
28
0
E, 36
◦
204
0
~36
◦
24
0
N). This area is about 249.3 km
2
and
represents only 2.21% of Qingdao, but more than 42% of its population, making it a densely
populated area within Qingdao and an area with a high COVID-19 infection risk (Figure 1).
To better understand the spatiotemporal risk of COVID-19 at the micro scale, we referred
to the idea of Ling (2020) regarding community grid management and considered the
advantages of the use of a hexagonal grid for dealing with adjacency problems, modified
area unit problems (MAUPs), and high-precision spatiotemporal modeling [
31
,
36
]. In our
study, a hexagonal grid with a side length of 250 m was used to divide the study area into
blocks, and 1684 independent hexagons were selected for further analysis [37,38].
Figure 1. The geographical location of the empirical area.

Int. J. Environ. Res. Public Health 2021,18, 13294 4 of 16
2.2. Data Sources and Measures
The data used in this study include: COVID-19 case data, POI data, OpenStreetMap
road network data, and WorldPop population age structure data. Among these, the case
data include information regarding the age, gender, address, and date of symptom onset
of all cases confirmed in the empirical area from January to May, 2020, from the Qingdao
Municipal Health Commission (wsjkw.qingdao.gov.cn, accessed on 1 June 2020). The
POI data were sourced from Amap (www.amap.com, accessed on 6 June 2020). In this
study, catering places, residential areas, shopping places, public service facilities, health-
care facilities, education places, and entertainment places were initially highlighted as
places where people gather. However, due to the strict lockdown measures implemented
in China since January 2020, the possibility of people gathering in most education and
entertainment venues in Qingdao has become negligible (Figure 2). Therefore, this study
excluded these variables, and the remaining five types of places that experience the greatest
amount of human activity and that represent the greatest possibility of disease transmission
within the context of the pandemic were selected as independent variables (catering places,
residential areas, shopping places, public service facilities, and health-care facilities). The
100 m-resolution raster data for people of various ages were sourced from WorldPop (www.
worldpop.org, accessed on 1 March 2021); the road network data came from OpenStreetMap
(www.openstreetmap.org, accessed on 1 June 2020).
Figure 2. Development and stage definition of COVID-19 in the empirical area from 14 January to 23 February.
In order to construct effective and reliable panel data to meet the computational
requirements of geographically and temporally weighted regression (GTWR) and according
to the date of onset of these cases (Figure 2), the local epidemic was divided into five stages
(Stage 1: 14 January to 25 January; Stage 2: 26 January to 3 February; Stage 3: 4 February to
5 February; Stage 4: 6 February to 10 February; Stage 5: 11 February to 23 February). Stage
1 represents the initial stage of the local epidemic; before the Chinese New Year, the end of
this stage, many people in China were engaging in annual large-scale population migration,
the so-called (pre-) Spring Festival travel rush, which enabled COVID-19 to spread rapidly
across the country. Stage 2 represents the accelerate stage of the local epidemic, which was
also the strictest traffic blockade period; after this stage, the traffic blockade of the Chinese
mainland, except for Hubei Province, was gradually relaxed. Stage 3 represents the peak
period of the epidemic in the empirical area, which was also the turning point of the local
epidemic; Due to the traffic control caused by the pandemic and the drastic weakening

Int. J. Environ. Res. Public Health 2021,18, 13294 5 of 16
of people’s willingness to travel, the scale of post-Spring Festival travel rush has shrunk
greatly, which made its contribution to the national spread of the epidemic limited. Stage 4
represents the decelerate duration of the local epidemic, and it was at the end of this stage
that people in Chinese mainland began to resume work and production in stages. Stage 5
represents the last stage of the local epidemic and the local epidemic was finally controlled.
2.3. Methodology
2.3.1. Mapping the Micro-Scale Spatiotemporal COVID-19 Risk
Existing theories generally hold that risk decays proportionally with the distance from
the source [
39
], and that the distance decay function it depends on has various forms (such
as subsection, gravity, Gaussian, etc.), among which the Gaussian distance decay function
has been widely proven to have unique advantages in simulating human travel rules; it
is also applicable to the preliminary mapping of epidemic risk [
40
]. In this study, kernel
density estimation (KDE) based on the Gaussian kernel function was used to spatially
smooth the epidemic data [
41
,
42
]. Kernel density estimation produces a smooth and
continuous surface on which each position in the study area is assigned a density value,
regardless of any administrative boundary. Considering the space of the empirical area
and the spatial range of COVID-19 cases, the bandwidth of the kernel function was set to
2.5 km and the average density values in each grid were calculated as the epidemic risk
values (Figure 3).
Figure 3. The overall workflow diagram of this empirical modeling study.
2.3.2. Facility Attractiveness (FA) and Optimized Gravity Model
The gravity model is a mathematical model that is suitable for the study of human
activities; it is an extension of Newton’s law of gravity in the field of social sciences [
43
,
44
].
This model indicates that the force between two places is proportional to their “mass” and
inversely proportional to the square of the distance between them, and that the “mass” in
the model can be replaced by equivalent demographic indicators [
45
]. In this study, the
density of facilities and the number of people in an area were used as modeling indicators.
The formula is expressed as follows:
FAit =k(FDi t)∑
j
(POPj)d−2
ij (1)

Int. J. Environ. Res. Public Health 2021,18, 13294 6 of 16
where FA
it
is the total attractiveness of facilities tin grid i;FD
it
is the number of facilities tin
grid i—that is, the facility density mentioned above; POP
j
is the population (100,000 people)
of grid j;dis the Euclidean distance between grid Iand grid j;kis a constant, which is
usually set to 1 in practical applications.
Previous literature has proven that the law of human travel within cities is more in
accordance with the Gaussian function than with the power function [
46
,
47
]. In addition,
the definition of “life circle” popularized by the modernized urban planning concept has
greatly reduced peopl’s daily travel ranges [
48
,
49
]; this is particularly evident in China
within the epidemiological context due to the strict community control and lockdown
measures imposed [
50
]. Moreover, different age groups have different travel abilities. Thus,
an age-hierarchical Gaussian optimized gravity model was constructed to make it more
suitable for use in empirical studies in the context of COVID-19 [51,52]:
FAit = (FDit)"∑
j
(POPj(20−69))Wij(20−69)+∑
j
(POPj(70+))Wij(70+)#(2)
Wij(20−69)=




