Revealing geographic transmission pattern of COVID-19 using neighborhood-level simulation with human mobility data and SEIR model: A case study of South Carolina

Abstract

Direct human physical contact accelerates COVID-19 transmission. Smartphone mobility data has emerged as a valuable data source for revealing fine-grained human mobility, which can be used to estimate the intensity of physical contact surrounding different locations. Our study applied smartphone mobility data to simulate the second wave spreading of COVID-19 in January 2021 in three major metropolitan statistical areas (Columbia, Greenville, and Charleston) in South Carolina, United States. Based on the simulation, the number of historical county-level COVID-19 cases was allocated to neighborhoods (Census block groups) and points of interest (POIs), and the transmission rate of each allocated place was estimated. The result reveals that the COVID-19 infections during the study period mainly occurred in neighborhoods (86%), and the number is approximately proportional to the neighborhood’s population. Restaurants and elementary and secondary schools contributed more COVID-19 infections than other POI categories. The simulation results for the coastal tourism Charleston area show high transmission rates in POIs related to travel and leisure activities. The results suggest that neighborhood-level infectious controlling measures are critical in reducing COVID-19 infections. We also found that households of lower socioeconomic status may be an umbrella against infection due to fewer visits to places such as malls and restaurants associated with their low financial status. Control measures should be tailored to different geographic locations since transmission rates and infection counts of POI categories vary among metropolitan areas.

1. Introduction

A novel coronavirus was reported in late December 2019 in Wuhan, China (Nishiura et al., 2020), and was later identified as Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). The coronavirus disease it caused was named COVID-19 (WHO, 2020). South Carolina (SC) in the United States (US) experienced four epidemic waves of COVID-19 from March 2020 to March 2022, causing 1.4 million cases and 17 thousand deaths. COVID-19 simulation and prediction, especially at the neighborhood level, plays an important role in health policymaking and disease prevention. COVID-19 simulation at the neighborhood level can identify the high-risk geographic locations with large numbers of new cases and help policymakers design appropriate disease control measures (e.g., mask-wearing and vaccination policy) and social distancing policies tailored to these areas (Wrigley-Field et al., 2021). For instance, in adjunction with social distancing and mask-wearing, prioritizing high-risk geographic neighborhoods for vaccination can effectively reduce COVID-19 transmission and mortality. Additionally, while the effectiveness of the COVID-19 vaccine against the new variants of the virus is unclear, COVID-19 simulation and prediction could inform proactive personal protective measures to curb disease transmission (Talic et al., 2021).

Direct human physical contact accelerates COVID-19 transmission (Tian et al., 2020, Zeng et al., 2022, Zhang et al., 2020). Human mobility, as a proxy of human physical contact, shows a close relationship with disease-spreading patterns (Hu et al., 2021b) and thus has been used in COVID-19 simulation and prediction studies. For instance, Zeng et al. (2021a) predicted the 3-, 7-, and 14-day COVID-19 incidence at state and county levels in SC using Twitter-based mobility data. Subsequently, they also examined whether the impact of human mobility on COVID-19 incidence differed by communities with different proportions of older adults (Zeng et al., 2021b). Similar mobility-based investigations were conducted based on various types of data sources at different geographic scopes. For example, (Hu et al., 2021a), applied travel statistics from mobile devices (i.e., trip per person, person-miles traveled, and proportion of staying in homes) to model the effectiveness of non-pharmaceutical interventions in the US. Fritz et al. (2022) trained machine learning and statistical regression models using Facebook Social Connectedness Index to predict COVID-19 cases in Germany. The historical mobility of Twitter users was also used to predict the worldwide spatiotemporal spreading of COVID-19 (Bisanzio et al., 2020, Li et al., 2020).

While many studies used mobility data to explore the patterns of COVID-19 transmission, most focused on relatively large scales such as countries (Hu et al., 2021b), states (Zeng et al., 2021a), or counties (Zeng et al., 2021b). Only a few tried to simulate and predict the spreading using fine-grained (geographic areas of small populations) mobility data. Among those, Chang et al. (2021a, 2021b) applied the cellphone mobility data between neighborhoods and points of interest (POIs) and then derived transmission rates and infection counts for each neighborhood (i.e., census block groups) and POI of the top 10 largest metropolitan statistical areas (MSAs). The researchers essentially allocated the infections into neighborhoods and POIs using SEIR (Susceptible, Exposed, Infection, Removed) epidemiological models, which can identify the places of high transmission rates and incidence counts. These findings can inform evidence-based disease control measures tailored to the POIs with large numbers of infections. However, these two studies focused on POIs analysis only without reporting neighborhood transmission patterns. With the absence of the neighborhood level transmission patterns, the observation of POIs only may not reflect the overall spreading trend of COVID-19.

Research indicates that COVID-19 may have different transmission rates among population groups. For example, the infection rates of the elderly over 70 years were two times higher than the teenagers (10–19 years) (Davies et al., 2020); a higher proportion of Black would increase the spread of COVID-19 (Zhai et al., 2021). A study on the early COVID-19 spreading in the northeastern US found that counties with higher poverty and disability had lower rates of infection but higher death rates. This might be attributed to their lower mobility and higher comorbidities (Abedi et al., 2021). However, Verma et al., (2021) reported a contradictory observation in New York City and Chicago, where lower-income groups had higher higher contact exposure and more cases. Levy et al. (2022) also documented the disparity of COVID-19 incidences among neighborhood socioeconomics, but they did not observe generality in the study area of three metro regions of the US (San Francisco, Seattle, and Wisconsin). Huang et al., (2022) investigated the correlation between human mobility and COVID-19 transmissibility at county level. They used mobility changes and pandemic vulnerability index to model reproduction numbers, and found that vulnerable counties suffered a higher infectious risk with increasing mobility.

In this study, we aim to investigate the geographic transmission pattern of COVID-19 in three MSAs in SC. Neighborhood level (Census block group, CBG) simulations of COVID-19 infections using human mobility data and SEIR epidemiological model were conducted in MSAs of Greenville-Anderson (Greenville), Charleston-North Charleston (Charleston), and Columbia. We estimated the transmission rates and infection counts for neighborhoods and POIs. Specifically, we aim to answer three questions:

(1) Which neighborhoods and POI categories had high transmission rates of COVID-19? We are interested in which types of places where the residents or visitors are more prone to infect COVID-19 than others. Thus, high-risk populations (e.g., the elderly) can stay away from those places.

(2) Which neighborhoods and POI categories have high COVID-19 incidence rates? Timely and appropriate responses can be applied to the places having high infection counts. For example, elementary schools with large infection cases may need special attention to decrease virus spreading.

(3) What are the correlations between the transmission rates and the socioeconomic status variables, including demographic, social determinants of health, and visited POIs? Investigation of the associations of these variables could inform resource allocation and effective and precise disease prevention and control.

2. Methodology

This study used smartphone mobility data to explore the transmission patterns of COVID-19 in SC. The three most populous MSAs, i.e., Greenville, Columbia, and Charleston, were selected (Fig. 1 a). The study period is from Dec. 29, 2020 to Feb. 8, 2021 (41 days), covering the main period of the second wave of COVID-19 spreading in SC (Fig. 1b). There is no new COVID-19 prevention policy issued in this period except for the vaccination started on Jan. 13, 2021 for individuals older than 70 (SC State House, 2021). Before the study period, restaurant capacity limits were lifted on Oct. 5, 2020 (SC State House, 2020), and about one-half of schools were in-person in 2020–2021 school year since Sept. 10, 2020 (Burbio, 2021).

Fig. 1.

(a). Study area. The three selected MSAs are located in the northwest, middle, and southeast of SC; Charleston is a coastal area of developed tourism and shipping business. (b). Four COVID-19 waves in South Carolina as of June 2022. Datasource: South Carolina Department of Health and Environmental Control (SCDHEC, 2022).

We adopted a simulation model (Chang et al., 2021a) based on mobility data and the SEIR model to estimate transmission rates and infection counts in neighborhoods and POIs. The evaluation (Section 2.3) for the simulation results contains three metrics: total case error, root mean square root (RMSE) of the daily case, and the error of infection rate by race (i.e., the White and Black). Note White, Black, and Asian stand for Non-Hispanic White, Non-Hispanic African Americans, and Non-Hispanic Asian in this paper. Based on the evaluated results, further analyses of the distribution of transmission rate and infection counts among CBGs and POIs were conducted (Section 2.4).

2.1. Datasets

SafeGraph datasets, including weekly Patterns, Geometry, and Core Places (SafeGraph, 2022c). The Weekly Patterns contains the hourly visit records of POIs (e.g., restaurants and grocery stores) and the aggregated numbers of visitors’ home CBGs on that week. The Geometry dataset includes the areas of recorded POIs. The Core Places dataset has the basic information of POIs, such as the location name and category in the North American Industry Classification System (NAICS) (US Cenus Bureau, 2022), including the top- and sub-category. About 10% of mobile devices in the US were sampled by SafeGraph (Squire, 2019).

New York Times Historical COVID-19 data(NYT COVID-19 data). This dataset contains the daily cumulated confirmed COVID-19 cases at the county level in the US. It was obtained from github.com/nytimes/covid-19-data. The aggregated daily cases and total cases of MSAs were applied to evaluate the simulated results.

South Carolina County Level COVID-19 Data by SCDHEC (SCDHEC COVID-19 data). This dataset (SCDHEC, 2022) provides COVID-19 county-level data, containing test count, case count, and death count for age and race groups. The case counts of the White and Black were used to assess those estimated from the simulation results.

