It's complicated: characterizing the time-varying relationship between cell phone mobility and COVID-19 spread in the US

The study investigates whether and how the association between cell phone mobility and COVID-19 infection rates varies across space and time in the United States. Early in the pandemic, mobility appeared strongly linked to transmission, but it is uncertain if this relationship persisted beyond spring 2020 or across different geographies. The authors aim to build interpretable models that can separate local and temporal effects despite incomplete, heterogeneous, and non-stationary data. The purpose is to assess the reliability of mobility as a leading indicator for outbreaks to inform public health decisions. The importance lies in clarifying when and where mobility metrics provide actionable insight, accounting for overlapping non-pharmaceutical interventions, changing behaviors (e.g., mask-wearing), and reporting challenges.

Prior work identified associations between infection rates and factors such as mask-wearing, weather, and demography, and studied the effects of NPIs like lockdowns. Many early mobility studies relied on limited time windows (often through June 2020), focused on major cities or state-level analyses, and commonly assumed a stationary relationship between mobility and infection rates. As behavior, guidance, and adherence evolved, coarse mobility may no longer reliably proxy risky person-to-person interactions, suggesting non-stationarity. Existing models also faced data limitations (reporting delays, day-of-week effects, variable testing, short observation periods) that complicate inference about local outbreaks over time. With few exceptions, earlier approaches did not allow the mobility–infection relationship to vary over space and time, potentially leading to overgeneralized conclusions.

Design: A hierarchical Bayesian multilevel regression relates weekly county-level infection growth rates to mobility, masks, temperature, and population, with time- and space-varying mobility effects. The model balances flexibility and interpretability to capture spatiotemporal heterogeneity without overfitting. Outcome: Weekly infection growth rate for county i and week t, defined as the log ratio of total inferred infections over two consecutive 2-week windows, y_it = log(r_it / r_i(t-1)), where r_it is the 2-week sum. Incidence is inferred from reported cases via statistical deconvolution to approximate true infection time series. Data: 2951 US counties (≈94% of 3143; 99.7% of population), Feb 2020–Feb 2021. Case data from The New York Times and NYC DOH. Mobility from Google Community Mobility Reports (six categories: grocery/pharmacy, residential, retail/recreation, workplace, transit, parks); robustness assessed with SafeGraph’s completely-at-home metric. Mask adherence from Pew, NYT/Dynata, and CMU Delphi; temperature and county population included. Mobility feature engineering: To mitigate strong collinearity among Google’s six series, compute the first principal component (PCA), enforcing a positive loading for workplace so higher values imply more time in public/less time at home. Use a 3-week moving average of this univariate mobility index. Mask featurization: Construct a state-level time series by combining surveys: Pew (June 7 and Aug 8, 2020), NYT/Dynata (county-level July 2–14, 2020), and CMU Delphi (state-level daily from Sept 8, 2020). Linearly interpolate between survey dates with a monotonicity constraint to avoid unrealistic increases; assume near-zero adherence until one week after CDC’s April 4, 2020 mask recommendation, then hold at the June 7 value through that date. Missing data imputation: Use MICE (multivariate imputation by chained equations) with predictive mean matching, including temporal trends via natural cubic splines within Census divisions and CSAs. Generate 25 multiply imputed datasets and average imputations for modeling. Exclusions: Remove counties with <250 total cases by Feb 20, 2021 (n=176); with extreme weekly absolute growth rate >2 (n=8); or >1.5 in counties with <50,000 population (n=8), to reduce outlier effects (e.g., prison outbreaks). Model specification: For county i in CSA c and state s at week t: y_it = α_c + X_it β + T_it θ + C_st γ + M_it γ_ct + ε_it, with ε_it ~ N(0, σ^2). Covariates include centered/scaled log population (X_it), weekly temperature (T_it), state-level mask adherence (C_st), and mobility (M_it). The mobility effect γ_ct varies by CSA and over time. Time-variation: Parameterize γ_ct via a weight matrix W and a CSA-specific vector ρ_c, with γ_ct = W_t ρ_c. Assume piecewise-constant effects over four 13-week “waves”: 2020-02-22–05-23; 2020-05-30–08-22; 2020-08-29–11-21; 2020-11-28–2021-02-20. This yields four coefficients per CSA. Hierarchical priors: Joint Gaussian for [α_c, ρ_c] with covariance Σ = diag(τ) Ω diag(τ); Ω ~ LKJ(2), τ half-t(df=3). The population-level intercept has a t prior (df=3). Flat improper priors on certain fixed effects as specified. To ensure physically plausible signs, post-process posterior samples to enforce γ_ct ≥ 0 via thresholding at zero (found comparable to log-normal parameterization but faster to sample). Estimation: Fit with R brms (Stan). Two chains, 7000 iterations (2000 warm-up), adapt_delta=0.9995, max_treedepth=25, thin by 5. Convergence diagnostics: R-hat < 1.05; effective sample sizes > 1000. Evaluate R² overall, by time, geography, population strata, and via ablations varying spatial clustering (none, region, CSA) and temporal flexibility (constant vs time-varying). Conduct sensitivity analysis using SafeGraph mobility metric instead of Google PCA. Modeling pitfalls and ablations: Demonstrate overfitting risks when allowing too much temporal flexibility (e.g., monthly varying mobility or temperature effects) and misleading inferences due to collinearity when using all six mobility series directly. Final model uses PCA mobility and wave-wise effects by CSA. Compare to overly rigid models (national or region-level constant effects) that wash out local temporal patterns.