e−1
2tij
3600 2
−e−1
2
1−e−1
2
,tij <3600
0, tij ≥3600
;Wij(70+) =




e−1
2sij
1200 2
−e−1
2
1−e−1
2
,sij <1200
0, sij ≥1200
(3)
The steps used for the construction of the age-hierarchical Gaussian optimized gravity
model were as follows (Figure 3):
(1)
We carried out a topology inspection and correction on OSM road network data and
calculated the mileage s
ij
between place iand place j. On this basis, the hierarchy of
the OSM road network was considered as well as the actual situation of Qingdao,
the average travel speed of roads was set for all levels, and the travel time t
ij
was
calculated. These two data points were used to replace the role of d
ij
in the traditional
gravity model in this study (Table 1).
Table 1. Hierarchical road speed setting.
Trip Mode Road Classification Speed
(km/h)
Walk Footway, Living Street, Path, Pedestrian, Residential, Service, Steps 5
Drive Tertiary/Unclassified/Secondary/Primary/Trunk 10/20/30/40/50
(2)
During the pandemic in the first half of 2020, almost all public transportation was
suspended in most parts of China, which made self-driving travel the only realistic
and convenient way to travel long distances. Since Chinese laws prohibit citizens
under the age of 18 and over the age of 70 from obtaining a motor vehicle driving
license, the possible travel modes used by people of different age groups would
have been quite different in the pandemic era. In order to take into account the
heterogeneity of the mobility and travel range of the age-hierarchical population, the
total population was divided into three groups according to their ages: 0–19 years old
(adolescent group), 20–69 years old (adult group), and 70+ years old (elderly group).
According to the previous references and the research group’s visit to Qingdao
[52–55]
:
a.
Due to campus closures and the strict community control measures imple-
mented during the first wave of the pandemic, most students (under 20 years
old) received their education online and lacked sufficient time or motivation
to travel [
53
]. Therefore, this group, which also had extremely limited travel
possibilities, was not included in the model used in this study.
b.
As most elderly people over 70 years old do not live with their children in
China, this group are likely to have a high travel frequency in order to carry

Int. J. Environ. Res. Public Health 2021,18, 13294 7 of 16
out necessary daily [
56
]. However, due to the limitations of transportation
modes and mobility levels, the range of activities of elderly people is generally
limited to less than 1200 m [
57
,
58
]. Therefore, in this model we set 1200 m as the
travel threshold for the 70+ age group in order to calculate the attractiveness of
various facilities to the elderly more reasonably.
c. Qingdao has become one of the cities in China with the longest average travel
times due to the separation of occupation areas and residential spaces [
59
]. The
20–69 age group is the most active group and has the largest travel range. Given
the diversity of their travel modes, setting our search threshold according to
mileage will lead to great deviations. Therefore, in this study referred to survey
results and adopted a travel time of 1 h (3600 s) as the travel threshold for the
20–69 age group.
d.
Possible travel routes exceeding the travel threshold of the two age groups
mentioned above were not considered in this model.
(3)
We replaced the power function distance decay function in (1) with the Gaussian
distance decay function corresponding to the travel threshold of each age group.
(4)
We then summed the calculation results of the multi-age models.
FAs are integrated variables based on the optimized gravity model. The number of
independent variables does not increase when they are used in various models compared
with traditional FD predictors, meaning that FA predictors have a wide application range
and prospect, which enables them to be tested together with the same highly flexible FDs
in different models to compare their advantages and disadvantages. This study will also
make use of this advantage of FA predictors to carry out further empirical evaluations of
their application efficiency.
2.3.3. Geographically and Temporally Weighted Regression (GTWR)
In order to solve the problem of spatial heterogeneity and autocorrelation when
modeling spatial information, the local estimation method represented by geographically
weighted regression (GWR) is widely used in empirical research in various fields. The
advantage of this method is that it can provide local estimators for each predictor [
60
].
On this basis, geographically and temporally weighted regression (GTWR), which takes
spatiotemporal heterogeneity into account, was proposed [
61
–
63
]. Compared with the
traditional GWR, which can only model in phases when processing data with both spatial
and temporal dimensions, this often leads to biased and unsmooth results in time series,
while the GTWR framework integrating the temporal autocorrelation of data is more
advantageous in spatiotemporal epidemiological modeling [
64
,
65
]. It can be expressed as:
Yi=β0(ui,vi,ti)+∑
k
βk(ui,vi,ti)Xik +εi(4)
where (u
i
,v
i
,t
i
) is the spatiotemporal coordinate for observation iand
β
(u
i
,v
i
,t
i
) is the
coefficient of the kth independent variable X
ik
for observation i. GTWR integrates spatial
coordinates with temporal coordinates by the following formula, so as to “upgrade” the
traditional spatial distance to the spatiotemporal distance to build the weight matrix.
Therefore, GTWR is suitable for solving both the spatial and temporal nonstationarity
of data:
dST
ij 2=˘hui−uj2+vi−vj2i+µti−tj2(5)
where
dST
ij
is the spatiotemporal distance between observation iand j;t
i
and t
j
are the time
coordinates of stages iand jwhich defined following the epi curve.
λ
and
µ
are the weights
for harmonizing the differing units between space and time. The bandwidth of GTWR is
selected by the Akaike Information Criterion correction (AICc), which converges to the
Akaike Information Criterion (AIC) when the sample size is large enough [66].

