2.1.1 Demographic data

Demographic data comes from the US Census Bureau, American Community Survey, 2014–2018 5-year estimates (United States Census Bureau, 2020). We label ZIP Codes by their majority racial or ethnic group using a 50% threshold. If a ZIP Code does not meet this threshold for any race or ethnicity, then we label it “Mixed.” Additional variables from the Census used for analysis include the median household size, median income, percentage of employed individuals, percentage of insured individuals, percentage of households with four or more people (i.e., overcrowded households), and percentage of buildings over 50 years as a proxy for the quality of ventilation. These additional variables are used to represent the trade-offs between socio-demographic characteristics and mobility metrics to achieve city-average case rates by demographic groups.

2.1.2 Mobility data

We rely on the SafeGraph Social Distancing Metrics dataset for mobility data (SafeGraph, 2021). SafeGraph aggregates anonymous cellphone-based movement data and provides estimates of (i) devices residing within a census block group and (ii) trips between each block group pair. We aggregate these data to the ZIP Code level to match the geographic resolution of the data available on COVID-19 cases in Chicago. Where the boundaries of census block groups do not perfectly fit within ZIP Codes, we split trips between ZIP Codes using weights provided by the US Housing and Urban Development (Wilson & Din, Reference Wilson and Din2018). Finally, we scale trips between ZIP Codes by applying a ZIP Code specific scaling factor. We calculate scaling factors by dividing a ZIP Code’s census population by its average number of devices between January 15 and February 15, 2020. We select this period as it precludes early January holiday travel and major COVID-19 disruptions in the United States. The average scaling factor in our data is 25 (Tables S1–S4). For each day in 2020, our final movement data is a set of 58-by-58 matrices with cells containing the estimated daily trips between and within each ZIP Code.

2.1.3 Population data

Daily population estimates are based on the number of smartphone devices residing within a ZIP Code in a 24-h period. We multiply the number of devices using the same ZIP-specific factors used to scale mobility data to estimate the daily population residing in a ZIP Code (Figure S1). Population size is allowed to vary over time to account for temporal fluctuations (e.g., people leaving/returning to the metro area), which recent census data shows were significant during the first year of the pandemic (Frey, Reference Frey2022).

2.1.4 COVID-19 case and test data

In Chicago, longitudinal ZIP Code level COVID-19 case data is provided weekly by the Department of Public Health for all 58 ZIP Codes starting March 1, 2020 (The City of Chicago, 2021). We first distribute these case counts uniformly across the days of the given week to obtain reported daily case counts, then the reported case count is corrected by considering testing disparities as well as the data from the covidestim project that provides daily estimates of the case count in Cook county ( https://covidestim.org/ ) (Chitwood et al., Reference Chitwood, Russi, Gunasekera, Havumaki, Klaassen, Pitzer and Menzies2022). To our knowledge, we rely on the most recent and highest quality data available to correct for the fact that not all COVID-19 cases are diagnosed (Pitzer et al., Reference Pitzer, Chitwood, Havumaki, Menzies, Perniciaro, Warren and Cohen2021; Bilal et al., Reference Bilal, Tabb, Barber and Roux2021). Our approach (detailed in Supplementary Materials (SM) section S1) also reflects effects of disparities in testing across demographic groups, thus offering a significant improvement over prior research that used a time-invariant scaling factor agnostic to demographic differences (Chang et al., Reference Chang, Pierson, Koh, Gerardin, Redbird, Grusky and Leskovec2020).

In Milwaukee, longitudinal ZIP Code level COVID-19 case and test data are provided daily by Wisconsin Department of Health Services (2022), thus no daily attribution from weekly reports was necessary. For more details, see SM section S7. These data are used for robustness analyses to reproduce the main results obtained in Chicago.

2.1.5 Data ethics

COVID-19 confirmed case counts for Chicago are aggregated to the ZIP Code level and published online by the Chicago Department of Public Health (The City of Chicago, 2021). SafeGraph mobility data covers individuals who consent to share their location data in third party mobile-phone applications. SafeGraph aggregates the location information of users who opt-in to the collection of anonymous geo-spatial data. The description of our project was reviewed by the New York University Abu Dhabi Institutional Review Board and a determination of “non-human subjects research” was issued as (i) the researchers were not engaged in collecting any data used in this paper, and thus were not interacting with human subjects; and (ii) the data used do not contain identifiable information, nor could be re-identified.

