Outcomes Associated With Social Distancing Policies in St Louis, Missouri, During the Early Phase of the COVID-19 Pandemic

Key Points Question Given the geographic heterogeneity of the COVID-19 pandemic, is it possible to assess the outcomes of delayed social distancing policies within any one geographic location? Findings In this decision analytical model of 1.3 million people in St Louis, Missouri, a delay of 2 weeks in public health policies initiated on March 17, 2020, was estimated to be associated with a nearly 6-fold total increase in deaths due to COVID-19 by June 15, 2020. Meaning These findings suggest that timely local social distancing policies are associated with the number of COVID-19–related hospitalizations and deaths; local public health policies may avoid more severe pandemic consequences even in a widespread pandemic.


eMethods. Overview of Compartmental Model
The Local Epidemic Modeling for Management & Action (LEMMA) model used in this analysis is a discrete time compartmental epidemic model. 1 The version of the model (V 1.0; https://github.com/LocalEpi/LEMMA/tree/StLouis) used in the current analysis is an eight compartment model, which extends the classic four compartment Susceptible-Exposed-Infectious-Removed structure to incorporate disease severity, hospitalization and ICU use. Specifically, the population is conceptualized as existing in one of 8 states: 1) Susceptible to infection; 2) Exposed to SARS Cov-2, but not yet Infectious; 3a) Infected with SARS Cov-2 and Infectious to others with a more severe infection that will (with delay) lead to hospitalization; 3b) Infected with SARS Cov-2 and Infectious to others with a mild infection that will not lead to hospitalization; 4a) Hospitalized, but not in the ICU; 4b) Hospitalized in the ICU; 5a) Deceased; 5b) Recovered and Immune.
Model dynamics are deterministic on a discrete time scale. Specifically, on each day a fixed proportion of exposed become infected, a fixed proportion of infected become either hospitalized or recover and a fixed proportion of those in the ICU either die or recover. The proportion of those susceptible that become exposed is proportional to the number of infected and the time-varying effective contact rate parameter. Key epidemiologic and context parameters are treated as unknown and estimated based on local input data and user-specified prior distributions using Bayesian inference methods. Specifically, in the version of the model used in this analysis, posterior distributions on the following parameters were estimated: Basic reproductive number R0 before Intervention; Number of Days from Infection to Becoming Infectious (Latent Period); Duration of infectiousness (days); Time from onset of infectiousness to hospitalization (days); Average Hospital Length of Stay for Patients not in ICU (Days); Average Hospital Length of Stay for Patients in ICU (Days); Percent of Infected that are Hospitalized; Percent of Hospitalized COVID-19 Patients That are Currently in the ICU; Mortality Rate among ICU COVID-19 Patients. In the version of the model used in this analysis, the timing and magnitude of changes in the effective contact rate (and by extension, the effective reproductive number) constituted additional parameters with posterior distributions estimated during model calibration.
Point estimates and credibility intervals for unknown parameters are generated based on data inputs using the Stan programming language. Stan uses Markov chain Monte Carlo methods, in particular the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. 2,3 As with compartmental models generally, additional assumptions of the model include a closed population and random mixing. The hospitalization model used in this analysis also made a number of simplifying assumptions, with the aim of decreasing the number of parameters to be estimated from data, an important consideration particularly early during the pandemic when reliable data available to calibrate the model were sparse. Specifically, the hospitalization model used here partitioned hospitalized patents into ICU and non-ICU patients, rather than explicitly modeling transitions between these states. It further made the simplifying assumption that all deaths occur among ICU patients. The current version of the LEMMA model (V 2.0) relaxes the above simplifying assumptions and uses a hospital model with more complexity. Due to the early stage of the epidemic to which it was applied, the version of the model used in this analysis further did not incorporate the possibility of waning immunity or re-infection. Version 2.0 allows for (user-specified) transitions from a recovered immune state back to a susceptible state.
In the current analysis, the model was calibrated to hospital census data only, given the sparsity of reliable testing data and other data sources available early during the pandemic. LEMMA supports the option to calibrate to multiple additional data sources, including deaths, cases, hospital admissions, ICU use, and, in Version 2.0, regional seroprevalence estimates and vaccine doses distributed. Incorporation of variants is also supported via input parameters on relative variant prevalence and growth rates, as well as epidemiologic characteristics of the variants (eg., relative transmissibility and severity, vaccine efficacy after first and second dose). Given the early stage of the epidemic to which it was applied, however, the current analysis employed a simpler model structure with no vaccine deployment and a single variant.
All code is open source and available on Github (https://github.com/LocalEpi/LEMMA/). Users can flexibly modify prior distributions on parameters, data inputs, and scenarios considered (including vaccine deployment, changes in effective contact rate, and variants) through either an Excel interface available on Github, or via an R shiny Application (https://localepi.shinyapps.io/LEMMA-Shiny; with automated data integration for all California counties).

eFigure 2. Projected Versus Actual COVID-19 Hospitalizations and Deaths
Using data from hospital census up until April 1 (Panel A) or May 1 (Panel B)indicated as black vertical line on those datesto calibrate the model, subsequent projections over time resemble actuals in both the number hospitalized over time as well as cumulative deaths. Projected and actuals were very similar over 12 weeks after last data input.