Int. J. Environ. Res. Public Health 2021,18, 13294 8 of 16
The model is based on the hypothesis of normal distribution, all independent variables
contained in GTWR should pass the statistical significance test under the OLS model frame-
work and there is no serious multicollinearity problem (Table 2). The modeling process
is based on the add-in program “Geographically and Temporarily Weighted Regression
(GTWR)” for the ArcMap 10.7 software, and the Origin 2021 and ArcGIS Pro software are
used to chart and visualize the results in 3D.
Table 2. Statistical description of the variables of FD and FA models.
Variables Characteristic Mean Std. Dev. Min Max VIF
Dependent variable Covid risk Dynamic 0.06 0.13 0 1.37 -
Independent variables
Facility density (FD)
Catering Static 0.75 2.43 0 36 1.92
Residences Static 2.24 3.33 0 26 1.62
Shopping Static 1.55 5.05 0 80 1.97
Public services Static 0.88 1.76 0 13 2.03
Health-care Static 0.86 1.95 0 22 1.38
Facility attractiveness (FA)
Catering Static 0.62 2.05 0 30.77 1.94
Residences Static 1.83 2.81 0 22.18 1.67
Shopping Static 1.29 4.30 0 68.38 1.98
Public services Static 0.72 1.47 0 11.25 2.07
Health-care Static 0.71 1.62 0 18.78 1.39
3. Model Results
Table 3shows the diagnostic information of model estimation under the OLS, TWR,
GWR, and GTWR frameworks with the same independent variables to prove the effect of
spatiotemporal information on the improvement in model performance. All independent
variables passed the significance level test of the OLS model. Among the four models
considered in this paper, the GTWR model outperformed all other models in terms of all
diagnostic coefficients. Based on the outstanding model efficiency of the models under the
GTWR framework and the spatiotemporal three-dimensional attribute of the empirical
data, in this study we use the GTWR framework for micro-scale spatiotemporal COVID-19
risk modeling.
Table 3. Global diagnostic information for the estimation with FDs and FAs under various regression frameworks.
Diagnostic Information Facility Density (FD) Facility Attractiveness (FA)
OLS TWR GWR GTWR OLS TWR GWR GTWR
Adjusted R20.0827 0.1594 0.4036 0.5159 0.0804 0.1555 0.4078 0.5694
Residual sum of squares 124.84 114.35 81.13 65.86 125.15 114.88 80.56 58.57
AICc −11,553 −12,258 −15,080 −16,813 −11,531 −12,219 −15,144 −17,690
Taking the FD and FA values of five types of gathering places as independent variables,
the risk value of COVID-19 in the Qingdao metropolitan area was modeled spatiotempo-
rally and spatiotemporally varying coefficients with local significance levels higher than
95% were visualized (Figure 4). Generally speaking, except for catering places and shop-
ping places, most of the significant GTWR coefficients of FD in various gathering places
were negative, demonstrating a negative impact on COVID-19 transmission risk. Resi-
dential areas and public service facilities had consistent negative effects in Shibei District,
Shinan District, and Licang District from the initial stage of the epidemic, and this effect
showed a decreasing trend from the city center to the central fringe. Variables that also
showed a strong negative influence in the central city were catering places and health-care
facilities. Although the influence of these two variables was not significant in the initial

Int. J. Environ. Res. Public Health 2021,18, 13294 9 of 16
stage, with the transmission of the epidemic they began to have significant effects in the
central city. However, shopping places were shown to increase the risk of transmission in
the city center during the research period, and this risk increased continuously. Similarly,
catering places at the junction of Shibei District and Licang District and public service
facilities and health-care facilities in Laoshan District also had remarkable positive effects.
Figure 4. Estimation results for the GTWR coefficients of FD (a) and FA (b) in various gathering places.
The result gained using the spatiotemporally varying coefficient of FAs was quite
different from the result gained from modeling using FDs as the core variable (Table 4).
Almost all the five types of gathering places played a positive role in the spread of the
epidemic on a large scale (Figure 4). This promotion was most obvious for the variables
of health-care facilities and which most areas were affected, and the intensity of this
impact was strengthened with the escalation of risks. The spatiotemporally nonstationary
characteristics of catering places and residential areas were similar, showing that Shinan
District was the core area exhibiting a restraining effect and Licang District was the core
area exhibiting a promoting effect. However, the area affected for catering places was wider
than that affected for residential areas and also showed strong restraining characteristics
in certain areas of Laoshan District, while the promotion effect of residential areas was
more remarkable in Licang District. The coefficients of shopping places and public service
facilities showed opposite spatiotemporal characteristics. These coefficients played a
significant role in the central city and the edge of the city center, respectively, and the
intensity of this role usually reached its peak in the final stage of the epidemic, similar to
the modeling results of FDs to a certain extent.

Int. J. Environ. Res. Public Health 2021,18, 13294 10 of 16
Table 4. Estimation summaries for the GTWR coefficients of the FD and FA models.
Variables Facility Density (FD) Facility Attractiveness (FA)
Min LQ Med UQ Max Min LQ Med UQ Max
Catering −10.57 −0.72 0.7 1.32 10.22 −18.33 −4.62 0.4 2.79 38.7
Residence −63.57 −6.82 −2.61 0.07 4.73 −7.63 0.87 3.39 7.22 25.9
Shopping −3.21 −0.48 0.11 0.76 9.72 −4.77 0.02 1.71 3.79 11.15
Public service −16.6 −3.9 −1.44 −0.13 3.37 −11.23 −2.33 1.1 5.86 29.24
Health-care −19.71 −2.4 −0.57 1.11 6.21 −1.41 2.49 5.2 9.61 40.35
Constant 0 0.02 0.04 0.09 0.53 0 0.01 0.03 0.07 0.42
Note: All coefficients illustrated in Table 4except for the intercept term need to be multiplied by 10−3.
4. Discussion
4.1. Comparison of Model Performance between FD and FA
Although, theoretically, facility attractiveness, which integrates the heterogeneity of
the regional population distribution, age structure, and facility distribution, is obviously
a more suitable indicator for COVID-19 risk modeling than facility density, the theoret-
ical advantages may not be well quantified in empirical studies, especially in different
spatiotemporal contexts [
16
,
22
,
23
]. Therefore, we illustrate and discuss the prediction
efficiency of FD and FA models at the global and local scales (different risk levels and
different administrative regions), respectively, below:
4.1.1. Global Explanatory Ability of the Models
According to the model diagnostic information for the whole spatiotemporal model,
FA is a better predictor for COVID-19 risk modeling than FD (Table 3). An FA model can
explain 56.9% of the spatiotemporal risk changes in the empirical area, which is 5.35%
more than that explained by the traditional model, and the improvement rate exceeds 10%.
At the same time, the AICc value of the model based on the FA predictor is also greatly
reduced, which proves that the FA model is more reasonable.
The cross-sectional explanatory ability of the FA model for spatial COVID-19 risk is
also stronger than that of the FD model (Table 5). The predictive ability of the FD and FA
models showed an upward trend in almost all the five stages, and the adjusted R
2
of the
FA model reached more than 0.6 at its highest point.
Table 5. Phased modeling results of the adjusted R2with FDs and FAs.
Epidemic Stage Adjusted R2 Improvement Rate
Facility Density (FD) Facility Attractiveness (FA)
Stage 1 0.3847 0.4808 24.99%
Stage 2 0.4190 0.4747 13.28%
Stage 3 0.5039 0.5629 11.72%
Stage 4 0.4950 0.5669 14.51%
Stage 5 0.5532 0.6179 11.70%
In addition, in all the five stages, the R
2
improvement rate of the FA model compared
with the FD model was over 10% and was the most obvious (25.0%) in the initial stage
of the epidemic, which proved that the effect of “upgrading” FDs to FAs to increase the
modeling effectiveness at the initial stage of the epidemic with a limited sample size was
remarkable. The reason for this good model performance and the improvement may be
that, in the latent and initial stage of the epidemic, due to the extremely limited number of
infected persons, it was difficult for these few and scattered people to transmit the virus
through short-term contact with crowds in open spaces. This means that areas with a
higher facility attractiveness—that is, areas where people are more likely to gather—were
crucial places in the spread of the epidemic [
29
,
30
]. At this time, due to the lack of virus
hosts in the sparsely populated urban fringe areas, the facilities in these areas played a less