2.3.1 New exposures

To compute the number of new exposures $N^{(t)}_{S_i \rightarrow E_i}$ at node $v_i$ at time $t$ , we assume that any susceptible visitor to node $v_j$ at time $t$ has the same independent probability $\lambda _j^{(t)}$ of being infected and transitioning from the susceptible to the exposed state. That is, we do not consider heterogeneity in transition rates by demographic groups. As there are $w_{i,j}^{(t)}$ visitors from node $v_i$ to node $v_j$ at time $t$ , and we assume that $S_i^{(t)}/ N_i^{(t)}$ fraction of them are susceptible, the number of new exposures among them is distributed according to $\text{Binom} ( w_{i,j}^{(t)} S_i^{(t)}/N_i^{(t)}, \lambda _j^{(t)} ) \approx \text{Pois} ( \lambda _j^{(t)} w_{i,j}^{(t)} S_i^{(t)}/N_i^{(t)} )$ . Rather than including heterogeneous mixing within each node as seen in other studies (Gozzi et al., Reference Gozzi, Tizzoni, Chinazzi, Ferres, Vespignani and Perra2021; Melegaro et al., Reference Melegaro, Fava, Poletti, Merler, Nyamukapa, Williams and Manfredi2017; Mossong et al., Reference Mossong, Hens, Jit, Beutels, Auranen, Mikolajczyk and Edmunds2008; Zhang et al., Reference Zhang, Litvinova, Liang, Wang, Wang, Zhao and Yu2020), our approach assumes homogeneous mixing of visitors. Thus, the number of new exposures among those from node $v_i$ is distributed as the sum of the above expression over all nodes, so that new exposures are distributed as

(1) \begin{equation} N^{(t)}_{S_i \rightarrow E_i} \sim \text{Pois} \left ( \dfrac{S_i^{(t)}}{N_i^{(t)}} \sum _{j=1}^n w_{i,j}^{(t)} \lambda _j^{(t)} \right ), \qquad \lambda _j^{(t)} = \dfrac{\psi _j^{(t)}}{a_j} \displaystyle \sum _{k=1}^n w_{k,j}^{(t)} \dfrac{I_k^{(t)}}{N_k^{(t)}}. \end{equation}

Here, the rate of infection $\lambda _j^{(t)}$ at node $v_j$ at time $t$ decreases with the area $a_j$ of the ZIP Code and increases with the inflow to node $v_j$ , the probability of infected people visiting, and the time-dependent and ZIP-specific parameter $\psi _j^{(t)}$ , capturing the risk that trips carry on average. This risk depends on many factors, for example, typical length, nature of exposure, use of protective equipment, such as mask wearing, and the possibilities for and adherence to social distancing guidelines and norms, etc. See Figure S8 for the temporal distribution of this parameter. The calculation of $\psi _j^{(t)}$ is detailed when model calibration is discussed below.

2.3.2 New infectious and removed cases

Exposed individuals become infectious at a rate that is inversely proportional to the mean latency period $\delta _E$ , which is assumed to be identical for all nodes. Similarly, infectious individuals transition to the removed state at a rate that is inversely proportional to the mean infectious period $\delta _I$ which is also considered to be identical for all nodes. Therefore, we assume that at each time step $t$ each exposed individual has a time-independent probability of first becoming infectious then of transitioning to the removed state, given by $N^{(t)}_{E_i \rightarrow I_i} \sim \text{Binom}\!\left( E_i^{(t)}, 1/\delta _E \right)$ and $N^{(t)}_{I_i \rightarrow R_i} \sim \text{Binom} ( I_i^{(t)}, 1/\delta _I)$ , respectively. According to previous studies (Chang et al., Reference Chang, Pierson, Koh, Gerardin, Redbird, Grusky and Leskovec2020), estimates for the mean latency and infectious periods are $\delta _E = 4$ days and $\delta _I = 3.5$ days, respectively. These are the parameters we adopt.

2.3.3 Initialization

We first identify the first day with non-zero estimated case count: March 7, 2020, the 67^th day of the year. We take this as day 0 ( $t = 0$ ) in the computational model. Additionally, we approximate the infectious and removed compartments at $t = 0$ as initially empty, that is, all infected individuals are in the exposed compartment (Chang et al., Reference Chang, Pierson, Koh, Gerardin, Redbird, Grusky and Leskovec2020). Finally, we assume that the same initial prevalence occurs in every ZIP Code, that is, every individual in each demographic group has the same independent probability $p_0$ of being exposed (Chang et al., Reference Chang, Pierson, Koh, Gerardin, Redbird, Grusky and Leskovec2020). Accordingly, the model is initialized as $S_i^{(0)} = (1-p_0) N_i^{(0)}$ , $E_i^{(0)} = p_0 N_i^{(0)}$ , $E_i^{(0)} = R_i^{(0)} = 0$ with $p_0 = 0.001$ . Studying the impact of different seeding probabilities are outside of the scope of our study.

