key: cord-0704981-sxrowvno
authors: Ma, K. C.; Menkir, T.; Kissler, S.; Grad, Y.; Lipsitch, M.
title: Modeling the impact of racial and ethnic disparities on COVID-19 epidemic dynamics
date: 2021-01-15
journal: nan
DOI: 10.1101/2021.01.15.21249881
sha: e786821ce396f0460537573c07aa95c99c2710ec
doc_id: 704981
cord_uid: sxrowvno

The impact of variable infection risk by race and ethnicity on the dynamics of SARS-CoV-2 spread is largely unknown. Here, we fit structured compartmental models to seroprevalence data from New York State and analyze how herd immunity thresholds (HITs), final sizes, and epidemic risk changes across racial and ethnic groups. A proportionate mixing model reduced the overall HIT, but more realistic levels of assortative mixing increased the threshold. Across all models, the burden of infection fell disproportionately on minority populations: in an assortative mixing model fit to Long Island census data, 80% of Hispanics or Latinos were infected when the HIT is reached compared to 33% of non-Hispanic whites. Our findings, which are meant to be illustrative and not best estimates, demonstrate how racial and ethnic disparities can impact epidemic trajectories and result in a disproportionate distribution of the burden of SARS-CoV-2 infection.

we aim to address these questions by fitting compartmental SEIR transmission models structured 53 by race and ethnicity to seroprevalence data from New York City and Long Island [16] . We focus 54 primarily on building and analyzing variable exposure models because observed disparities in in- 55 fection rates in US cities have been strongly attributed to differences in mobility and exposure [25- 56 27] . Because of the challenges in acquiring racial and ethnic COVID-19 data [28] , including social 57 contact data that can be used in transmission models, we analyzed a range of model structures 58 that are compatible with the seroprevalence data and analyze how those assumptions affect esti-59 mates of the HIT and final epidemic size. We also characterize which groups have the highest risk 60 for infection and how that changes over time. These results highlight the importance of developing 61 COVID-19 transmission models that incorporate patterns of epidemic spread across racial and eth-62 nic groups. 63 

SEIR model 65 We initially modeled transmission dynamics in a homogeneous population using an SEIR compart- . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 15, 2021. ; for a homogeneous model. 79 We extended this model to incorporate multiple racial and ethnic groups by including SEIR com- 80 partmental variables for each group, which interact through a social contact matrix that governs the 81 interactions between and within groups. In matrix form, the structured SEIR model is given by: 

Given mean duration of infectiousness 1/γ, the next-generation matrix G, representing the average 99 number of infections in group i caused by an infected individual in group j, is given by (q1 T ) • M/γ. 100 5 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted January 15, 2021. ; https://doi.org/10.1101/2021.01.15.21249881 doi: medRxiv preprint eigenvalue of matrix G, and R t at time t was calculated by computing the dominant eigenvalue of 102 (q1 T ) • M t /γ, where the elements in M t are given by c i←j * S i (t). To hold R 0 values across model 103 types constant, we re-scaled transmission matrices to have the same dominant eigenvalue. We also 104 calculated the instantaneous incidence rate of infection at some time t for all groups by calculating 105 the force of infection λ(t) = (BI(t)) • S(t).

Structured model variants 107 Simplifying assumptions are needed to constrain the number of variables to estimate in B given 108 limited data. Under the variable susceptibility model, we set the contact rates c i←j to all be 1, in-109 dicating no heterogeneity in exposure, but allowed the q j in the susceptibility vector to vary (i.e., 110 B = q1 T ). 111 Under each of two variable exposure models, in contrast, we set the susceptibility factors q j to be 112 equal. The simplest variable exposure model we analyzed was the proportionate mixing model, 113 which assumes that the contact rate for each pair of groups is proportional to the size and activity 114 level (i.e., total number of contacts per unit time) of the two groups [32] . Denoting a i as the activ-115 ity level for a member of group i and a as the 1 × p vector of a i s, the ijth entry in the transmission 116 matrix is given by:

and the overall transmission matrix B can be written as:

Finally, under the assortative mixing assumption, we extended this model by partitioning a fraction 119 of contacts to be exclusively within-group and distributed the rest of the contacts according to pro-120 portionate mixing (with δ i,j being an indicator variable that is 1 when i = j and 0 otherwise):

Model fitting and data sources 123 6 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted January 15, 2021. ; https://doi.org/10.1101/2021.01.15.21249881 doi: medRxiv preprint the a i in the variable exposure models and the q i in the variable susceptibility models using max-125 imum likelihood fits to seroprevalence data from New York, which was collected from over 15,000 126 adults in grocery stores from April 19-28th [16] . We assumed that the seroprevalence data were 127 collected via a binomial sampling process: at a given time point t s representing the time of the sero-128 survey, the number of seropositive cases 

where L is the number of census block groups, N j,i is the number of people from demographic 143 group j in census block i, N j is the total number of people from demographic group j across the 144 city, and T i is the total number of people in census block group i. The interpretation is that the aver- . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted January 15, 2021. ; https://doi.org/10.1101/2021.01.15.21249881 doi: medRxiv preprint arg min

Using the best-fit values, we then conducted maximum-likelihood to fit the activity levels as de- Long Island resulted in even more pronounced exposure differences because of greater between-177 group differences in seropositivity (e.g., the seropositivity in Hispanics or Latinos relative to non-178 8 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 15, 2021. ; https://doi.org/10.1101/2021.01.15.21249881 doi: medRxiv preprint Figure 4) . For example, for an R 0 of 3, the HIT de-184 creases to 58% in NYC and 40% in Long Island, compared to 67% under the homogeneous model. 185 The HIT overall is reached after cumulative incidence has disproportionately increased in certain 186 minority groups: at the HIT, 75% of Hispanics or Latinos and 63% of non-Hispanic Black people 187 were infected compared to 46% of non-Hispanic whites in NYC, and 77% of Hispanics or Latinos 188 and 48% of non-Hispanic Black people were infected compared to 29% of non-Hispanic whites in 189 Long Island (Figure 2 ). 190 The estimated activity ratios indicate higher activity levels for minority groups such as Hispanics or 191 Latinos and non-Hispanic Black people, which is in line with studies using cell phone mobility data 192 [25], but the magnitudes of the activity level ratios are substantially higher than expected. This may 193 reflect some of the limitations of the proportionate mixing assumption, which does not allow for pref-194 erential within-group contacts and hence must fit observed seropositivity differences solely by scal-195 ing activity levels. To address this, we augment our model by partitioning a specified fraction of 196 9 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 15, 2021. ; https://doi.org/10.1101/2021.01.15.21249881 doi: medRxiv preprint 206 We assessed a range of values for because the serosurvey data cannot be used to also fit the 207 optimal value; given limited numbers of data points, all of the models can fit exactly to the single 208 seroprevalence time point we consider. To inform plausible assortativity levels, we instead used ad-209 ditional data on demographic distributions from the American Community Survey US census [33] . 210 We calculated the exposure index, which represents the average neighborhood's demographic com-211 10 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 15, 2021. ; https://doi.org/10.1101/2021.01.15.21249881 doi: medRxiv preprint position from the perspective of an individual from a given racial or ethnic group (Supplementary   212   Tables 1 and 2) , and used these results to fit . The exposure index describes contacts based on 213 proximity but may not capture contacts in other settings, such as work, beyond one's immediate 214 neighborhood of residence. The census data were compatible with assortative mixing matrices in 215 which 43% and 32% of contacts were exclusively within-group in NYC and Long Island, respec-216 tively (Supplementary Figure 7) . After fitting to seroprevalence data using these optimal levels, 217 we observed that the groups with higher activity levels remained the same as under proportionate 218 mixing, but the magnitudes of differences were now lower and more concordant with reported mo- Using these census-informed assortative mixing models, we then considered how the relative in-229 cidence rates of infection in demographic groups could change over the course of the epidemic. 