Int. J. Environ. Res. Public Health 2021,18, 13294 11 of 16
pivotal role in the transmission of the epidemic [
67
,
68
], meaning that the FA predictor had
the most obvious optimization effect compared with FD in the initial stage of the epidemic.
However, with the spread of virus, there is no such huge shortage of infected people in
sparsely populated areas [
69
]. The magnitude of the role played by facilities in different
areas in epidemic transmission tended to be similar, and the optimization effect of the FA
predictor declined. However, due to the exponential development of the epidemic [
70
],
FA predictors, which have a larger differentiation in space because of the overlap of the
facilities’ density and their effect on causing people to gather, still have advantages over
traditional facility densities.
4.1.2. Local Explanatory Ability of Grids with Different Risk Levels
It is necessary to test the prediction ability of the model in grids with different risk
levels. The model should be able to accurately identify high-risk grids and avoid overes-
timating the risk in low-risk areas to the greatest extent in order to prevent unnecessary
problems caused by epidemic prevention and control and ensure people’s freedom of travel
and the urban vitality in low-risk areas as much as possible. According to the risk value
obtained in our Gaussian kernel density analysis, grids were divided into four grades:
Level 1 contained grids with a risk value in the top first third among grids with a value
greater than 0, Level 2 contained grids with a risk value in the top two thirds among
grids with a value greater than 0, Level 3 contained grids with a risk value greater than
0, and Level 4 contained all grids in the empirical area (Figure 5). From the perspective
of their ability to predict the risk, both FDs and FAs were relatively stable in low-risk and
medium-low-risk areas, being stable between 30% and 60%. Compared with low-risk areas,
the stability of the prediction ability of the model in medium-high and high-risk areas,
especially in high-risk areas, declined. The temporal stability of the prediction effectiveness
was not as good as the performance for low-risk areas, and the risk prediction ability in
the initial stage of the epidemic was also limited. From the perspective of improving the
efficiency of the model by changing the predictor, the explanatory ability of FA compared
with that of the FD model was improved by 10–30% in most conditions, proving that
the improvement effect was remarkable. It is worth noting that the prediction ability of
the FA model was greatly improved (107.2%) in high-risk areas compared with the FD
model in the initial stage of the epidemic, which also shows the significance of population
density and age-hierarchical travel capacity in model optimization at the initial stage of
the epidemic.
4.1.3. Local Explanatory Ability of Grids in Different Administrative Regions
The optimized model should have the ability to predict the risk of COVID-19 in densely
populated areas and economic agglomeration areas in order to maximize socio-economic
cost savings. Therefore, the explanatory ability of the model in different administrative
regions was compared (Figure 5). The FA model had the strongest ability to predict the
risk in Laoshan District, with its ability generally being between 55% and 75%. However,
the optimized effect was the least obvious there, and most of the time the model perfor-
mance was still slightly inferior to that of the traditional model. The fitting efficiencies for
Shibei District and Licang District were similar, with both consistently being around 50%,
demonstrating a good prediction ability. In the second stage of the epidemic, the FD model
was shown to be slightly better than the FA model, but this phenomenon was gradually
reversed with the spread of the epidemic. Shinan District is in the old city of Qingdao and
also its center; it is a densely populated area and a place where many elderly people live.
Although the fitting efficiency of the GIS-based spatiotemporal model in this area is often
inferior to that in the other three districts, the effectiveness of the model greatly improved
over time from about 40% to about 70%. In addition, the FA model showed the highest
level of improvement in this area, which emphasizes the advantages of the optimized
method adopted by this research in modeling densely populated areas and aging areas,
which are some of the areas most susceptible to epidemics.

Int. J. Environ. Res. Public Health 2021,18, 13294 12 of 16
Figure 5.
Comparison of the effectiveness of the model prediction between FDs and FAs in two types of application scenarios:
(
a
) temporal trend of the effectiveness of the differentiation of the two models (the colored surface is the optimized model,
while the gray surface and side filling represent the traditional model); (b) improvement rate.
4.2. Limitation and Prospection
The estimation and comparison results obtained for the models’ performances (global
and local fitting effectiveness), as shown above, prove the usefulness of the novel predictor,
facility attractiveness (FA), in the spatiotemporal risk modeling of COVID-19 and its
superiority over the traditional predictor of “facility density”. This advantage is mainly
reflected in the initial stage of the epidemic, as the initial prediction of epidemic risk is
often regarded to be weak in previous studies based on the “densities” model [
71
,
72
].
Theoretically, the outbreak of a regional epidemic is often started by the entry of a virus
carrier in the beginning, and the impact of the effect of gathering on the micro-scale
COVID-19 spatiotemporal risk is not obvious at this stage. Models based on facility
attractiveness weighted by population density can make up for this deficiency of traditional
models
[72–74]
. At the same time, because the limited travel capacity of the elderly means
that facilities beyond their travel range cannot be made more “attractive”, the lower FAs
value seen in these areas will also separate them from areas where there are more adults
who have a stronger travel ability and who are more likely to come into contact with viruses
from outside the area, thus reducing the cost of an indiscriminate lockdown [
55
,
58
]. In
addition, the FA model also has good prediction efficiency for high-risk areas and potential
high-risk areas (densely populated areas), which makes it possible to target high-risk areas
quickly and accurately at the initial stage of the epidemic. This is beneficial to hierarchical
prevention and control strategies for regional epidemics.
However, this model is just the beginning. Limited by the length of this study and the
limitation of our empirical area, when constructing the FA predictor, we selectively ignored
some other factors that may affect the attractiveness of facilities, such as the complex
relationship between the weak travel ability of the elderly and their high possibility of