2.3.4 Calibration of the model

Calibration of the SEIR model is performed by estimating the value of the unknown parameter $\psi _i^{(t)}$ for each day $t$ based on the new infections $C_i^{(t)}$ occurring on that specific day among the people residing in the ZIP Code. The time-dependent and ZIP-specific parameter $\psi _j^{(t)}$ captures the risk that trips carry on average (see the “New exposures” section above for further details).

For each ZIP Code, the estimate $C_i^{(t)}$ is the realization of the random variable $N^{(t)}_{S_i \rightarrow E_i}$ . Since $N^{(t)}_{S_i \rightarrow E_i}$ follows a Poisson distribution, its expected value can be decomposed as

\begin{equation*} \begin{aligned} \mathbb{E} \left [ N^{(t)}_{S_i \rightarrow E_i} \right ] &= \displaystyle \dfrac{S_i^{(t)}}{N_i^{(t)}} \sum _{j=1}^n w_{i,j}^{(t)} \lambda _j^{(t)} = \displaystyle \dfrac{S_i^{(t)}}{N_i^{(t)}} \sum _{j=1}^n w_{i,j}^{(t)} \dfrac{\psi _j^{(t)}}{a_j} \sum _{k=1}^n w_{k,j}^{(t)} \dfrac{I_k^{(t)}}{N_k^{(t)}}, \\[5pt] &= \dfrac{S_i^{(t)}}{N_i^{(t)}} \left ( \dfrac{\psi _i^{(t)}}{a_i} w_{i,i}^{(t)} \sum _{k = 1}^n w_{k,i}^{(t)} \dfrac{I_k^{(t)}}{N_k^{(t)}} + \sum _{j \neq i}^n w_{i,j}^{(t)} \dfrac{\psi _j^{(t)}}{a_j} \sum _{k = 1}^n w_{k,j}^{(t)} \dfrac{I_k^{(t)}}{N_k^{(t)}} \right ), \end{aligned} \end{equation*}

thus yielding

(2) \begin{equation} \mathbb{E} \left [ N^{(t)}_{S_i \rightarrow E_i} \right ] = \dfrac{S_i^{(t)}}{N_i^{(t)}} \left ( \psi _i^{(t)} \rho _i^{(t)} \dfrac{w_{i,i}^{(t)}}{N_i^{(t)}} \sum _{k = 1}^n \dfrac{w_{k,i}^{(t)}}{N_k^{(t)}} I_k^{(t)} + \sum _{j \neq i}^n \psi _j^{(t)} \rho _j^{(t)} \dfrac{w_{i,j}^{(t)}}{N_j^{(t)}} \sum _{k = 1}^n \dfrac{w_{k,j}^{(t)}}{N_k^{(t)}}I_k^{(t)} \right ), \end{equation}

where $\rho _i^{(t)} = N_i^{(t)}/ a_i$ is the population density of node $v_i$ on day $t$ . When estimating $\psi _i^{(t)}$ , we assume that $\psi _j^{(t)} \approx \psi _j^{(t-1)}$ , corresponding to the assumption that contributions from nodes are not expected to change drastically on a daily basis. With this, we estimate $\psi _i^{(t)}$ as

(3) \begin{equation} \hat \psi _i^{(t)} = \dfrac{C_i^{(t)} \frac{N_i^{(t)}}{S_i^{(t)}} - \displaystyle \sum _{j \neq i}^n \hat \psi _j^{(t-1)} \rho _j^{(t)} \frac{w_{i,j}^{(t)}}{N_j^{(t)}} \sum _{k = 1}^n \frac{w_{k,j}^{(t)}}{N_k^{(t)}}I_k^{(t)}}{\rho _i^{(t)} \frac{w_{i,i}^{(t)}}{N_i^{(t)}} \displaystyle \sum _{k = 1}^n \frac{w_{k,i}^{(t)}}{N_k^{(t)}} I_k^{(t)}} \end{equation}