American Community Survey 2019 5-year estimate (ACS 2019) at the CBG level. We applied the latest 5-year estimates when this study was conducted. Although ACS 2019 does not exactly align with the study period (January 2021), any population changes during this period are anticipated to be negligible and unlikely to affect the simulation results. In addition, the block group boundaries adopted in later ACS products have been changed (Berry, 2022; US Census, 2021), imposing challenges to match the mobility data coded in 2010–2019 Census boundaries (SafeGraph. 2022b, SafeGraph., 2022b). Therefore, ACS 2019 was preferred.

Note that the adopted model can accept mask-wearing proportion (IHME, 2022) for simulation. We did not use this data because the statewide mask-wearing proportion in the study period (2020.12.29–2021.02.08) is relatively stable (70 – 73%) and the granularity of MSAs is missing.

2.2. Simulation model

We adopted Chang et al. (2021a)’s model to simulate the COVID-19 spreading in the study area. Necessary modifications were made to fit our study, such as neighborhood results storage because Chang et al. (2021a)’s work focused on POI only. The model assumes that people get infected merely in two types of places: their home neighborhoods (CBGs in this study) and POIs. The following introduces the simulation model.

Each CBG $(c_i$) has its own SEIR model, which maintains the number of individuals in 4 sequential stages for hour $\text{t}$: Susceptible ($S_{c_i}^{\left(t\right)}$), Exposed ($E_{c_i}^{\left(t\right)}$), Infectious ($I_{c_i}^{\left(t\right)}$), and Removed ($R_{c_i}^{\left(t\right)}$); Fig. 2 illustrates the evolution of 4 stages.

Fig. 2.

Evolution of 4 stages of the SEIR model. (a): Susceptible (S) individuals have a probability (transmission rate) of being Exposed ($E$) to the virus; (b) the Exposed individuals become Infectious ($I$) after the latency period, and then make their close contacts become Exposed; (c) If the Infectious individuals in (a) are cured or dead, they become Removed ($R$) after the infectious period; Exposed individuals in (b) become newly infectious, while some Susceptible individuals become newly Exposed.

For CBG $c_i$, its population $N_{c_i}=S_{c_i}^{\left(t\right)}+E_{c_i}^{\left(t\right)}+I_{c_i}^{\left(t\right)}+R_{c_i}^{\left(t\right)}$, and the transition between four stages at hour $\text{t}$ are:

$$\begin{array}{c}{N}_{S_{\mathit{ci}}\to E_{\mathit{ci}}}^{\left(t\right)}{\mathit{CBG}}_{S_{\mathit{ci}}\to E_{\mathit{ci}}}^{\left(t\right)}+{\mathit{POI}}_{S_{\mathit{ci}}\to E_{\mathit{ci}}}^{\left(t\right)}\end{array}$$ (1)

$$\begin{array}{c}\begin{array}{c}{\mathrm{C}\mathrm{B}\mathrm{G}}_{{\mathrm{S}}_{\mathrm{c}\mathrm{i}}\to {\mathrm{E}}_{\mathrm{c}\mathrm{i}}}^{\left(\mathrm{t}\right)}Binomial\left({\mathrm{S}}_{{\mathrm{c}}_{\mathrm{i}}}^{\left(\mathrm{t}\right)},{\mathrm{\lambda }}_{{\mathrm{c}}_{\mathrm{i}}}^{\left(\mathrm{t}\right)}\right)\#\end{array}\end{array}$$ (2)

$$\begin{array}{c}{\mathit{POI}}_{S_{\mathit{ci}}\to E_{\mathit{ci}}}^{\left(t\right)}{\sum }_{j=1}^{n}Poission\left(v_{c_i}^{\left(t\right)}{\lambda }_{p_j}^{\left(t\right)}\right)\#\end{array}$$ (3)

$\begin{array}{c}{\mathrm{N}}_{{\mathrm{E}}_{\mathrm{c}\mathrm{i}}\to {\mathrm{I}}_{\mathrm{c}\mathrm{i}}}^{\left(\mathrm{t}\right)}Binomial({\mathrm{E}}_{{\mathrm{c}}_{\mathrm{i}}}^{\left(\mathrm{t}\right)},1/{\mathrm{\delta }}_{\mathrm{E}})\end{array}$(4)$\begin{array}{c}{\mathrm{N}}_{{\mathrm{I}}_{\mathrm{c}\mathrm{i}}\to {\mathrm{R}}_{\mathrm{c}\mathrm{i}}}^{\left(\mathrm{t}\right)}Binomial({\mathrm{I}}_{{\mathrm{c}}_{\mathrm{i}}}^{\left(\mathrm{t}\right)},1/{\mathrm{\delta }}_{\mathrm{I}})\end{array}$(5).

$N_{S_{\mathit{ci}}\to E_{\mathit{ci}}}^{\left(t\right)}$: the number of new exposures of CBG $c_i$ at hour $\text{t}$.

${\mathit{CBG}}_{S_{\mathit{ci}}\to E_{\mathit{ci}}}^{\left(t\right)}$: new exposures occur in CBG $c_i$ at hour $\text{t}$. $\mathrm{B}\mathrm{i}\mathrm{n}\mathrm{o}\mathrm{m}\mathrm{i}\mathrm{a}\mathrm{l}\left({\mathrm{S}}_{{\mathrm{c}}_{\mathrm{i}}}^{\left(\mathrm{t}\right)},{\mathrm{\lambda }}_{{\mathrm{c}}_{\mathrm{i}}}^{\left(\mathrm{t}\right)}\right)$ means the susceptible people $S_{c_i}^{\left(t\right)}$ have a probability of ${\lambda }_{c_i}^{\left(t\right)}$ to be exposed.

${\lambda }_{c_i}^{\left(t\right)}$: transmission rate of CBG $c_i$ at hour $\text{t}$. ${\lambda }_{c_i}^{\left(t\right)}=\left(1+r_{\mathrm{\beta }}\frac{t}{T}\right){\beta }_{\mathit{base}}\frac{I_{c_i}^{\left(t\right)}}{N_{c_i}}$, it is subject to a changeable coefficient $(1+r_{\mathrm{\beta }}\frac{t}{T}){\beta }_{\mathit{base}}$ and the proportion of infectious people in $c_i$, i.e., $\frac{I_{c_i}^{\left(t\right)}}{N_{c_i}}$. The denotation of ${\mathrm{\beta }}_{\mathit{base}}$ is the base transmission rate, shared with all CBGs, $T$ is the simulation period; $r_{\mathrm{\beta }}$ is the slope of a linear function to capture the dynamic of ${\mathrm{\beta }}_{\mathit{base}}$. For example, if ${\mathrm{\beta }}_{\mathit{base}}$ does not change with $t$, $r_{\mathrm{\beta }}=0$; if ${\mathrm{\beta }}_{\mathit{base}}$ increases with $t$, $r_{\mathrm{\beta }}>0$, and vice versa.

${\mathit{POI}}_{S_{\mathit{ci}}\to E_{\mathit{ci}}}^{\left(t\right)}$: new exposures of visitors from CBG $c_i$ when they visit POIs at hour $\text{t}$. There are $\text{n}$ POIs in total in an MSA.

$v_{c_i}^{\left(t\right)}$: the susceptible visitor number from CBG $c_i$. $v_{c_i}^{\left(t\right)}=\frac{S_{c_i}^{\left(t\right)}}{N_{c_i}}{\mathrm{w}}_{\mathit{ij}}^{\left(\mathrm{t}\right)}$, where $\frac{S_{c_i}^{\left(t\right)}}{N_{c_i}}$ is the susceptible fraction of the population in CBG $c_i$, ${\mathrm{w}}_{\mathit{ij}}^{\left(\mathrm{t}\right)}$ is the visitor count from $c_i$ to POI $p_j$ at hour $\text{t}$.

${\lambda }_{p_j}^{\left(t\right)}$: the transmission rate of POI $p_j$ at hour $\text{t}$. The new exposures among those visitors follow distribution as $Binomial\left(v_{c_i}^{\left(t\right)}{,\lambda }_{p_j}^{\left(t\right)}\right)\approx Poission\left(v_{c_i}^{\left(t\right)}{\lambda }_{p_j}^{\left(t\right)}\right)$. ${\mathrm{\lambda }}_{p_j}^{\left(t\right)}:=\mathrm{\psi }{d}_{\mathit{pj}}^2\frac{I_{p_j}^{\left(t\right)}}{a_{p_j}}$, where $\psi$ is the base transmission rate shared with all POIs, $d_{\mathit{pj}}$ is the median dwelling time in POI $p_j$, $\frac{I_{p_j}^{\left(t\right)}}{a_{p_j}}$ is the density of infectious visitors in POI $p_j$, $I_{p_j}^{\left(t\right)}$ is the number of infectious visitors, and $a_{p_j}$ is the area of $p_j$. $I_{p_j}^{\left(t\right)}={\sum }_{i=1}^m\frac{I_{c_i}^{\left(t\right)}}{N_{c_i}}{w}_{\mathit{ij}}^{\left(t\right)}$, $m$ is the CBGs count.

$N_{E_{\mathit{ci}}\to I_{\mathit{ci}}}^{\left(t\right)}$: the number of infected individuals in $c_i$ at hour $\text{t}$. The model assumes that all Exposed individuals will become Infectious during the latency period.

$${\mathrm{\delta }}_{\mathrm{E}}:\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}$$

$N_{I_{\mathit{ci}}\to R_{\mathit{ci}}}^{\left(t\right)}$: the number of removed individuals in $c_i$ at hour $\text{t}$. The model assumes that all Infectious individuals will be Removed.

${\delta }_I$: infectious period.