Int. J. Environ. Res. Public Health 2021,18, 13294 13 of 16
infection [
33
,
55
]; the sanitation and disinfection of public facilities [
75
]; the effect of social
distancing and the impact of epidemic prevention measures taken at the individual level,
such as wearing masks [
76
,
77
]; the different behavior characteristics of human beings
from different social classes and with different living conditions within cities [
78
]; racial
differences, which, although almost nonexistent in this empirical area, are very important
in Europe and US [
46
]; factors such as temperature, precipitation and humidity, which some
previous studies claim should be considered more and which greatly affect human travel
habits within cities [
79
–
81
]. The construction of FA predictors is not only a formula, but
also a reference for thinking. Researchers should combine the characteristics of the study
area and modify this model to adapt it to specific local situations. In addition, due to the
lack of micro-scale data for the early stage of the epidemic in China’s most epidemic-prone
areas, the discussion of this study mainly focuses on the initial stage of the epidemic; the
sensitivity and universality of this model need to be supported by subsequent multi-scale
and multi-perspective empirical studies.
Different from traditional models, which require behavior data at the individual
level and complicated calculation processes [
73
,
74
], the availability of data and strong
predictability of multivariate geographic data in COVID-19 risk modeling highlight the
need for further spatiotemporal epidemiology research to be carried out, especially research
on spatiotemporal risk modeling based on GIS and using geographic methods and spatial
analysis techniques [
10
,
12
]. More attention should be paid to participation forms and the
improvement of the prediction ability of geographic and spatiotemporal analysis methods
in applications. This is not only the case for the COVID-19 pandemic but also for the
optimization of the regionalized emergency response ability next time human beings have
to face a global health crisis.
5. Conclusions
This study highlights the importance of considering the heterogeneity of population
mobility in order to gain a better understanding of the driving factors spatiotemporally
influencing epidemic diffusion in micro-scale areas. Considering this aspect in models will
allow us to capture the impact of gathering in various places (the exposure and probability
of people gathering) on epidemic transmission more accurately. Therefore, a predictor
calculated based on the optimized gravity model, facility attractiveness (FA), is proposed.
Geographically and temporally weighted regression is used to measure the effectiveness
of this predictor and the spatiotemporal nonstationarity of the influence for the various
facilities on epidemic diffusion. The modeling results show that the predictor is superior
to the traditional “densities” indicator, especially in areas considered to be high-risk and
densely populated during the initial stage of the epidemic. Considering that the novel
predictor can only be used with easily accessible data and a relatively simple operation
process, it can provide an optimal means for researchers in relevant fields to predict the
micro-scale risk of a pandemic.
Author Contributions:
Conceptualization, S.Z.; data curation, S.Z., M.W. and Z.Y.; methodology,
S.Z.; formal analysis, S.Z.; writing—original draft preparation, S.Z.; writing—review and editing, S.Z.
and B.Z.; visualization, S.Z.; supervision, B.Z.; funding acquisition, B.Z. All authors have read and
agreed to the published version of the manuscript.
Funding:
This research was funded by the National Social Science Foundation of China (No. 18BJY086).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement:
Publicly available datasets were analyzed in this study. The COVID-19
case data can be found in the Qingdao Municipal Health Commission: [wsjkw.qingdao.gov.cn]; The
POI data can be found in Amap: [www.amap.com]; The raster data for people of various ages can be
found in WorldPop: [www.worldpop.org]; The road network data can be found in OpenStreetMap:
[www.openstreetmap.org].