to ensure that $C_i^{(t)} = \mathbb{E} \!\left[ N^{(t)}_{S_i \rightarrow E_i} \right]$ , where we relied on the estimate $\hat \psi _j^{(t-1)}$ from the previous time step of $\psi _j^{(t-1)}$ . Therefore, the estimation algorithm is as follows. First, we initialize $\hat \psi _j^{(0)} = 0$ for $j = 1,2,\dots,n$ . Then, for $t = 1,2,\dots, t_{\text{stop}}$ we compute $\hat \psi _i^{(t-1)}$ from (3) for $i = 1,2,\dots,n$ . Although this approach yields a slightly suboptimal solution (as we are solving decoupled scalar optimization problems instead of solving them jointly), it produces negligible prediction error (Figure S9) as the slight imprecisions due to substituting the unknown quantity $\psi _j^{(t)}$ with $\psi _j^{(t-1)}$ calculated in the previous round are further attenuated as contributions from between-ZIP trips are typically dominated by those from within-ZIP trips (Tables S1–S4).

While the fit produces almost no error at the group level, there are 8 small ZIP Codes belonging to the same group (Majority White) in close proximity to each other where error is considerably higher than in all other ZIP Codes. Further analysis reveals that in all these ZIP Codes the movement pattern shows significantly lower homophily (here the percentage of trips occurring within the same ZIP Code) than the population average (Figure S9), thus a possible explanation is misattribution of trips among neighboring ZIP Codes. Therefore, we next considered combining these 8 ZIP Codes, leading to no significant changes in the distribution of trips, population, area, movement pattern, and epidemic progression (Figure S10), while ZIP Code level performance of the model accuracy increases dramatically, virtually eliminating all error (Figure S9). Therefore, in what follows, we combine these ZIP Codes (60601, 60602, 60603, 60604, 60605, 60606, 60654, and 60661), and treat this aggregate as a single node.

2.4.1 Source of exposures

Considering new exposures among people residing in ZIP Code $i$ , it follows from (1) that those that are due to trips to ZIP Code $j$ and to ZIP Codes in group $G_k$ are distributed according to Poisson processes with parameters $S_i^{(t)}/N_i^{(t)} w_{i,j}^{(t)} \lambda _j^{(t)}$ and $S_i^{(t)}/N_i^{(t)} \sum _{j \in G_k} w_{i,j}^{(t)} \lambda _j^{(t)}$ , respectively. Therefore, the group level average probabilities that exposure in group $G_i$ happens due to trips within one’s own ZIP Code and one’s own group, respectively, are given at time $t$ by

\begin{equation*} p_i^{(t)} = \dfrac{1}{n_i} \displaystyle \sum _{j \in G_i} \dfrac{w_{j,j}^{(t)} \lambda _j^{(t)}}{\sum _{k=1}^n w_{j,k}^{(t)} \lambda _k^{(t)}}, \qquad q_i^{(t)} = \dfrac{1}{n_i} \displaystyle \sum _{j \in G_i} \dfrac{\sum _{k \in G_i} w_{j,k}^{(t)} \lambda _k^{(t)}}{\sum _{k=1}^n w_{j,k}^{(t)} \lambda _k^{(t)}}, \end{equation*}

where $n_i$ is the number of nodes in group $G_i$ . For more details, see SM Tables S1–S4.

2.4.2 Eliminating case rate disparities

Considering (1), the number of new exposures in ZIP Code $i$ at time $t$ follows a Poisson distribution with parameter

(4) \begin{equation} \dfrac{S_i^{(t)}}{N_i^{(t)}} \sum _{j=1}^n w_{i,j}^{(t)} \lambda _j^{(t)} = \dfrac{S_i^{(t)}}{N_i^{(t)}} \sum _{j=1}^n w_{i,j}^{(t)} \dfrac{\psi _j^{(t)}}{a_j} \displaystyle \sum _{k=1}^n w_{k,j}^{(t)} \dfrac{I_k^{(t)}}{N_k^{(t)}}. \end{equation}