- Strong first-wave association: Mobility strongly predicted weekly infection growth rates during Feb 29–May 23, 2020, especially in the most populous counties and urban CSAs (e.g., New York City). Sharp mobility drops coincided with declining infection growth. - Non-stationarity across time and space: The mobility–infection relationship varied markedly across regions and waves. Effects were near zero across much of the South and parts of the West/Midwest in the first wave; signals weakened in the second wave; were strongest in the Midwest in the third wave; and appeared stronger in parts of winter 2020–21 but with often modest R². - Model performance patterns: R² was highest early in the pandemic and in high-population counties (>250,000). Rural counties (<25,000) had low R². The Northeast had the best fit; the South the poorest. High performance coincided with extremely low mobility levels in the first wave; by waves 3–4, differences in R² by mobility level were minimal, indicating a weakened association. - Quantitative performance (Table 1, final model): CSA-clustered, time-varying mobility effects achieved overall R² ≈ 0.261; by region: Midwest ≈ 0.364, Northeast ≈ 0.404, South ≈ 0.151, West ≈ 0.250. Simpler models markedly underperformed (e.g., no clustering, constant effect overall R² ≈ 0.163; Northeast ≈ 0.186 vs 0.404 for final model). - Mask adherence effect: Modeling masks as a national, time-constant effect estimated that a 10% absolute increase in mask adherence corresponds to an expected ≈2% decrease in infection growth rate. Including masks increased overall R² by ≈10% in the four weeks after April 4, 2020. - Robustness to mobility source: Using SafeGraph’s completely-at-home metric produced conclusions similar to Google PCA. During Mar–Jun 2020, absolute correlations between SafeGraph and all six Google mobility categories were high; these correlations decayed by May–Oct 2020, indicating that coarse mobility measures began capturing different aspects of movement and less reliably proxying risky contacts. - Modeling lessons: Overly flexible models (e.g., freely time-varying effects for mobility and temperature) overfit and can ascribe misleading effects. Overly rigid models (national or region-level constants) average over important local effects, changing substantive conclusions (e.g., incorrectly inferring persistent mobility effects in NYC during wave 3).

The study demonstrates that the mobility–COVID-19 relationship is highly time- and location-dependent. Mobility was a robust predictor only during the initial wave and particularly in populous, urban areas. As behaviors and policies evolved (e.g., increased masking, hygiene, social distancing), coarse cell phone mobility became a poorer proxy for risky in-person interactions, leading to weakened and heterogeneous associations. This addresses the central question by showing that mobility is not a stable leading indicator across the pandemic timeline and geographies. Modeling implications are that analyses must either target specific periods and locales or explicitly incorporate spatiotemporally varying effects; otherwise, models risk both overfitting (with excessive flexibility) and underfitting (with overly rigid assumptions), yielding spurious or averaged-out conclusions. For public health, reliance on coarse mobility alone is insufficient; other factors must be incorporated to assess potential transmission risk, and interpretations should be localized and time-aware.

The authors introduce an interpretable multilevel Bayesian framework with CSA-level, wave-wise mobility effects to characterize spatiotemporal variability in the association between mobility and COVID-19 infection growth. Using one year of county-level US data, they find strong associations during spring 2020 in populous areas, but substantial weakening and heterogeneity thereafter. Mobility thus does not serve as a reliable, universal leading indicator of transmission across time and space. The work cautions against both overly flexible and overly rigid modeling choices and underscores the need for time- and place-specific analyses. Future research should incorporate evolving factors such as variants and vaccination, improved measures of risky contacts, hospitalization data at fine spatial scales, and mobility dimensions relevant to settings like schools, as well as better treatment of seasonality.

- Differential testing and reporting: Persistent, location- and time-varying differences in testing and reporting affect inference. Growth-rate modeling helps but cannot address long-term testing trends fully. - Outcome data constraints: County-level hospitalization data are limited, preventing use of potentially more stable outcomes. - Mask adherence data: Limited detail early in the pandemic complicates disentangling mask and mobility effects; mask feature construction relies on survey interpolation and assumptions (e.g., monotonicity, zero adherence before mid-April). - Missing data and imputation: Mobility and temperature series required imputation (MICE), embedding assumptions that are difficult to verify. - Short observation window: Only one year of data limits the ability to model or correct for seasonality (e.g., temperature effects). - Mobility measure coarseness: Google’s six categories are coarse and may not capture key contexts (e.g., school/university movements); the best proxy may vary over time and by location. - Modeling choices: Mobility effects constrained to four 13-week waves may miss subtler dynamics; the regression framework estimates associations but cannot simulate counterfactuals as compartmental models can.