Int. J. Environ. Res. Public Health 2021,18, 13294 14 of 16
Acknowledgments:
The authors wish to express their great appreciation for Shengli Zhu and Shixuan
Lyu (Shandong Normal University) for their suggestions concerning the original research idea. We
would also like to gratefully acknowledge the anonymous reviewers who helped to improve this
paper through their thorough review.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
Wu, F.; Zhao, S.; Yu, B.; Chen, Y.-M.; Wang, W.; Song, Z.-G.; Hu, Y.; Tao, Z.-W.; Tian, J.-H.; Pei, Y.-Y.; et al. A new coronavirus
associated with human respiratory disease in China. Nature 2020,579, 265–269. [CrossRef] [PubMed]
2. Van Dorn, A.; Cooney, R.E.; Sabin, M.L. COVID-19 exacerbating inequalities in the US. Lancet 2020,395, 1243–1244. [CrossRef]
3.
Zambrano-Monserrate, M.A.; Ruano, M.A.; Sanchez-Alcalde, L. Indirect effects of COVID-19 on the environment. Sci. Total
Environ. 2020,728, 138813. [CrossRef] [PubMed]
4.
Nicola, M.; Alsafi, Z.; Sohrabi, C.; Kerwan, A.; Al-Jabir, A.; Iosifidis, C.; Agha, M.; Agha, R. The socio-economic implications of
the coronavirus pandemic (COVID-19): A review. Int. J. Surg. 2020,78, 185–193. [CrossRef] [PubMed]
5.
Gössling, S.; Scott, D.; Hall, C.M. Pandemics, tourism and global change: A rapid assessment of COVID-19. J. Sustain. Tour.
2020
,
29, 1–20. [CrossRef]
6.
Clark, A.; Jit, M.; Warren-Gash, C.; Guthrie, B.; Wang, H.H.X.; Mercer, S.W.; Sanderson, C.; McKee, M.; Troeger, C.; Ong, K.L.;
et al. Global, regional, and national estimates of the population at increased risk of severe COVID-19 due to underlying health
conditions in 2020: A modelling study. Lancet Glob. Health 2020,8, e1003–e1017. [CrossRef]
7.
Sun, Z.; Di, L.; Sprigg, W.; Tong, D.; Casal, M. Community venue exposure risk estimator for the COVID-19 pandemic. Health
Place 2020,66, 102450. [CrossRef]
8.
Studdert, D.M.; Hall, M.A. Disease Control, Civil Liberties, and Mass Testing—Calibrating Restrictions during the Covid-19
Pandemic. N. Engl. J. Med. 2020,383, 102–104. [CrossRef]
9.
Pearce, N.; Vandenbroucke, J.P.; VanderWeele, T.J.; Greenland, S. Accurate Statistics on COVID-19 Are Essential for Policy
Guidance and Decisions. Am. J. Public Health 2020,110, 949–951. [CrossRef]
10.
Jaya, I.G.N.M.; Folmer, H. Bayesian spatiotemporal forecasting and mapping of COVID-19 risk with application to West Java
Province, Indonesia. J. Reg. Sci. 2021,61, 849–881. [CrossRef]
11.
Jiang, P.; Fu, X.; Van Fan, Y.; Klemeš, J.J.; Chen, P.; Ma, S.; Zhang, W. Spatial-temporal potential exposure risk analytics and urban
sustainability impacts related to COVID-19 mitigation: A perspective from car mobility behaviour. J. Clean. Prod.
2021
,279,
123673. [CrossRef]
12.
Li, J.; Wang, X.; He, Z.; Zhang, T. A personalized activity-based spatiotemporal risk mapping approach to the COVID-19
pandemic. Cartogr. Geogr. Inf. Sci. 2021,48, 275–291. [CrossRef]
13.
Franch-Pardo, I.; Napoletano, B.M.; Rosete-Verges, F.; Billa, L. Spatial analysis and GIS in the study of COVID-19. A review. Sci.
Total Environ. 2020,739, 140033. [CrossRef]
14.
Zhou, C.; Su, F.; Pei, T.; Zhang, A.; Du, Y.; Luo, B.; Cao, Z.; Wang, J.; Yuan, W.; Zhu, Y.; et al. COVID-19: Challenges to GIS with
Big Data. Geogr. Sustain. 2020,1, 77–87. [CrossRef]
15.
Rader, B.; Scarpino, S.V.; Nande, A.; Hill, A.L.; Adlam, B.; Reiner, R.C.; Pigott, D.M.; Gutierrez, B.; Zarebski, A.E.; Shrestha, M.;
et al. Crowding and the shape of COVID-19 epidemics. Nat. Med. 2020,26, 1829–1834. [CrossRef]
16.
Hamidi, S.; Sabouri, S.; Ewing, R. Does Density Aggravate the COVID-19 Pandemic? Early Findings and Lessons for planners. J.
Am. Plan. Assoc. 2020,86, 495–509. [CrossRef]
17.
Hamidi, S.; Zandiatashbar, A. Compact development and adherence to stay-at-home order during the COVID-19 pandemic: A
longitudinal investigation in the United States. Landsc. Urban Plan. 2020,205, 103952. [CrossRef]
18. Banai, R. Pandemic and the planning of resilient cities and regions. Cities 2020,106, 102929. [CrossRef]
19.
Barak, N.; Sommer, U.; Mualam, N. Urban attributes and the spread of COVID-19: The effects of density, compliance and
socio-political factors in Israel. Sci. Total Environ. 2021,793, 148626. [CrossRef]
20. Rocklöv, J.; Sjödin, H. High population densities catalyse the spread of COVID-19. J. Travel Med. 2020,27, taaa038. [CrossRef]
21.
Han, Y.; Yang, L.; Jia, K.; Li, J.; Feng, S.; Chen, W.; Zhao, W.; Pereira, P. Spatial distribution characteristics of the COVID-19
pandemic in Beijing and its relationship with environmental factors. Sci. Total Environ. 2021,761, 144257. [CrossRef] [PubMed]
22.
Mollalo, A.; Vahedi, B.; Rivera, K.M. GIS-based spatial modeling of COVID-19 incidence rate in the continental United States. Sci.
Total Environ. 2020,728, 138884. [CrossRef] [PubMed]
23.
Kadi, N.; Khelfaoui, M. Population density, a factor in the spread of COVID-19 in Algeria: Statistic study. Bull. Natl. Res. Cent.
2020,44, 138. [CrossRef] [PubMed]
24.
Xu, Y.; Song, Y.; Cai, J.; Zhu, H. Population mapping in China with Tencent social user and remote sensing data. Appl. Geogr.
2021
,
130, 102450. [CrossRef]
25.
Yao, Y.; Liu, X.; Li, X.; Zhang, J.; Liang, Z.; Mai, K.; Zhang, Y. Mapping fine-scale population distributions at the building level by
integrating multisource geospatial big data. Int. J. Geogr. Inf. Sci. 2017,31, 1220–1244. [CrossRef]
26.
Bouffanais, R.; Lim, S.S. Cities—Try to predict superspreading hotspots for COVID-19. Nat. Cell Biol.
2020
,583, 352–355.
[CrossRef]