Introduce

(5) \begin{equation} \beta _i^{(t)} = \psi _i^{(t)} \dfrac{N_i^{(t)}}{a_i} \left ( \dfrac{w_{i,i}^{(t)}}{N_i^{(t)}} \right )^2 \qquad \text{and} \qquad \gamma _i = \dfrac{I_i^{(t)}}{N_i^{(t)}}, \end{equation}

and note that from (4) it follows that the number of new exposures $N^{(t)}_{S_i \rightarrow E_i}$ in ZIP Code $i$ at time $t$ can be approximated as a Poisson distribution with parameter $\beta _i^{(t)} S_i^{(t)} I_i^{(t)}/ N_i^{(t)}$ since

\begin{equation*} \dfrac{S_i^{(t)}}{N_i^{(t)}} \sum _{j=1}^n w_{i,j}^{(t)} \lambda _j^{(t)} \approx \beta _i^{(t)} \gamma _i^{(t)} S_i^{(t)}. \end{equation*}

if $w_{i,j}^{(t)}/ w_{i,i}^{(t)} \ll 1/n$ , $\gamma _i^{(t)}/ \gamma _j^{(t)} \approx 1$ , and $\beta _i^{(t)}/\beta _j^{(t)} \approx 1$ , which are confirmed in Figure S10b, Figure S3, and Figure S12a, respectively. Therefore, epidemic progression in ZIP Code $i$ is largely determined by $\beta _i^{(t)}$ , encompassing the evolution of three major ZIP-specific factors: the parameter $\psi _i^{(t)}$ , population density $N_i^{(t)}/ a_i$ , and within-ZIP trip rate $w_{i,i}^{(t)}$ according to (5). While separately none of these factors displays a strong correlation with case rate, their combination in $\beta _i^{(t)}$ defined in Equation (5) has significant predictive power regarding case rate (Figure S12).

While between-ZIP trips are crucial at the beginning of the pandemic (Brinkman & Mangum, Reference Brinkman and Mangum2022; Hâncean et al., Reference Hâncean, Slavinec and Perc2021; Wells et al., Reference Wells, Sah, Moghadas, Pandey, Shoukat, Wang and Galvani2020), once started, within-ZIP trips largely drive the epidemic progression, as they are significantly more frequent (Tables S1–S4). As a result, we can approximate the transmission rate at ZIP Code $i$ as $\beta _i^{(t)}$ neglecting the effects of between-ZIP trips in two ways. First, by omitting trips leading to other ZIP Codes, we do not take into account the corresponding exposures. Second, by discarding incoming trips, thus the risk they carry, we also underestimate the infection rate at ZIP Code $i$ . Therefore, $\beta _i^{(t)}$ quantifies the average number of individuals that a disease carrier would infect daily (Kermack & McKendrick, Reference Kermack and McKendrick1927) in a network of disconnected nodes.

When matching a group level characteristic, within the selected group we modify both the mean and temporal evolution of this characteristic such that they match the group level mean and temporal evolution in the target group.

2.4.3 Structural effects

To analyze the effects of network segregation among demographic groups, we manipulate the levels of homophily in the movement matrices. We measure homophily as the percentage of trips occurring within the same ZIP Code and the same group.

We reduce homophily (i.e., reduce segregation in the mobility network) via Laplace smoothing (Manning et al., Reference Manning, Raghavan and Schütze2008) on all outgoing trips originating in nodes from a given group, focusing on one group at a time, while all other trips (originating in different groups) remain unchanged. This is achieved by transforming the movement matrices via the following rescaling of the weights (i.e., redirecting trips among ZIP Codes): $ \bar w_{i,j}^{(t)} \leftarrow (w_{i,j}^{(t)} + \alpha n d^2)/(1 + \alpha n d)$ with $d = \frac{1}{n}\sum _{j=1}^N w_{i,j}^{(t)}$ , where $n$ is the number of nodes in the graph (i.e., number of ZIP Codes). This scaling has four important properties. First, for $\alpha = 0$ we have $\bar w_{i,j}^{(t)} = w_{i,j}^{(t)}$ , thus we recover the original mobility patterns. Second, as $\alpha \rightarrow \infty$ we have $\bar w_{i,j}^{(t)} \rightarrow d$ , that is, outgoing edges will have uniform weights, corresponding to homogeneous movement. Third, for all values of $\alpha$ we have $\sum _{j=1}^n \bar w_{i,j}^{(t)} = nd = \sum _{j=1}^n w_{i,j}^{(t)}$ , so that the overall movement volume (outgoing trip rate) for any of the nodes remains unchanged. Finally, for all values of $\alpha$ the ordering of trips remain unchanged, i.e., if $w_{i,j}^{(t)} \lt w_{i,k}^{(t)}$ then $\bar w_{i,j}^{(t)} \lt \bar w_{i,k}^{(t)}$ .