In fact, ${\beta }_{\mathit{base}}\text{and}\psi$ are scale factors for the actual transmission rates; we call them base transmission rates for an intuitive understanding in this paper. The initialization of $S_{c_i}^{\left(0\right)},E_{c_i}^{\left(0\right)},I_{c_i}^{\left(0\right)}$, and $R_{c_i}^{\left(0\right)}$ were according to NYT COVID-19 data: all $c_i$ in the same county were assigned values according to the confirmed cases and population proportion to the county. The new exposures occurred in CBG $\mathit{ci}$ (${\mathit{CBG}}_{S_{\mathit{ci}}\to E_{\mathit{ci}}}^{\left(0\right)}$) equate COVID-19 infections ($I_{c_i}^{\left({\delta }_E\right)}$) at hour ${\delta }_E$. $I_{c_i}^{\left({\delta }_E\right)}$ can be derived from the daily county level confirmed cases (NYT COVID-19), confirmed lag (${\delta }_c$), detected rate of infection ($r_c$, rate of confirmed cases to the actual infections), and CBG population (ACS 2019); we assume the CBG infection rate is the same as its home county in the beginning of the simulation, so the $I_{c_i}^{\left({\delta }_E\right)}$ is proportionate to county confirmed cases. The model also assumes the daily case occurred evenly within 24 h. Thus, the CBG new exposures ${\mathit{CBG}}_{S_{\mathit{ci}}\to E_{\mathit{ci}}}^{\left(0\right)}$ is 1/24 of the CBG daily infections on the day of ${\delta }_E$/24. Therefore, the ${\lambda }_{c_i}^{\left(0\right)}$ in the same county had the same value. Fig. A1 shows in more detail how the most critical value $E_{c_i}^{\left(t\right)}$ is estimated.

Fig. A1.

Estimation of exposure $E_{c_i}^{\left(t\right)}$. The length of the color bars indicates the mean latency period (${\delta }_E$); the model assumes that all exposure will become infectious during the ${\delta }_E$. The exposure in CBG $\mathit{ci}$ ($E_{c_i}^{\left(t\right)}$) is the sum of new exposures in the previous ${\delta }_E$hours; note the figure ignores the infections that occurred in points of interest (POIs) for simplification. $N_{S_{\mathit{ci}}\to E_{\mathit{ci}}}^{\left(t\right)}$, $N_{S_{\mathit{ci}}\to E_{\mathit{ci}}}^{\left(t-1\right)}$, $...,$and, $N_{S_{\mathit{ci}}\to E_{\mathit{ci}}}^{\left(t-{\delta }_E\right)}$ are the new exposures in hour $t$, $t-1$, …, and ${\delta }_E$, respectively. In the model initialization, we let $E_{c_i}^{\left(0\right)}=I_{c_i}^{\left({\delta }_E\right)}·{\delta }_E$.

Recall the model assumes that exposed individuals become infectious during the latency period (${\delta }_E$ hours), so the exposure number is the infection number ${\delta }_E$ hours later. To include uncertainty, all initial and new values of the four compositions in SEIR models were generated 30 times following Poisson or Binomial distribution. Essentially, the model ran 30 stochastic realizations of the binomial and Poisson distribution, and averaged the outputs as the final number.

In summary, there are three parameters in the simulation need to estimate: (1) ${\beta }_{\mathit{base}}$, base transmission rate, shared with all CBGs; (2) $\psi$, the base transmission rate shared with all POIs; and (3) $r_{\mathrm{\beta }}$, the slope of the linear function to capture the dynamic of ${\beta }_{\mathit{base}}$. The model used grid search to determine the optimal values of free parameters. We assumed that $r_{\mathrm{\beta }}$ would not change dramatically, so we set its range to [-0.5, 1]. Chang et al. (2021a) provide plausible ranges of ${\beta }_{\mathit{base}}$ and $\psi$ for the first COVID-19 wave of 10 metropolitan areas in the US empirically; however, these ranges did not fit the second wave in SC in our experiments, so we adjusted them until the simulation generated results fitting to the reality. Specifically, a grid search used 1050 combinations of 10, 15, and 7 possible values with equal intervals for ${\beta }_{\mathit{base}}$, $\psi$ and $r_{\mathrm{\beta }}$, respectively. The parameter set whose simulation result was mostly close to the actual confirmed cases from NYT COVID-19 data was selected as the optimal model. Each MSA was simulated respectively. A parameter table for the final model can be found in Table A1 in Appendix A.

2.3. Evaluation metrics

The evaluation of the simulation contains three metrics: total case error, RMSE of the daily case, and the error of infection rate by race (i.e., the White and Black). The total case error is the ratio of the difference between the simulated case and the NYT COVID-19 case to the latter. The simulated daily CBG cases were aggregated into MSA-level and compared with the NYT COVID-19 data to compute RMSE. The race infection rates were compared with SCDHEC COVID-19 data.

Equations (6), (7) were used to compute the RMSE of the daily case. The simulated number of confirmed COVID-19 infections, i.e., $N_{\mathit{cases}}^{\left(dayd\right)}$, can be estimated by Equation (6) where $r_c$ is the detected rate of infected individuals, $m$ is the total number of CBG, and ${\delta }_c$ is confirming lag, set to 168 h, or 7 days (Li et al., 2020). $D$ in Equation (7) is the number of days in the simulation period, and ${\widehat{N}}_{\mathit{cases}}^{\left(dayd\right)}$ is the actual confirmed cases from NYT COVID-19 data. $N_{\mathit{cases}}^{\left(dayd\right)}$ is the daily county-level aggregation of simulated infections in each CBG. The ground truth is ${\widehat{N}}_{\mathit{cases}}^{\left(dayd\right)}$, which was smoothed using a 14-days window to eliminate the confirmed cases fluctuation due to delay or correction. The simulation result of the smallest RMSE is preferred.

$$\begin{array}{c}{N}_{\mathit{cases}}^{\left(dayd\right)}=r_c{\sum }_{i=1}^m{\sum }_{t=24\left(d-1\right)+1-{\delta }_c}^{24d-{\delta }_c}{N}_{E_{\mathit{ci}}\to I_{\mathit{ci}}}^{\left(t\right)}\#\end{array}$$ (6)

$$\begin{array}{c}\mathit{RMSE}=\sqrt{\frac{1}{D}{\sum }_{d=1}^D\left(N_{\mathit{cases}}^{\left(dayd\right)}-{\widehat{N}}_{\mathit{cases}}^{\left(dayd\right)}\right)}\#\end{array}$$ (7)

The latency period ${\delta }_E$ was set to 96 h (Chang et al., 2021a; Lauer et al., 2020), ${\delta }_I$ was 84 h (Cdc, 2021, Li et al., 2020), and $r_c$ was empirically set to 65%. CDC (2021) has an estimation as 25% for $r_c$ from February 2020 to September 2021 but this value contributed divergent results in our study period; we then tested a group of values and found that 65% could make the model convergent.

White and Black were the top 2 races in the study area, taking up 67% and 25% of the population. We estimated the White and Black cases using the product of simulated cases and race ratios of CBGs, then aggregated them into the MSA level. The race infection rate was the quotient of the race case divided by the race population. SCDHEC released COVID-19 cases by race but left about 20% of the total cases as unknown; we redistributed these unknown cases into race groups according to ratios of the known cases among races.

2.4. Transmission pattern analysis

After obtaining the optimal parameter set, its associated simulation results, including the hourly transmission rate and infection counts of each neighborhood and POI category, were extracted for transmission pattern analysis. We computed the mean transmission rate and the sum of infection counts of each place and then compared CBGs and POI categories, respectively. The CBGs and POI categories having transmission rates and infection counts at the top ranks were identified as COVID-19 hot spots.

2.4.1. Transmission rate analysis

This analysis focuses on the transmission rates of CBGs and POIs was applied to three MSAs, respectively. All hourly transmission rates, i.e., ${\lambda }_{c_i}^{\left(t\right)}$ and ${\lambda }_{p_j}^{\left(t\right)}$ in the 30 stochastic realizations, were averaged as ${\overline{\lambda }}_{c_i}$ and ${\overline{\lambda }}_{p_j}$, indicating the hourly mean COVID-19 transmission rates for CBG $c_i$ and POI $p_j$. Next, the mean transmission rate of each POI category, ${\overline{\lambda }}_{p_K}$, was calculated by averaging the ${\overline{\lambda }}_{p_j}$ values of all POIs in this category. ${\overline{\lambda }}_{p_K}$ reflects the infecting risk when visiting the $K$ category POI. In this study, the POI attribute of the top-category in NAICS was applied as the POI category (81 categories in this study). Finally, we mapped the distribution of ${\overline{\lambda }}_{c_i}$ and compared the ${\overline{\lambda }}_{p_K}$.

2.4.2. Infection count analysis

Infection count analysis investigated the distribution pattern of the number of infected individuals among CBGs and POI categories, respectively. The first step is to sum the hourly infection counts in the study period. Since the model assumes that all Exposed individuals will become Infectious, the hourly exposed counts of each place were summed up as the infection counts, denoted as ${\mathit{CBG}}_{S_{\mathit{ci}}\to E_{\mathit{ci}}}$ and ${\mathit{POI}}_{S_{\mathit{pj}}\to E_{\mathit{pj}}}$. The former reflects the infection count that occurred in CBG $c_i$, and the latter indicates the infection count occurred in POI $p_j$. $\mathrm{P}\mathrm{O}{I}_{S_{\mathit{pj}}\to E_{\mathit{pj}}}={\sum }_{t=0}^{24\left(d-1\right)}{\sum }_{c=1}^{m}Poission\left(v_{c_i}^{\left(t\right)}{\mathrm{\lambda }}_{p_j}^{\left(t\right)}\right)$. For each category, we have ${\mathit{POI}}_{S_K\to E_K}$ to present the sum of POIs infections in $K$ category. According to Equation (1), for the residents in CBG $c_i$, we can have $N_{S_{\mathit{ci}}\to E_{\mathit{ci}}}={\mathit{CBG}}_{S_{\mathit{ci}}\to E_{\mathit{ci}}}{+POI}_{S_{\mathit{ci}}\to E_{\mathit{ci}}}$, where $N_{S_{\mathit{ci}}\to E_{\mathit{ci}}}$ is the total infection count, and ${\mathit{POI}}_{S_{\mathit{ci}}\to E_{\mathit{ci}}}$ is the total infection count that occurred in POIs. Infection count analysis was applied to the three MSAs respectively, and a comparison of the proportion of ${\mathit{POI}}_{S_K\to E_K}$ was conducted. Thus, we can observe whether MSAs have different patterns of infections via POIs.