Int. J. Environ. Res. Public Health 2021,18, 13294 15 of 16
27.
Zhou, Y.; Xu, R.; Hu, D.; Yue, Y.; Li, Q.; Xia, J. Effects of human mobility restrictions on the spread of COVID-19 in Shenzhen,
China: A modelling study using mobile phone data. Lancet Digit. Health 2020,2, e417–e424. [CrossRef]
28.
Zhan, C.; Tse, C.K.; Fu, Y.; Lai, Z.; Zhang, H. Modeling and prediction of the 2019 coronavirus disease spreading in China
incorporating human migration data. PLoS ONE 2020,15, e0241171. [CrossRef]
29.
Li, Q.; Bessell, L.; Xiao, X.; Fan, C.; Gao, X.; Mostafavi, A. Disparate patterns of movements and visits to points of interest located
in urban hotspots across US metropolitan cities during COVID-19. R. Soc. Open Sci. 2021,8, 201209. [CrossRef]
30.
Lak, A.; Sharifi, A.; Badr, S.; Zali, A.; Maher, A.; Mostafavi, E.; Khalili, D. Spatio-temporal patterns of the COVID-19 pandemic,
and place-based influential factors at the neighborhood scale in Tehran. Sustain. Cities Soc. 2021,72, 103034. [CrossRef]
31.
Zhang, S.; Yang, Z.; Wang, M.; Zhang, B. “Distance-Driven” Versus “Density-Driven”: Understanding the Role of “Source-Case”
Distance and Gathering Places in the Localized Spatial Clustering of COVID-19—A Case Study of the Xinfadi Market, Beijing
(China). GeoHealth 2021,5, e2021GH000458. [CrossRef]
32.
Prem, K.; Liu, Y.; Russell, T.W.; Kucharski, A.J.; Eggo, R.M.; Davies, N.; Jit, M.; Klepac, P.; Flasche, S.; Clifford, S.; et al. The Effect
of Control Strategies to Reduce Social Mixing on Outcomes of the COVID-19 Epidemic in Wuhan, China: A Modelling Study.
Lancet Public Health 2020,5, e261–e270. [CrossRef]
33.
Davies, N.G.; Klepac, P.; Liu, Y.; Prem, K.; Jit, M.; Eggo, R.M. Age-dependent effects in the transmission and control of COVID-19
epidemics. Nat. Med. 2020,26, 1205–1211. [CrossRef]
34.
Illenberger, J.; Nagel, K.; Flötteröd, G. The Role of Spatial Interaction in Social Networks. Netw. Spat. Econ.
2013
,13, 255–282.
[CrossRef]
35.
van den Berg, P.; Kemperman, A.; Timmermans, H. Social Interaction Location Choice: A Latent Class Modeling Approach. Ann.
Assoc. Am. Geogr. 2014,104, 959–972. [CrossRef]
36.
Birch, C.P.D.; Oom, S.P.; Beecham, J.A. Rectangular and hexagonal grids used for observation, experiment and simulation in
ecology. Ecol. Model. 2007,206, 347–359. [CrossRef]
37.
Ling, C.; Wen, X. Community grid management is an important measure to contain the spread of novel coronavirus pneumonia
(COVID-19). Epidemiol. Infect. 2020,148, e167. [CrossRef]
38.
Li, Z.; Gao, G.F. Strengthening public health at the community-level in China. Lancet Public Health
2020
,5, e629–e630. [CrossRef]
39.
Schläpfer, M.; Dong, L.; O’Keeffe, K.; Santi, P.; Szell, M.; Salat, H.; Anklesaria, S.; Vazifeh, M.; Ratti, C.; West, G.B. The universal
visitation law of human mobility. Nat. Cell Biol. 2021,593, 522–527. [CrossRef]
40.
Luo, W.; Qi, Y. An enhanced two-step floating catchment area (E2SFCA) method for measuring spatial accessibility to primary
care physicians. Health Place 2009,15, 1100–1107. [CrossRef]
41.
Liu, S.; Qin, Y.; Xie, Z.; Zhang, J. The Spatio-Temporal Characteristics and Influencing Factors of Covid-19 Spread in Shenzhen,
China—An Analysis Based on 417 Cases. Int. J. Environ. Res. Public Health 2020,17, 7450. [CrossRef]
42.
Yao, Y.; Shi, W.; Zhang, A.; Liu, Z.; Luo, S. Examining the diffusion of coronavirus disease 2019 cases in a metropolis: A space
syntax approach. Int. J. Health Geogr. 2021,20, 17. [CrossRef]
43. Carey, H.C. Principles of Social Science; JB Lippincott & Company: Philadelphia, PA, USA, 1867; Volume 3.
44. Stewart, J.Q. Demographic Gravitation: Evidence and Applications. Sociometry 1948,11, 31–58. [CrossRef]
45.
Flowerdew, R.; Aitkin, M. A method of fitting the gravity model based on the poisson distribution. J. Reg. Sci.
1982
,22, 191–202.
[CrossRef]
46.
Dai, D. Black residential segregation, disparities in spatial access to health care facilities, and late-stage breast cancer diagnosis in
metropolitan Detroit. Health Place 2010,16, 1038–1052. [CrossRef]
47.
Luo, W.; Wang, F. Measures of Spatial Accessibility to Health Care in a GIS Environment: Synthesis and a Case Study in the
Chicago Region. Environ. Plan. B Plan. Des. 2003,30, 865–884. [CrossRef]
48.
McGrail, M.; Humphreys, J.S. Measuring spatial accessibility to primary health care services: Utilising dynamic catchment sizes.
Appl. Geogr. 2014,54, 182–188. [CrossRef]
49.
Liu, T.; Chai, Y. Daily life circle reconstruction: A scheme for sustainable development in urban China. Habitat Int.
2015
,50,
250–260. [CrossRef]
50.
Kraemer, M.U.G.; Yang, C.-H.; Gutierrez, B.; Wu, C.-H.; Klein, B.; Pigott, D.M.; Open COVID-19 Data Working Group; du Plessis,
L.; Faria, N.R.; Li, R.; et al. The effect of human mobility and control measures on the COVID-19 epidemic in China. Science
2020
,
368, 493–497. [CrossRef] [PubMed]
51.
Li, L.; Du, Q.; Ren, F.; Ma, X. Assessing Spatial Accessibility to Hierarchical Urban Parks by Multi-Types of Travel Distance in
Shenzhen, China. Int. J. Environ. Res. Public Health 2019,16, 1038. [CrossRef]
52.
Shao, F.; Sui, Y.; Yu, X.; Sun, R. Spatio-temporal travel patterns of elderly people—A comparative study based on buses usage in
Qingdao, China. J. Transp. Geogr. 2019,76, 178–190. [CrossRef]
53.
Ministry of Education of China and Ministry of Industry and Information Technology of China. Notice of Arrangement for
“Suspension of School Does Not Stop Learning” during the Postponement for the Opening of Primary and Secondary Schools.
2020. Available online: http://www.moe.gov.cn/srcsite/A06/s3321/202002/t20200212_420435.html (accessed on 12 February
2020).
54.
Wang, X.; Lei, S.M.; Le, S.; Yang, Y.; Zhang, B.; Yao, W.; Gao, Z.; Cheng, S. Bidirectional Influence of the COVID-19 Pandemic
Lockdowns on Health Behaviors and Quality of Life among Chinese Adults. Int. J. Environ. Res. Public Health
2020
,17, 5575.
[CrossRef]