We increase homophily for a selected group in two ways. In the first scenario, we isolate each demographic group, one at a time. When isolating group $G_i$ , we remove all trips between the selected group and other groups, and rescale the remaining edge weights according to

\begin{equation*} w_{j,k}^{(t)} \leftarrow \left \{ \begin{array}{c@{\quad}l} w_{j,k}^{(t)} \frac{\sum _{h = 1}^n w_{j,h}^{(t)}}{\sum _{h \notin G_i} w_{j,h}^{(t)}} & j, k \notin G_i, \\[12pt] w_{j,k}^{(t)} \frac{\sum _{h = 1}^n w_{j,h}^{(t)}}{\sum _{h \in G_i} w_{j,h}^{(t)}} & j, k \in G_i, \\[5pt] 0 & \text{otherwise.} \end{array} \right . \end{equation*}

so that all (outgoing) trip rates remain unchanged and preserved outgoing trips maintain the same relative importance for each node. In the second scenario, we isolate nodes within each demographic group, one at a time according to

\begin{equation*} w_{j,k}^{(t)} \leftarrow \left \{ \begin{array}{c@{\quad}l} \sum _{h = 1}^n w_{j,h}^{(t)} & j = k \in G_i, \\[8pt] w_{j,k}^{(t)} \frac{\sum _{h = 1}^n w_{j,h}^{(t)}}{\sum _{h \notin G_i} w_{j,h}^{(t)}} & j,k \notin G_i, \\ 0 & \text{otherwise.} \end{array} \right . \end{equation*}

This way, we remove edges between nodes in the selected group, as well as trips that lead to ZIP Codes in other demographic groups, and we increase the frequency of within-ZIP trips to preserve the trip rate. The above transformation also rescales the remaining edges in the network so that all (outgoing) trip rates remain unchanged, and the preserved outgoing trips maintain the same relative importance for each node in all other groups.

To reiterate, all manipulations of the movement matrices preserve the overall movement volume (outgoing trip rate) for all ZIP Codes. This is crucial as the counterfactual computational experiments we conduct provide us with results that relate to the structure of mobility, rather than to its volume. For more details, see SM section S5.

2.4.4 Achieving equal group outcomes in case rate

We first generate counterfactuals by modifying both vulnerability and trip rate (while maintaining their temporal evolution) in each group according to $\psi _j^{(t)} \leftarrow f_{\psi } \psi _j^{(t)}$ and $w_{j,k}^{(t)} \leftarrow f_w w_{j,k}^{(t)}$ where the scaling factors $f_{\psi }$ and $f_w$ are selected (for each group separately) as follows: $f_{\psi }$ is sampled from a uniform distribution over $[0.5,2]$ , whereas $f_w$ is computed as $\sqrt{f_{\beta }/ f_{\psi }}$ where $f_{\beta } = f_{\psi } f_w^2$ is chosen randomly from the range $[0.05,1]$ . This way the group level $\beta$ is determined randomly over the range $[0.05,1]$ , and this change is achieved randomly by modifying both the vulnerability via $\psi _j^{(t)}$ and the movement quantity via $w_{j,k}^{(t)}$ . For $\beta \lt 0.6$ , the relationship between group level mean $\beta$ and case rate is approximately linear (Figure S12). With this, we can compute not only how $\beta$ should have changed for a given group to achieve a certain case rate outcome, but we can also translate these to changes into vulnerability and trip rate according to (5). Similarly, for six of the most relevant socio-economic differences (median household size, median income, percentage of employed, percentage of insured, overcrowdedness, and percentage of buildings over 50 years old), we first calculate the correlation between them and both the case rate and $\beta$ , then relying on linear regression analysis we compute the required change in these socio-demographic factors to achieve a particular group level case rate outcome. For more details, see SM section S6.

2.4.5 Other counties

As our approach is underpinned by the relative isolation of ZIP Codes (high homophily), we consider 15 of the largest metropolitan areas: Chicago, IL; Columbus, OH; Dallas, TX; Detroit, MI; Fort Worth, TX; Houston, TX; Indianapolis, IND; Los Angeles, CA; Las Vegas, NV; Miami, FL; New York, NY; Philadelphia, PA; Phoenix, AZ; San Diego, CA; Seattle, WA. In these cities, there are 5 demographic groups (not necessarily in every city): Majority Asian, Majority Black, Majority Latinx, Majority White, and Mixed. The movement patterns in all these counties display a high degree of homophily (Figures S4–S7, Table S5). Therefore, we expect that our analytical approach can be extended to other major US cities provided that the required data become available. At present, a major bottleneck is the lack of geographically fine-grained data on COVID-19 cases and testing frequency.