2.4.3. Correlation analysis

We conducted two Pearson’s correlation analyses to identify the association between socioeconomic status variables and COVID-19 spreading at the CBG level and POI level, respectively. At the CBG level, the correlation between the mean CBG transmission rate (${\overline{\lambda }}_{c_i}$) and the following variables were analyzed:

(1) Demographic backgrounds drived from ACS 2019, including population and proportions of the senior, White, Black, Hispanic race, and Asian race.

(2) Social Determinants of Health, containing the median household income, per capita building area, and proportions of poverty (population living below the federal poverty threshold), high-school diploma attainment (population of 25 years and over with the highest diploma from a high school), unemployed (unemployed civilian labor force), uninsured (population without health insurance), living with severe rent burden (household whose rent large than 30% of income), and living with severe mortgage burden (household whose mortgage large than 30% of income).

(3) The building area, computed from footprints generated from satellite images by a Microsoft research team (Microsoft, 2022) ; only residential buildings are kept according to OpenStreetMap land use data (OpenStreetMap, 2022) and the SafeGraph Core POI dataset. The other variables came from ACS 2019.

(4) POI characteristics, which consist of the mean transmission rate of visited POIs, per capita visit count to POIs, and infection count from POIs (${\mathit{POI}}_{S_{\mathit{ci}}\to E_{\mathit{ci}}}$), calculating from the SafeGraph datasets and simulated results.

At the POI level, we analyzed the correlation between the POI transmission rate (${\overline{\lambda }}_{p_j}$) and the POI area, total visits, and infection count in POIs (${\mathit{POI}}_{S_{\mathit{pj}}\to E_{\mathit{pj}}}$). We removed the top 5% and bottom 5% values (outliers) of variables to keep the correlation analyses robust and ensure that the results reflect the correlation of the most values.

3. Results

3.1. Simulation and evaluation results

We extended the search range by running simulation several time before focalizing to the current range (Table A2). In the adopted range, there were 2–4 fitted models for each MSA, and their parameter sets are close. The number of cases from the simulation model successfully converged with the actual confirmed cases with small RMSEs. We report and analyze the results from the model with the smallest RMSE in this paper.

As illustrated in Fig. 3 , the simulated daily cases for each MSA (Greenville, Columbia, and Charleston) were close to the smoothed confirmed cases from NYT COVID-19 data; RMSEs were within 10% of the smoothed confirmed cases for all three MSAs (Table 1 ). The total simulated confirmed cases fit the actual cases within a minor error in the simulation period for all three MSAs: Greenville (-5%), Columbia (-2%), and Charleston (-7%) (Table 1). Both actual and simulated infections increased with the increase of the MSA population. During the study period, the number of POI visits decreased Sundays and dropped remarkably on Christmas day (Dec. 25), but the weekday mobility trend was relatively stable except for the holiday week of Merry Christmas and New Year (Fig. A2). Such a stable mobility pattern in the study period met the model assumptions, i.e., linearly changing and static base transmission rate in CBGs and POIs, respectively. The minor RMSEs showed that the simulation was valid in the three MSAs with a population of about 0.8 million; previous studies (Chang et al., 2021b, Chang et al., 2021a) have not tested this population range and have expressed concern on smaller MSAs. This study fills the gap.

Fig. 3.

Simulation results of the daily cases and the RMSEs for the three MSAs. Shaded areas denote the 2.5th and 97.5th percentiles of the simulated daily confirmed cases from 30 stochastic realizations. SC: South Carolina; RMSEs: Root mean square roots; MSAs: Metropolitan statistical areas.

Table 1.

Simulation and evaluation results.

	Greenville	Columbia	Charleston
Population	895,942	824,278	774,508
CBG count	510	479	396
POI count	7,871	6,550	6,158
POI visit count	5,397,442	4,435,937	3,825,345
Confirmed cases	37,064	25,481	21,204
Simulated confirmed cases	35,166	24,760	19,702
Total case error	−5%	−2%	−7%
RMSE of daily case	67	54	47

CBG: Census block group; POI: Point of interest; RMSEs: Root mean square root.

Fig. A2.

Number of visits was in a stable pattern during the study period. Daily POI visits have a weekly fluctuation pattern with a decrease on Sundays (troughs), and dropped remarkably on Christmas day (Dec. 25, the lowest trough). POI: Point of interest.

Table 2 shows the error of infection rate of the White and Black between the SCDHEC COVID-19 data and simulated results. In the study period, the SCDHEC records show that the White and Black have similar chances of getting infected (3.3% vs. 3.1%), and the simulated results accurately reflect this pattern, showing that the estimated race infection rates have minor gaps (0.1% – 0.4%) to SCDHEC records in each MSA. Despite the absence of race consideration in the model parameters and input data, the simulation results still well matched the actual infection records by race. Such consistency was first reported in the literature to our knowledge, and it supports the simulation validity in this study.

Table 2.

Infection rate error of the White and Black.

MSA	White			Black
	SCDHEC	Simulated	Error	SCDHEC	Simulated	Error
Charleston	2.8%	2.6%	−0.2%	2.6%	2.5%	−0.1%
Columbia	3.0%	3.2%	0.2%	2.9%	2.8%	−0.1%
Greenville	3.8%	3.9%	0.1%	4.3%	3.9%	−0.4%
Total	3.3%	3.3%	0.0%	3.1%	2.9%	−0.2%

SCDHEC: South Carolina Department of Health and Environmental Control.

3.2. Transmission rates distribution in CBGs

Fig. 4 shows the mean transmission rates (${\overline{\mathrm{\lambda }}}_{{\mathrm{c}}_{\mathrm{i}}}$) at the CBG level of the three MSAs. It reveals that the CBGs with high mean transmission rates are mostly scattered in Pickens County in Greenville MSA and Lexington County in Columbia MSA. The mean transmission rates show clear boundaries among countries due to the identical initialization inside a county. However, spatial patterns of the transmission rate within each county are revealed as that some CBGs have higher or low transmission rates than their neighbors. For example, there is a clear hot spot in Pickens County (Greenville MSA) and a cold spot in Charleston County (Charleston MSA). Fig. 4 reveals that residents face different infection risks among neighborhoods. Most CBGs in Greenville MSA had relatively high transmission rates, and Charleston MSA had low rates. Clearly, mean transmission rates varied among CBGs.

Fig. 4.

Mean transmission rates (${\overline{\mathrm{\lambda }}}_{{\mathrm{c}}_{\mathrm{i}}}$) of CBGs. A high ${\overline{\lambda }}_{c_i}$ means a person has a high probability of infection in CBG $c_i$ in an hour. (Blank areas are water bodies or military areas, which were excluded from this study). CBG: Census block group.

Fig. 5 presents the trends of simulated CBG transmission rates $\left({\lambda }_{c_i}^{\left(t\right)}\right)$ of the top 15 populous CBGs of each MSA, whichfurther explains the stableness of the CBGs transmission rates among counties and the variance inside the same county. Most of CBGs experienced a peak and then decreased to a lower level than the beginning. The overall trends matched the wave of confirmed cases (Fig. 3). The CBG transmission rates ${\lambda }_{c_i}^{\left(t\right)}$ were initialed using the county level confirmed cases, so CBGs in the same county had the same ${\lambda }_{c_i}^{\left(0\right)}$; CBGs in counties having high infection rates would have high ${\lambda }_{c_i}^{\left(0\right)}$. Although the model kept altering ${\lambda }_{c_i}^{\left(t\right)}$ in simulation, but mean transmission rates (${\overline{\mathrm{\lambda }}}_{{\mathrm{c}}_{\mathrm{i}}}$) from the same county trended to cluster to ${\lambda }_{c_i}^{\left(0\right)}$. Thus, ${\overline{\lambda }}_{c_i}$ in the same county CBGs in Fig. 4 seems stick to the identical initial value since they keep similar altering paces (decrease after a peak), so it is expected that a high ${\lambda }_{c_i}^{\left(0\right)}$ will still have a high ${\overline{\lambda }}_{c_i}$ and vice versa.

Fig. 5.

The transmission rates of the top 15 CBGs in three MSAs. Each line presents a CBG. The overall trends matched the confirmed case curve in Fig. 3.

The ${\lambda }_{c_i}^{\left(t\right)}$ variance within the same county resulted from its definition: ${\lambda }_{c_i}^{\left(t\right)}=\left(1+r_{\mathrm{\beta }}t\right){\beta }_{\mathit{base}}\frac{I_{c_i}^{\left(t\right)}}{N_{c_i}}$ (Section 2.2); it is subject to the linear changing coefficient $r_{\mathrm{\beta }}$ and the proportion of the infectious people $\frac{I_{c_i}^{\left(t\right)}}{N_{c_i}}$, while $I_{c_i}^{\left(t\right)}$ was dependent on the initial status of four SEIR components, mobility matrix (${\mathrm{w}}_{\mathit{ij}}^{\left(\mathrm{t}\right)}$), and POI characteristics (area $a_{p_j}$, median dwelling time $d_{\mathit{pj}}$, and base transmission rate $\psi$). The complex combination of appropriate values of the above variables let ${\lambda }_{c_i}^{\left(t\right)}$ meet the curve of the lagged confirmed cases, validating the model assumptions to some degree.