230 Early comparisons of infection and mortality rates have helped to identify racial and ethnic groups 231 at high risk and the risk factors for infection [18] [19] [20] [21] [22] [23] [24] , but these studies often rely on cross-sectional 232 snapshots of epidemiological patterns. The challenge is that these metrics can change over time: 233 for instance, county level correlations of monthly incidence and mortality rates with percent peo-234 ple of color rose and fell in multiple regions as the epidemic progressed [39] . The reasons for these 235 changes are multifaceted, but even independent of the effect of interventions or behavioral changes, 236 models of epidemic spread in structured populations imply that incidence rate ratios for high-risk 237 groups can decrease substantially as the epidemic progresses because of depletion of susceptible 238 individuals from these groups [40, 41] . In line with this, we observe that instantaneous incidence 239 rate ratios are elevated initially in high-activity groups relative to non-Hispanic whites, but this trend 240 reverses after the epidemic has peaked -a consequence of the fact that a majority of individuals 241 have already become infected (Figure 3) . Similarly, cumulative incidence ratios remain elevated in 242 high-activity racial and ethnic groups throughout the epidemic, but the magnitude decreases as the 243 11 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 15, 2021. ; Figure 3 : Dynamics of incidence rate ratios relative to non-Hispanic whites in assortative mixing models fitted to census and serosurvey data. Dashed line represents the peak overall incidence for the epidemic. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 15, 2021. ; https://doi.org/10.1101/2021.01.15.21249881 doi: medRxiv preprint That is, we did not model the impact of non-pharmaceutical interventions such as stay-at-home poli-291 cies, closures, or the like, either in reducing the overall transmission rate or in the relative changes 292 in activity levels for different groups. Empirical evidence suggests that during periods of lockdown, 293 certain neighborhoods that are disproportionately wealthy and white tend to show greater declines 294 in mobility than others [27, 51] . These simplifying assumptions were made to aid in illustrating the 295 key findings of this model, but for more detailed predictive models, the extent to which activity level 296 differences change can be evaluated using mobility data and longitudinal survey data [25, 43] . 297 In summary, we have explored how deterministic transmission models can be extended to study the CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 15, 2021. The serosurvey data were compatible with variable susceptibility models in which Hispanics or Lati-314 nos, non-Hispanic Black people, non-Hispanic Asians, and multiracial or other people had 2.25, 315 1.62, 0.86, and 1.28 times the susceptibility to infection relative to non-Hispanic whites in NYC, re-316 spectively, and 4.32, 1.96, 0.92, and 2.48 times the susceptibility to infection relative to non-Hispanic 317 whites in Long Island, respectively. As with variable exposure models, these differences in suscep-318 tibility lowered herd immunity levels and final epidemic sizes relative to the homogeneous model 319 (Supplementary Figure 1 ), but to a lesser extent; for instance, variable susceptibility models resulted 320 in HITs ∼10% greater than HITs under proportionate mixing for Long Island. 321 The difference between these models is that incorporating heterogeneity in susceptibility only af- CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 15, 2021. ; https://doi.org/10.1101/2021.01.15.21249881 doi: medRxiv preprint

We conducted sensitivity analyses to assess whether assumptions on epidemic timing, and num-342 ber and distribution of initial infected individuals affected parameter and HIT estimates. Varying 343 the timing of epidemic start did not substantially affect HIT estimates, as long as the time between 344 epidemic start and serosurvey t s was reasonable large (e.g., > 20 days) and assortativity was low 345 ( < 0.8) (Supplementary Figure 9) . The distribution and number of initial infected individuals also 346 did not substantially affect HIT estimates for low levels of assortativity ( < 0.8) (Supplementary 347 Figures 10 and 11) . We limited our analyses to models with less than 0.8. 348 17 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. did not substantially affect HIT estimates, as long as the time between epidemic start and 401 serosurvey was reasonable (e.g., > 20 days) and assortativity was low ( < 0.8).

28 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted January 15, 2021. ; https://doi.org/10.1101/2021.01.15.21249881 doi: medRxiv preprint

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