Int. J. Environ. Res. Public Health 2021,18, 13294 16 of 16
55.
Lee, P.M.Y.; Huang, B.; Liao, G.; Chan, C.K.; Tai, L.-B.; Tsang, C.Y.J.; Leung, C.C.; Kwan, M.-P.; Tse, L.A. Changes in physical
activity and rest-activity circadian rhythm among Hong Kong community aged population before and during COVID-19. BMC
Public Health 2021,21, 836. [CrossRef]
56.
Sun, X.; Lucas, H.; Meng, Q.; Zhang, Y. Associations between living arrangements and health-related quality of life of urban
elderly people: A study from China. Qual. Life Res. 2011,20, 359–369. [CrossRef]
57.
Xu, Y.; Zhou, D.; Liu, K. Research on The Elderly Space-time Behavior Visualization and Community Healthy Livable Environment.
Archit. J. 2019,S1, 90–95.
58. Liu, S.; Wang, Y.; Zhou, D.; Kang, Y. Two-Step Floating Catchment Area Model-Based Evaluation of Community Care Facilities’
Spatial Accessibility in Xi’an, China. Int. J. Environ. Res. Public Health 2020,17, 5086. [CrossRef]
59.
Wang, Z.; Gao, G.; Liu, X.; Lyu, W. Verification and Analysis of Traffic Evaluation Indicators in Urban Transportation System
Planning Based on Multi-Source Data–A Case Study of Qingdao City, China. IEEE Access 2019,7, 110103–110115. [CrossRef]
60.
Brunsdon, C.; Fotheringham, S.; Charlton, M. Geographically Weighted Regression. J. R. Stat. Soc. Ser. D
1998
,47, 431–443.
[CrossRef]
61.
Huang, B.; Wu, B.; Barry, M. Geographically and temporally weighted regression for modeling spatio-temporal variation in
house prices. Int. J. Geogr. Inf. Sci. 2010,24, 383–401. [CrossRef]
62.
Wang, H.; Wang, J.; Huang, B. Prediction for spatio-temporal models with autoregression in errors. J. Nonparametric Stat.
2012
,24,
217–244. [CrossRef]
63.
Wu, B.; Li, R.; Huang, B. A geographically and temporally weighted autoregressive model with application to housing prices. Int.
J. Geogr. Inf. Sci. 2014,28, 1186–1204. [CrossRef]
64.
Ge, L.; Zhao, Y.; Sheng, Z.; Wang, N.; Zhou, K.; Mu, X.; Guo, L.; Wang, T.; Yang, Z.; Huo, X. Construction of a Seasonal
Difference-Geographically and Temporally Weighted Regression (SD-GTWR) Model and Comparative Analysis with GWR-Based
Models for Hemorrhagic Fever with Renal Syndrome (HFRS) in Hubei Province (China). Int. J. Environ. Res. Public Health
2016
,
13, 1062. [CrossRef]
65.
Chen, Y.; Chen, M.; Huang, B.; Wu, C.; Shi, W. Modeling the Spatiotemporal Association Between COVID-19 Transmission and
Population Mobility Using Geographically and Temporally Weighted Regression. GeoHealth 2021,5. [CrossRef]
66.
Burnham, K.P.; Anderson, D.R. Multimodel Inference: Understanding AIC and BIC in Model Selection. Sociol. Methods Res.
2004
,
33, 261–304. [CrossRef]
67.
Wu, S.-S.; Zhuang, Y.; Chen, J.; Wang, W.; Bai, Y.; Lo, S.-M. Rethinking bus-to-metro accessibility in new town development: Case
studies in Shanghai. Cities 2019,94, 211–224. [CrossRef]
68.
Zhao, P.; Wan, J. Land use and travel burden of residents in urban fringe and rural areas: An evaluation of urban-rural integration
initiatives in Beijing. Land Use Policy 2021,103, 105309. [CrossRef]
69.
Matthews, K.A.; Ullrich, F.; Gaglioti, A.H.; Dugan, S.; Chen, M.S.; Hall, D.M. Nonmetropolitan COVID-19 Incidence and Mortality
Rates Surpassed Metropolitan Rates Within the First 24 Weeks of the Pandemic Declaration: United States, March 1–October 18,
2020. J. Rural Health 2021,37, 272–277. [CrossRef] [PubMed]
70.
Zhao, S.; Lin, Q.; Ran, J.; Musa, S.S.; Yang, G.; Wang, W.; Lou, Y.; Gao, D.; Yang, L.; He, D.; et al. Preliminary estimation of the
basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: A data-driven analysis in the early
phase of the outbreak. Int. J. Infect. Dis. 2020,92, 214–217. [CrossRef]
71.
Alberti, T.; Faranda, D. On the uncertainty of real-time predictions of epidemic growths: A COVID-19 case study for China and
Italy. Commun. Nonlinear Sci. Numer. Simul. 2020,90, 105372. [CrossRef]
72.
Neuberger, A.; Paul, M.; Nizar, A.; Raoult, D. Modelling in infectious diseases: Between haphazard and hazard. Clin. Microbiol.
Infect. 2013,19, 993–998. [CrossRef]
73. House, T.; Keeling, M.J. Epidemic prediction and control in clustered populations. J. Theor. Biol. 2011,272, 1–7. [CrossRef]
74.
Anirudh, A. Mathematical modeling and the transmission dynamics in predicting the Covid-19—What next in combating the
pandemic. Infect. Dis. Model. 2020,5, 366–374. [CrossRef]
75.
Caruso, B.A.; Freeman, M.C. Shared sanitation and the spread of COVID-19: Risks and next steps. Lancet Planet. Health
2020
,4,
E173. [CrossRef]
76.
Courtemanche, C.; Garuccio, J.; Le, A.; Pinkston, J.; Yelowitz, A. Strong Social Distancing Measures in the United States Reduced
The COVID-19 Growth Rate. Health Aff. 2020,39, 1237–1246. [CrossRef]
77.
Chu, D.K.; Akl, E.A.; Duda, S.; Solo, K.; Yaacoub, S.; Schünemann, H.J.; EI-harakeh, A.; Bognanni, A.; Lotfi, T.; Loeb, M.; et al.
Physical distancing, face masks, and eye protection to prevent person-to-person transmission of SARS-CoV-2 and COVID-19: A
systematic review and meta-analysis. Lancet 2020,395, 1973–1987. [CrossRef]
78.
Bambra, C.; Riordan, R.; Ford, J.; Matthews, F. The COVID-19 pandemic and health inequalities. J. Epidemiol. Community Health
2020,74, 964–968. [CrossRef]
79.
Sasikumar, K.; Nath, D.; Nath, R.; Chen, W. Impact of Extreme Hot Climate on COVID-19 Outbreak in India. GeoHealth
2020
,4,
e2020GH000305. [CrossRef]
80.
Menebo, M.M. Temperature and precipitation associate with Covid-19 new daily cases: A correlation study between weather and
Covid-19 pandemic in Oslo, Norway. Sci. Total Environ. 2020,737, 139659. [CrossRef]
81.
Qi, H.; Xiao, S.; Shi, R.; Ward, M.P.; Chen, Y.; Tu, W.; Su, Q.; Wang, W.; Wang, X.; Zhang, Z. COVID-19 transmission in Mainland
China is associated with temperature and humidity: A time-series analysis. Sci. Total Environ. 2020,728, 138778. [CrossRef]