Further, the simulation period can be roughly divided into two stages according to the existence of these county clusters. In the first stage, i.e., before Jan. 10, 2021, ${\lambda }_{c_i}^{\left(t\right)}$ mostly kept the initial value with some growth, the initial status ($E_{c_i}^{\left(0\right)}$) imposed strong constraints to ${\lambda }_{c_i}^{\left(t\right)}$. In the second stage, the transmission rates of the selected CBGs converged to a similar range. This division raises interesting questions: To what degree, the initial values of CBG transmission rates ${\lambda }_{c_i}^{\left(0\right)}$ affect the simulation outputs? If the model assumptions and simulation are valid, which stage’s transmission rates are more reliable? More fine-grained and detailed data in CBG level are needed to answer these questions.

3.3. Transmission rates distribution in POI categories

Fig. 6 shows the mean transmission rates (${\overline{\mathrm{\lambda }}}_{p_j}$) of the top 15 POI categories of the three MSAs. A high ${\overline{\mathrm{\lambda }}}_{p_j}$means a person has a high probability of being infected in POI $p_j$ in a hour. The most infectious POI categories were Support Activities for Road Transportation (e.g., vehicle roadside assistance or repairing), Specialized Freight Trucking (e.g., goods moving), and Home Health Care Services. Drinking Places (Alcoholic Beverages) and General Medical Surgical Hospitals also had high transmission rates. The differences between POI categories are mild: the first one’s transmission rate is about 1.6 times the fifteenth. Table A3 lists the complete sub-categories of the mentioned top categories in the paper; readers can check these categories for a better understanding.

Fig. 6.

Mean transmission rates (${\overline{\mathrm{\lambda }}}_{p_j}$) of top 15 POI categories. A high ${\overline{\mathrm{\lambda }}}_{p_j}$ means a person has a high probability of infection in POI $p_j$. POI: Point of interest.

However, while looking into each MSA, POI transmission rates demonstrated different patterns. Overall, Charleston had the height transmission rates, reflecting its developed shipping and traveling business. Charleston Port ranked 27th in the US by water cargo tonnage (US DOT, 2022), and is one of the top tourism cities in the US (R. Chang, 2022). It was expected that Charleston would show a different mobility and COVID-19 transmission pattern. Most of the top 15 POI categories in Charleston have higher transmission rates (Fig. 7 ), especially those related to the cargo shipping and tourism industry, such as Support Activities for Road Transportation, Specialized Freight Trucking, Drinking Places (Alcoholic Beverages), Traveler Accommodation, and Restaurants and Other Eating Places. Interestingly, not a category in the top 15 shares a similar transmission rate in the three MSAs, meaning COVID-19 susceptible groups in different MSAs need to avoid specific POI categories rather than following prevention policies of other MSAs.

Fig. 7.

Transmission rates of top-15 POI categories among the three MSAs. POI: Point of interest; MSAs: Metropolitan statistical areas.

3.4. Infection counts distribution in CBGs

Similar to the CBG transmission rates, the simulated infection counts were not evenly distributed among CBGs (Fig. 8 ). A few CBGs in central counties of MSAs had remarkably high infection counts; the peripheral counties or areas of MSAs had low infections. On average, a CBG had 88 COVID-19 infections in the study period. A few CBGs had dramatically higher infections than others, while most CBGs had low infections<100, presenting a long-tail distribution (Fig. A3). In general, the infection counts were proportional to the population. Table 3 shows the simulated infection counts that occurred in CBGs and POIs, i.e., the sum of $N_{S_{\mathit{ci}}\to E_{\mathit{ci}}}$, ${\mathit{CBG}}_{S_{\mathit{ci}}\to E_{\mathit{ci}}}$, and ${\mathit{POI}}_{S_{\mathit{ci}}\to E_{\mathit{ci}}}$ of each MSA in the study period. In the three MSAs, most simulated infections occurred in CBGs (86%). Charleston MSA had the highest POI infection count proportion (18%). We noticed that simulated cased occurred in CBGs and POIs show strong correlation with population ($r>0.84,p<0.001$). Generally, the model distributed most new case to CBGs, indicating that in this stage POI disease transmission may not play a critical role.

Fig. 8.

Infection counts distribution among CBGs.

Fig. A3.

Histogram of CBG infection counts. Most CBGs have<100 COVID-19 infections that occurred in the simulation; a few CBGs have much higher infections. CBG: Census block group.

Table 3.

Simulated infection counts in CBGs and POIs.

	CBG (proportion)	POI (proportion)	Subtotal
Charleston	24,792 (82%)	5,519 (18%)	30,311
Columbia	33,556 (88%)	4,536 (12%)	38,092
Greenville	47,444 (88%)	6,658 (12%)	54,102
Total	105,792 (86%)	16,713 (14%)	122,505

CBG: Census block group; POI: Point of interest.

There are two potential reasons why the majority of simulated cases were concentrated in CBGs from a data perspective: 1) Incomplete POI and visit coverage. Each MSA contains 6,000 – 8,000 POIs; however, SafeGraph’s POI database increased 254% from Jul. 2021 to Jul. 2022 (SafeGraph, 2022a), meaning their previous POIs cover fewer places. Also, the sampling rate of visitation is not verified and may miss visits. Thus, the SafeGraph data might under-represent the mobility intensity. 2) Insufficient parameter search range. It is possible that there are several possible parameter sets (${\beta }_{\mathit{base}}$, $\psi$, and $r_{\mathrm{\beta }}$) can achieve similar results (S. Chang, Pierson, et al., 2021; S. Chang, Wilson, et al., 2021). Although the selected parameter set obtained the lowest RMSE, the search range may miss other possible ones whose base transmission rates for CBGs (${\beta }_{\mathit{base}})$ and POIs ($\psi )$ are more fit the reality. However, we have no available data to verify or calibrate the base transmission rates, CBG cases and POI cases directly. The total daily simulated cases occurred in POIs (Fig. A4) also have the similar trend with the SCDHEC COVID-19 confirmed cases. We conclude that the parameter set fits the aggregated COVID-19 cases, but not necessary fits every aspect of reality.

Fig. A4.

The daily total simulated cases in POIs. The weekly smoothed trend is similar to the total simulated cases (CBG + POI, see Fig. 3). Note the POIs cases shown include the visitors outside the three MSAs.

3.5. Infection counts in POI categories

Fig. 9 shows the top 15 categories (i.e., top-category in NAICS) that occurred most COVID-19 infections in the simulation; most categories were the commonly visited categories, such as restaurants. It is noteworthy that the Elementary and Secondary Schools category ranked second position, following the Restaurants and Other Eating Places. This trend was consistent with the official confirmed case data (SCDHEC, 2022) which indicates that during the study period, the highest proportion of COVID-19 infections in South Carolina was among children and teenagers (<20 years old), accounting for 18.3% of total cases. Other Amusement and Recreation Industries (e.g., fitness centers, golf clubs) and Religious Organizations ranked at third and fourth place respectively. This distribution confirm that the effectiveness of conventional prevention policies, such as closing schools and limiting restaurant capacities.

Fig. 9.

Infection counts from the top 15 POI categories of three MSAs.

When zooming into the MSA level, the infection counts show different patterns. For a better comparison between MSAs, POI category ratios were computed, which is the ratio of the infection count of a category to the total infection count of all categories within an MSA. Although Restaurants and Other Eating Places and Elementary and Secondary Schools still ranked in the first two positions, their category ratios vary among MSAs (Fig. 10 ). For example, the category ratio of Restaurants and Other Eating Places was slightly more than Elementary and Secondary Schools (23% vs. 21%) in Greenville, but the difference between these two categories is much larger in Charleston (30% vs. 8%). Differentiae contribution of the same POI categories among MSAs suggesting that prevention policies should be customized locally such as at MSA level. For example, Elementary and Secondary Schools can keep open in Columbia and Charleston but not Greenville.

Fig. 10.

Infection ratios of the top 15 POI categories among three MSAs. (category ratio: the ratio of the infection count of a category to the total infection count of all categories). POIs: Points of interest; MSAs: Metropolitan statistical areas.

Similar to the findings in Chang et al. (2021a)'s simulation of large MSAs, the infection counts of POIs concentrated on top POI categories. For example, the top-5 categories across the tree MSAs took up 53% of infection counts, and the top 15% POIs consisted of 79% of infections. This concentration of infections may be leveraged to design targeted prevention policies such as closing only the hotspots within a category rather than the entire category to minimize the economic impact of infection diseases.

3.6. Correlation analysis

Table 4 presents the correlation analysis results with the mean CBG transmission rates (${\overline{\lambda }}_{c_i}$). Several variables show significant correlations with CBG transmission rates, although the pattern varies among MSAs. For example, ${\overline{\lambda }}_{c_i}$ was significantly associated with population in Greenville ($r=0.264,p<0.001$) and Columbia ($r=0.133,p<0.01$) but not in Charleston. ${\overline{\lambda }}_{c_i}$ showed opposite associations with the mean transmission rate of visited POIs in Greenville ($r=-0.124,p<0.01$) compared with Columbia ($r=0.429,p<0.001$) and Charleston ($r=0.403,p<0.001$). Per capita visit count to POIs had a positive correlation in Columbia ($r=0.425,p<0.001$) and Charleston ($r=0.174,p<0.001$), but not in Greenville. Per capita infection counts from POIs also had high positive correlations in Columbia ($r=0.442,p<0.001$) and Charleston ($r=0.344,p<0.001$) but demonstrated a weak negative correlation in Greenville ($r=-0.091,p<0.05$). The CBG capita building area showed a negative correlation with CBG transmission rate in Greenville and Charleston ($r<=-0.137,p<0.001$).,

Table 4.

CBG level variables and their correlation with CBG transmission rates. The descriptive statistics of the variables are listed in Table A4.

Variables		Pearson correlation coefficient (r)
		Greenville	Greenville	Greenville
Demographic background	Population	0.264***	0.133**	0.091
	%Senior	−0.134**	0.081	−0.080
	%White	0.022	0.487***	0.102*
	%Black	−0.092*	−0.486***	−0.106*
	%Hispanic	0. 117*	−0.011	−0.116*
	%Asian	0.135*	−0.075	−0.084
	%Poverty	−0.200***	−0.167***	−0.013
	% Less or equal high school education	−0.196***	−0.021	−0.144**
Social Determinants of Health	Median household income	0.221***	0.135**	0.103*
	% Unemployed	−0.143**	−0.185***	0.002
	% Uninsured	−0.011	−0.128**	−0.189***
	% Living with severe rent burden	0.025	−0.035	0.017
	% Living with severe mortgage burden	−0.022	−0.169***	0.026
	Per capita building area (m2)	−0.278***	0.040	−0.137**
POI characteristic	Mean transmission rate of visited POIs	−0.124**	0.429***	0.403***
	Per capita visit count to POIs	−0.078	0.425***	0.174***
	Per capita infection count from POIs	−0.091*	0.442***	0.344***

Note: * p < 0.05, ** p < 0.01, ***p < 0.001; CBG: Census block group; POIs: Points of interest.

In Columbia, ${\overline{\lambda }}_{c_i}$ showed a much stronger positive correlation with the proportion of the White ($r=0.487,p<0.001$), while Greenville and Charleston did not present significant associations. Since the White is the dominant race in quantity and the Black was the largest minority in the study area, the correlation direction between ${\overline{\lambda }}_{c_i}$ and the Black proportion is the opposite of the White. The median household income had a positive correlation with ${\overline{\lambda }}_{c_i}$ across all three MSAs (Greenville, $r=$ 0.221, $p<0.001$; Columbia, $r=$ 0.135 $,p<0.01$; Charleston, $r=0.103,p<0.05$). The proportion of households living with severe mortgage burdens tended to have a negative correlation with ${\overline{\lambda }}_{c_i}$ ($r=-0.169,p<0.001$) in Columbia, but no significant association was found in Greenville and Charleston. The per capita building area shows negative correlations with ${\overline{\lambda }}_{c_i}$ in Greenville ($r=-0.278,p<0.001$) and Charleston ($r=-0.137,p<0.01$). The scatter plots of CBG transmission rates and three selected variables (median household income, per capita visit count to POIs, and mean transmission rate of visited POIs) further revealed the varying correlation patterns among the three MSAs (Fig. A5).

Fig. A5.

CBG transmission rates demonstrated different patterns among MSAs; the solid lines are the trend lines of the point cluster. (a) At the same CBG income level, Greenville had high transmission rates, and Charleston had low rates. (b) Charleston CBGs had fewer per capita visit counts and low transmission rates than Greenville and Columbia. (c) Greenville CBGs had high transmission rates, although their mean visited POI transmission rates were low; Charleston showed the opposite pattern. CBG: Census block group; MSA: Metropolitan statistical areas.

Although the correlation between CBG transmission rates and demographic background, Social Determinants of Health, and POI characteristic presented differently among MSAs, there were some shared aspects can be highlighted: (1) the ratio of Black had negative correlation; (2) the median household income, visited POIs’s transmission rate,and per capita infection count from POIs had positive correlation.

Regarding POIs, we analyzed the correlation between their transmission rate (${\overline{\lambda }}_{p_j}$) and areas, total visits, and simulated cases (${\mathit{POI}}_{S_{\mathit{pj}}\to E_{\mathit{pj}}}$). The result is shown in Table 5 . The POI transmission rates had negative correlations with the POI areas ($r<=-0.137,p<0.001$) and a positive correlation with visits to them ($r>=0.127,p<0.001$)), as the model assumes crowded and popular POIs lead to the high transmission rate. The infection counts from POIs had a strong correlation with POI transmission rates ($r>0.84,p<0.001$). All three investigated MSAs shared similar patterns. The results also indicated crowded and popular places had higher infectious risks and infections.

Table 5.

Correlation analysis results of transmission rates at the POI level. The descriptive statistics of the variables are listed inTable A5.

Variables	Pearson correlation coefficient (r)
	Greenville	Columbia	Charleston
POI area (m2)	−0.137***	−0.141***	−0.167***
POI visits	0.127***	0.127***	0.152***
POI simulated cases	0.845***	0.847***	0.868***

Note: *p < 0.05, ** p < 0.01, ***p < 0.001; POI: Point of interest.

However, POIs with high visits and transmission rates did not necessarily have high infection counts and vice versa, although the mean POI transmission rate had a strong positive association with infections in POIs. These correlations and discrepancies were expected according to the model assumption in Equation (3), the POI transmission rate ${\lambda }_{p_j}^{\left(t\right)}$ is subject to the proportion of infectious visitors, mean dwell time, and area, while the simulated cases depend on the transmission rate ${\lambda }_{p_j}^{\left(t\right)}$, visitor count, and susceptible ratios of visitors’ home CBGs. Fig. 11 shows the POIs with more than 30 infections that occurred in the MSAs. These POIs mostly located in the urban area of MSAs. Appropriately utilizing this information can help local authorities to close hotspot POIs to reduce infection and notify highly susceptible individuals to avoid high-risk places. Fig. A6 demonstrates an example: two POIs, a middle school and a full-service restaurant, both had high transmission rates, but the middle school yielded higher infections due to the high visitor count. Such restaurants contributing fewer cases may not need to close during the pandemic, but the vulnerable groups should stay from those places with high transmission rates; on the other hand, school closures seem reasonable due to their high infections.

Fig. 11.

Spatial distribution of major POI spreaders in the three MSAs.

Fig. A6.

The transmission rate, visit count, and simulated cases were not necessarily synchronous, showed by two POIs in Charleston (a middle school and a full-service restaurant). The restaurant has less visits than the school, but has a close transmission rate and a lower simulated cases. Also, the school’s hourly transmission rates clearly show two visitor peak times (morning and afternoon) of weekdays and weekends.

4. Discussion

4.1. Applicability of the mobility-based simulation method

The simulation of infectious disease transmission requires appropriate and robust human mobility data. In recent years, fine-grained SafeGraph mobility datasets have been one of the most used datasets for mobility studies. Our simulation in SC demonstrated that medium-size MSAs (0.7 – 0.9 million residents, ranking from 60 to 74 in population among 384 MSAs) can still benefit from a relatively sparse mobility dataset. Previous studies mainly focus on MSAs of large populations. For example, Chang et al. (2021a) focused on the top 10 MSAs in the US, which have significantly larger populations, ranging from 7 to 27 times the size of the three MSAs examined in this study. This study demonstrated the feasibility of using mobility-based simulation methods on MSAs of about 0.8 million population with low total case errors and low RMSEs of daily cases. Moreover, the simulation results align with the infection rates among White and Black individuals recorded by SCDHEC (ground truth), providing further evidence of the accuracy of the simulations.

The model utilized in this study is data-driven and can accommodate digitalized pharmaceutical or non-pharmaceutical interventions, provided that they can be parameterized or have data proxies such as vaccination rate, mask-wearing proportion, and lockdowns (mobility decrease as proxy). In contrast, some non-pharmaceutical interventions, such as hand hygiene, are challenging to be considered in the simulation. While including additional data can enhance model accuracy, it may also hinder model generality if the data are not widely available. Furthermore, model debuggability and explainability may be impacted by the increased complexity. The current model uses grid search to pick the possible value combination of three free parameters. More parameters can be added, such as polynomial coefficients for non-linear changes of base CBG and POI base transmission rates. However, adding more parameters may increase computation exponentially. As a result, heuristic parameter searching is required when estimating additional parameters.

4.2. Insights into measures to curb COVID-19 spreading based on the simulation results

4.2.1. Effective control measures are needed to decrease disease transmission in neighborhoods

According to the simulation results, the infections that occurred in CBGs account for 86% of total cases, indicating that the disease control measures implemented at the neighborhood level might prevent COVID-19 transmission effectively. In January 2021, the restaurant restrictions in SC were lifted (McMaster, H., & Governor, S. C. O. of the, 2020), and schools were reopened (SC Department of Education, 2020). The surge of COVID-19 infections at the neighborhood level suggests that effective disease control measures tailored to high-risk geographic locations are needed, such as reducing parties and family gatherings or highlighting the importance of personal protective measures and vaccination. In addition, the concentration of infection counts and the strong positive correlation between infection count and neighborhood populations suggest that it is important to impose control measures on the identified hot spots timely. Other less populated neighborhoods may requre relatively less stringent measures to reduce the impact on daily life.

4.2.2. The need for region-specific control measures

The simulation results reveal distinct patterns of COVID-19 transmission among the three MSAs in the second wave, suggesting that disease control measures tailored to different geographic locations need to be carefully developed by local authorities. For example, Charleston MSA is a popular coastal destination for US tourists, and its commercial shipping also plays an important role in the local economy. The simulation shows that, compared with the other two MSAs, COVID-19 transmission rates in Charleston MSA are two times higher in the POI categories related to transportation and tourism, such as Support Activities for Road Transportation, Specialized Freight Trucking, Drinking Places (Alcoholic Beverages), Traveler Accommodations, and Restaurants and Other Eating Places. Therefore, the Charleston authority might need special restrictions on these POIs to balance the COVID-19 pandemic, disease control, and economic recovery. In Greenville, the ratios of infections in POI categories of Elementary and Secondary Schools and Automotive Repair and Maintenance were significantly higher than the other two MSAs. Appropriate measures are needed to reduce disease transmission via these two POI categories in Greenville MSA. Despite the noted difference, the ratios of infections in Restaurants and Other Eating Places among the three MSAs were similar (23%–30%) and ranked at the top position. Therefore, the restriction on restaurants remains the most universal and effective control measure regardless of region.

4.2.3. Lower-socioeconomic status may act as an umbrella against COVID-19 in certain cases

The correlation analysis at the neighborhood level (CBG) shows that ${\overline{\lambda }}_{c_i}$ was positively associated with the lower socioeconomic status (SES) in the three MSAs, such as poverty, low rate of higher education, low median household income, unemployed, uninsured, and severe mortgage burden (Table 4), which is consistent with Abedi et al. (2021). CBGs with lower SES might have lower mobility (fewer POI visits) due to relatively low financial status, which results in a lower COVID-19 transmission rate. Huang et al., (2022)’s work observed a similar trend that mobility reduced less in the less vulnerable counties during the 2020 lockdown summer in the US. Mobility data from SafeGraph shows that the per capita visits to Malls and Full-Service Restaurants of the top decile CBGs in median household income were two times more than the bottom decile (Fig. A7). Similarly, the per capita time spent on Nature Parks and Other Similar Institutions, Elementary and Secondary Schools of the top decile CBGs in median household income was also two times more than the bottom decile (Fig. A8). The observation of fewer POI visits in the low SES population at the CBG level in part explains why the White has a higher infection rate than the Black since the White is associated with higher SES in the study area. For example, the percent of the White population in CBGs shows a positive correlation with median house income ($r=0.489,p<0.001)$, and negative correlations with poverty ($r=-0.437,p<0.001)$, less higher education ($r=-0.386,p<0.001)$, unemployed ($r=-0.355,p<0.001$), uninsured ($r=-0.314,p<0.001$) and severe mortgage burden ($r=-0.245,p<0.001$).

Fig. A7.

Per capita visits in the study area. The high-income household had more visits to malls and restaurants. (Decile 1: lowest median household income; Decile 10: highest median household income).

Fig. A8.

Per capita time spend (minute) in the study area. The high-income household spent more time on nature parks, schools, malls, and restaurants. (Decile 1: lowest median household income; Decile 10: highest median household income).

4.3. Implications in the disease control for future pandemics

The simulation results of the three MSAs in SC suggest that disease transmission modeling based on fine-grained mobility data can be a promising tool to support evidence-based disease control measures and public health emergency responses. First, the neighborhood- and POI-level simulation provides detailed spatial information on transmission rates and infection counts. This information enables high-risk or vulnerable populations, such as senior residents, to make informed decisions and avoid places with high transmission rates, reducing their risk of contracting COVID-19. Second, the local authorities can impose necessary disease control measures on neighborhoods and POIs with large amounts of new cases to reduce disease transmission. Third, the transmission patterns revealed in this study demonstrate that the transmission rate and infection count may vary significantly among MSAs. Therefore, state-level disease control measures may not be universally effective for all regions. Such simulation results can guide the local authorities to develop timely and appropriate measures tailored to different geographic and economic characteristics. Simulations based on fine-grained mobility data bring the opportunity to develop data-driven policy decision-making in developing and adapting emergency responses to pandemics and other public health emergencies.

4.4. Limitations

While the findings are promising, some limitations of the study should be noted. The first limitation is the coverage of SafeGraph datasets. Although SafeGraph data has covered the entire US since 2018, it does not contain all POIs and is still being developed (SafeGraph, 2022c). Another issue is potential sampling bias. SafeGraph has a large proportion of mobile devices – about 10% (Squire, 2019), but the representativeness of the data for different population groups such as age and race and reliability of visitation counts need further exploration. The investigation is needed to evaluate and calibrate the mobility matrix derived from SafeGraph data.

Another limitation is that the timing and initialization of the simulation may affect the results. Because the model assumed a linear trend of the base transmission rate (${\beta }_{\mathit{base}}$) among all CBGs during the simulation period, the simulation period cannot be too long; otherwise, the linear trend may fail to capture the actual changing pattern of the base transmission rate. Therefore, our simulation cannot cover the entire second wave of COVID-19 in South Carolina; instead, we started at the time point (Dec. 29, 2020) when daily cases surged to 300 – 1000 in each MSA. Further research can introduce higher-order functions to present the dynamics of the transmission rate. Meanwhile, numerical optimization techniques are also needed to solve parameters of those high-order functions rather than grid search.

In addition, subject to the data source, only two types of places (home neighborhoods and POIs) were considered in the model verification. While the aggregated simulated infection count well fit the actual data (<10% RMSE), there are no medical records to verify the simulated infection count at the CBG level.

Lastly, fine-grained population data are prone to be influenced by migration. For example, dozens of thousands of students came back to universities in Jan. 2021 then might change CBG’s population (also $S_{c_i}^{\left(t\right)},E_{c_i}^{\left(t\right)},I_{c_i}^{\left(t\right)},R_{c_i}^{\left(t\right)}$, and mobility patterns) near campuses. It is unclear how these changes will affect the SEIR models. Future simulations should avoid population changes or calibrate SEIR using additional data or methods, such as geo-tagged social media posts, property price data, postal service address change requests (Schmahmann et al., 2022), or smartphone data (Nelson & Frost, 2022).

5. Conclusion

This study used fine-grained smartphone mobility data to simulate the COVID-19 spreading in three MSAs in South Carolina, generating transmission rates and infection counts at both the neighborhood and POI levels.. The aggregated confirmed cases in the simulation matched the COVID-19 historical case trend at the MSA level with low errors in three metrics: total cases, daily case RMSE, and the White and Black cases. This study found that 86% of simulated infections occurred in neighborhoods rather than POIs, suggesting that disease control measures in neighborhoods are critical to suppressing disease spreading during the study period. This imbalance of infection count between neighborhoods and POIs was rarely reported in previous studies. The patterns of transmission rates of neighborhoods and POIs significantly varied across MSAs, suggesting that general disease control measures may not be suitable for all sub-regions. The simulation results can help local authorities develop effective and tailored measures according to regional geographic and economic characteristics. For example, the local authorities can advocate the vulnerable population to avoid places with high transmission rates, or limit visits to hotspot neighborhoods and POIs with high cases. Therefore, the neighborhood-level simulations based on fine-grained mobility data and the SEIR model bring the opportunity to customize pandemic response in a data-driven manner. However, more approaches and ground truth data are required to directly verify the simulation results, so we urge caution when interpreting the findings and encourage further investigation into simulation models and techniques.

Data availability statement: All data used in this study were retrieved from publicly accessible sources via the following links. SafeGraph mobility data: https://shop.safegraph.com/; New York Times historical COVID-19 data: https://github.com/nytimes/covid-19-data; American Community Survey 2019 5-year estimate: https://www.census.gov/data/developers/data-sets/acs-5 year.html; South Carolina County-Level COVID-19 data by SCDHEC: https://scdhec.gov/covid19/covid-19-data/south-carolina-county-level-data-covid-19. The code for the study is provided at: https://github.com/GIBDUSC/covid-mobility-tool.

Funding: This work was supported by National Science Foundation (grant number: 2028791), National Institutes of Health (grant number: 3R01AI127203-04S1), and University of South Carolina COVID-19 Internal Funding Initiative (grant number: 135400–20-54176). The funders had no role in study design, data collection and analysis, decision to publish or preparation of this article.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A.

(See Fig. A1, Fig. A2, Fig. A3, Fig. A4, Fig. A5, Fig. A6, Fig. A7, Fig. A8 & Table A1, Table A2, Table A3, Table A4, Table A5 ).

Table A1.

Model parameters.

Parameter	Description	Value / Source
${\beta }_{\mathit{b}\mathit{a}\mathit{s}\mathit{e}}$	Base transmission rate among all CBG	Need to estimate
${\mathit{r}}_{\beta }$	Change rate of ${\beta }_{\mathit{b}\mathit{a}\mathit{s}\mathit{e}}$ in the simulation period	Need to estimate in the range of [-0.5, 1]
$\mathit{\psi }$	Transmission scaling factor for all POI	Need to estimate
${\mathit{\delta }}_{\mathit{E}}$	Mean latency period	96 h (S. Chang, Pierson, et al., 2021; Lauer et al., 2020)
${\mathit{\delta }}_{\mathit{I}}$	Mean infectious period	84 h (Cdc, 2021, Li et al., 2020)
${\mathit{\delta }}_{\mathit{c}}$	Mean lag period to be confirmed	7 days (Li et al., 2020)
${\mathit{r}}_{\mathit{c}}$	Detected rate of infection	65%, empirically searched.
${\mathit{N}}_{{\mathit{c}}_{\mathit{i}}}$	Total population of CBG ${\mathit{c}}_{\mathit{i}}$	ACS 2019
${\mathbf{w}}_{\mathit{i}\mathit{j}}^{\left(\mathbf{t}\right)}$	Mobility matrix from CBG ${\mathit{c}}_{\mathit{i}}$ to POI ${\mathit{p}}_{\mathit{j}}$ at hour $\mathit{t}$	SafeGraph
${\mathit{a}}_{{\mathit{p}}_{\mathit{j}}}$	Area of POI ${\mathit{p}}_{\mathit{j}}$	SafeGraph
${\mathit{d}}_{\mathit{p}\mathit{j}}$	Median visitor dwell time ${\mathit{p}}_{\mathit{j}}$	SafeGraph
${\mathit{S}}_{{\mathit{c}}_{\mathit{i}}}^{\left(0\right)}$	Initial susceptible population in CBG ${\mathit{c}}_{\mathit{i}}$	NYT COVID-19 data
${\mathit{E}}_{{\mathit{c}}_{\mathit{i}}}^{\left(0\right)}$	Initial exposed population in CBG ${\mathit{c}}_{\mathit{i}}$	NYT COVID-19 data
${\mathit{I}}_{{\mathit{c}}_{\mathit{i}}}^{\left(0\right)}$	Initial infectious population in CBG ${\mathit{c}}_{\mathit{i}}$	NYT COVID-19 data
${\mathit{R}}_{{\mathit{c}}_{\mathit{i}}}^{\left(0\right)}$	Initial removed population in CBG ${\mathit{c}}_{\mathit{i}}$	NYT COVID-19 data

Table A2.

Searching range and parameter sets. The parameter sets include the best fitted model and those with RMSEs<1.2 times of the best one. Fitted models of each MSA has similar parameters in the study area.

MSA / Searching range	# parameter sets	${\beta }_{\mathit{base}}$	$r_{\mathrm{\beta }}$	$\psi$
Searching range	–	$\left[0.002,0.04\right]$	[-0.5, 1]	$\left[5,100\right]$
Greenville	2	[0.0147, 0.0150]	[-0.5, −0.5]	[5.0 – 5.1]
Columbia	4	[0.0147, 0.0153]	[-0.375, – 0.583]	[9.2, 11.8]
Charleston	2	[0.150, 0.0154]	[-0.5, −0.5]	[18.9, 19.5]

Table A3.

Sub-categories for the mentioned top-categories in this paper.

Top-category	Sub-category
Restaurants and Other Eating Places	Full-Service Restaurants
	Limited-Service Restaurants
	Cafeterias, Grill Buffets, and Buffets
	Snack and Nonalcoholic Beverage Bars
Elementary and Secondary Schools	Elementary and Secondary Schools
Other Amusement and Recreation Industries	Golf Courses and Country Clubs
	Skiing Facilities
	Marinas
	Fitness and Recreational Sports Centers
	Bowling Centers
	All Other Amusement and Recreation Industries
Religious Organizations	Religious Organizations
Offices of Physicians	Offices of Physicians (except Mental Health Specialists)
	Offices of Physicians, Mental Health Specialists
General Medical and Surgical Hospitals	General Medical and Surgical Hospitals
Offices of Dentists	Offices of Dentists
Traveler Accommodation	Hotels (except Casino Hotels) and Motels
	Casino Hotels
Automotive Repair and Maintenance	General Automotive Repair
	Automotive Transmission Repair
	Other Automotive Mechanical and Electrical Repair and Maintenance
	Automotive Body, Paint, and Interior Repair and Maintenance
	Automotive Glass Replacement Shops
	Automotive Oil Change and Lubrication Shops
	Car Washes
	All Other Automotive Repair and Maintenance
Drinking Places (Alcoholic Beverages)	Drinking Places (Alcoholic Beverages)
Offices of Other Health Practitioners	Offices of Chiropractors
	Offices of Optometrists
	Offices of Mental Health Practitioners (except Physicians)
	Offices of Physical, Occupational and Speech Therapists, and Audiologists
	Offices of All Other Miscellaneous Health Practitioners
Personal Care Services	Barber Shops
	Beauty Salons
	Nail Salons
	Diet and Weight Reducing Centers
	Other Personal Care Services
Health and Personal Care Stores	Pharmacies and Drug Stores
	Cosmetics, Beauty Supplies, and Perfume Stores
	Optical Goods Stores
	Food (Health) Supplement Stores
	All Other Health and Personal Care Stores
Agencies, Brokerages, and Other Insurance Related Activities	Insurance Agencies and Brokerages
Sporting Goods, Hobby, and Musical Instrument Stores	Sporting Goods Stores
	Hobby, Toy, and Game Stores
	Sewing, Needlework, and Piece Goods Stores
	Musical Instrument and Supplies Stores
Support Activities for Road Transportation	Motor Vehicle Towing
Specialized Freight Trucking	Used Household and Office Goods Moving
	Specialized Freight (except Used Goods) Trucking, Long-Distance
Accounting, Tax Preparation, Bookkeeping, and Payroll Services	Tax Preparation Services
Accounting, Tax Preparation, Bookkeeping, and Payroll Services	Other Accounting Services
Agencies, Brokerages, and Other Insurance Related Activities	Insurance Agencies and Brokerages
Activities Related to Credit Intermediation	Mortgage and Nonmortgage Loan Brokers
	Financial Transactions Processing, Reserve, and Clearinghouse Activities
	Other Activities Related to Credit Intermediation
Other Financial Investment Activities	Portfolio Management
	Investment Advice
	Miscellaneous Financial Investment Activities
Building Equipment Contractors	Plumbing, Heating, and Air-Conditioning Contractors
	Other Building Equipment Contractors

Table A4.

Descriptive statistics of the variables for correlation analysis of CBG transmission rate.

Variables		Mean			Std.			Min			25%			50%			75%			Max
		Grn	Clm	Clt	Grn	Clm	Clt	Grn	Clm	Clt	Grn	Clm	Clt	Grn	Clm	Clt	Grn	Clm	Clt	Grn	Clm	Clt
Demographic background	Population	1761	1694	1959	1003	1379	1490	361	223	28	1050	905	1038	1498	1314	1578	2203	2018	2329	7139	14,051	10,396
	%Senior	17.20	16.47	16.09	7.79	8.88	8.95	0.00	0.00	0.00	11.93	10.48	10.38	16.13	15.03	15.24	21.03	21.55	20.67	52.81	50.41	61.60
	%Whilte	75.67	57.85	65.55	20.85	29.69	24.22	0.00	0.00	0.00	65.17	32.89	48.97	81.97	65.48	69.98	92.24	83.50	84.42	100.00	100.00	100.00
	%Black	17.81	35.85	28.57	19.32	29.42	24.32	0.00	0.00	0.00	3.46	9.55	9.63	10.71	27.94	23.15	25.14	57.98	42.23	96.31	100.00	100.00
	%Hispanic	6.70	4.97	5.16	8.81	6.97	7.41	0.00	0.00	0.00	0.66	0.00	0.68	3.48	2.45	2.60	9.07	6.44	6.62	59.04	45.52	50.81
	%Aisan	1.46	1.82	1.48	3.23	3.56	2.86	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	1.43	2.24	1.69	30.24	34.37	20.62
	%Poverty	15.42	17.19	15.06	13.14	14.78	14.03	0.00	0.00	0.00	5.62	6.17	4.65	11.48	13.69	10.54	21.86	24.49	22.09	76.54	82.92	76.55
	% High school education	22.69	23.71	22.95	9.66	12.23	11.36	0.00	0.00	0.00	15.58	14.98	14.83	22.46	23.32	22.62	28.63	31.89	30.45	56.35	65.61	59.71
Social Determinants of Health	Median household income	53,866	53,850	64,368	24,586	27,956	32,218	0	0	0	38,185	36,346	42,219	50,663	51,409	58,525	65,885	68,897	82,586	204,792	214,643	214,306
	% Unemployed	3.13	3.89	2.82	3.07	3.60	3.05	0.00	0.00	0.00	0.91	1.18	0.73	2.47	3.10	2.21	4.33	5.43	4.03	19.20	19.68	26.00
	% Uninsured	11.24	9.95	10.84	7.64	7.52	8.83	0.00	0.00	0.00	6.01	4.43	4.24	9.51	8.46	8.86	15.09	12.99	14.40	46.72	49.88	54.76
	% Living with severe rent burden	38.45	42.06	40.74	23.19	24.69	23.36	0.00	0.00	0.00	23.00	24.63	25.93	37.50	44.57	41.99	54.82	58.14	55.08	100.00	100.00	100.00
	% Living with severe mortgage burden	12.84	15.92	18.37	9.07	10.82	12.05	0.00	0.00	0.00	7.11	8.82	11.06	11.22	14.41	17.64	17.06	20.83	24.39	64.44	70.00	100.00
	Per capita building area (m2)	93	97	95	38	50	228	15	0	0	69	67	59	86	87	76	111	115	97	395	399	4514
POI characteristic	Mean transmission rate of visited POIs	9.22E-05	7.32E-05	1.11E-04	7.31E-05	2.15E-05	2.63E-05	2.22E-05	3.31E-05	6.09E-05	4.66E-05	5.89E-05	9.60E-05	5.89E-05	6.97E-05	1.07E-04	1.12E-04	8.32E-05	1.20E-04	5.82E-04	1.90E-04	3.66E-04
	Per capita visit count to POIs	3.2	2.7	2.5	1.4	1.5	2.6	0.3	0.2	0.4	2.1	1.6	1.6	3.0	2.4	2.2	3.9	3.8	3.0	11.4	8.1	47.6
	Per capita Infection count from POIs	0.0073	0.0055	0.0073	0.0040	0.0019	0.0020	0.0021	0.0017	0.0034	0.0045	0.0042	0.0060	0.0056	0.0053	0.0070	0.0092	0.0065	0.0082	0.0237	0.0144	0.0253

Note: Grn: Greenville; Clm: Columbia; Clt: Charleston; CBG: Census block group; POI: Point of interest.

Table A5.

Descriptive statistics of the variables for correlation analysis of POI transmission rate.

Variables	Mean			Std.			Min			25%			50%			75%			Max
	Grn	Clm	Clt	Grn	Clm	Clt	Grn	Clm	Clt	Grn	Clm	Clt	Grn	Clm	Clt	Grn	Clm	Clt	Grn	Clm	Clt
POI area	569	1740	967	4300	101,015	18,389	3	1	0	27	26	24	52	54	52	122	136	122	124,872	8,167,508	1,256,654
Total POI visits	636	630	549	1762	1688	1552	11	12	15	111	113	108	251	248	230	578	596	510	56,115	55,396	51,734
Infection count from POIs	1.2	1.7	2.1	9.5	7.4	5.8	0.0	0.0	0.0	0.0	0.1	0.1	0.2	0.3	0.4	0.7	1.0	1.7	525.8	306.4	132.5

Note: Grn: Greenville; Clm: Columbia; Clt: Charleston; POI: Point of interest.

Data availability

I have shared the data/code at the Attach File step.