Impact of Social Distancing Measures on Coronavirus Disease Healthcare Demand, Central Texas, USA

Social distancing orders have been enacted worldwide to slow the coronavirus disease (COVID-19) pandemic, reduce strain on healthcare systems, and prevent deaths. To estimate the impact of the timing and intensity of such measures, we built a mathematical model of COVID-19 transmission that incorporates age-stratified risks and contact patterns and projects numbers of hospitalizations, patients in intensive care units, ventilator needs, and deaths within US cities. Focusing on the Austin metropolitan area of Texas, we found that immediate and extensive social distancing measures were required to ensure that COVID-19 cases did not exceed local hospital capacity by early May 2020. School closures alone hardly changed the epidemic curve. A 2-week delay in implementation was projected to accelerate the timing of peak healthcare needs by 4 weeks and cause a bed shortage in intensive care units. This analysis informed the Stay Home-Work Safe order enacted by Austin on March 24, 2020.


Section 1. COVID-19 Epidemic Model Structure and Parameters
The model structure is diagrammed in Appendix Figure 1 and described in the equations below.
For each age and risk group, we build a separate set of compartments to model the transitions between the states: susceptible (S), exposed (E ), symptomatic infectious (I Y ), asymptomatic infectious (I A ), symptomatic infectious that are hospitalized (I H ), recovered (R ), and deceased (D). The symbols S, E, I Y , I A , I H , R, and D denote the number of people in that state in the given age/risk group and the total size of the age/risk group is N = S + E + I Y + I A + I H + R + D .
The model for individuals in age group a and risk group r is given by: where A and K are all possible age and risk groups, ω A , ω Y , ω H are relative infectiousness of the I A , I Y , E compartments, respectively, is transmission rate, φa,i is the mixing rate between age group a, i ∈ A, γ A ,γ Y , γ H are the recovery rates for the I A , I Y , I H compartments, respectively, is the exposed rate, is the symptomatic ratio, is the proportion of symptomatic individuals requiring hospitalization, is rate at which hospitalized cases enter the hospital following symptom onset, is mortality rate for hospitalized cases, and is rate at which terminal patients die.
Initial conditions, school closures and social distancing policies are shown in Appendix Table 1. We model stochastic transitions between compartments using the -leap method (1,2) with key parameters given in Appendix Table 2. Hospitalization parameters are shown in Appendix Table 3. Assuming that the events at each time-step are independent and do not impact the underlying transition rates, the numbers of each type of event should follow Poisson distributions with means equal to the rate parameters. We thus simulate the model according to the following equations: IaH,r (t + 1) − IaH,r (t) = P 5 − P 6 − P 7 Ra,r (t + 1) − Ra,r (t) = P 3 + P 4 + P 6 and where F a,r denotes the force of infection for individuals in age group and risk group and is given by: individuals (S) progress to exposed (E) and then to either symptomatic infectious (I Y ) or asymptomatic infectious (IA). All asymptomatic cases eventually progress to a recovered class where they remain protected from future infection (R ); symptomatic cases are either hospitalized (I) or recover. Mortality (D ) varies by age group and risk group and is assumed to be preceded by hospitalization.
*The parameter β is fitted through constrained trust-region optimization in SciPy/Python (14). Given a value of β, a deterministic simulation is run based on central values for each parameter, from which we can compute the implied R0 (β). We (1) track the daily number of new cases It (both symptomatic and asymptomatic) during the exponential growth portion of the epidemic (2), compute the log of the number of new cases: yt = log (It) and (3) use least squares to fit a line to this curve: log (It) = y0 + g × t. We then estimate the reproduction number R0 (β) of the simulation for that specific value of β as R0 (β) = 1 Γ + g × 1 where Γ is the generation time given by Γ = δ(R0 − 1)/log(2). The optimizing function runs until the resulting value of R0 (β) does not get closer to the target value.
We (1)   Estimates provided by each of the region's hospital systems and aggregated by regional public health leaders Appendix

COVID-19 complications
High-risk conditions for influenza and data sources for prevalence estimation are shown in Appendix Table 8. We estimate age-specific proportions of the population at high risk of complications from COVID-19 based on data for Austin, TX and Round-Rock, TX from the CDC's 500 cities project (Appendix Figure 2) (15). We assume that high risk conditions for COVID-19 are the same as those specified for influenza by the CDC (10). The CDC's 500 cities project provides city-specific estimates of prevalence for several of these conditions among adults (16). The estimates were obtained from the 2015-2016 Behavioral Risk Factor Surveillance System (BRFSS) data using a small-area estimation method known as multilevel regression and poststratification (11,12). It links geocoded health surveys to high spatial resolution population demographic and socioeconomic data (12).
Projected weekly incident COVID-19 cases are shown in Appendix Figure 3, and projected COVID-19 healthcare demand and cumulative deaths are shown in Appendix Figure 4.

Estimating High-Risk Proportions for Adults
To estimate the proportion of adults at high risk for complications, we use the CDC's 500 cities data, as well as data on the prevalence of HIV/AIDS, obesity and pregnancy among adults (Appendix Table 2).
The CDC 500 cities dataset includes the prevalence of each condition on its own, rather than the prevalence of multiple conditions (e.g., dyads or triads). Thus, we use separate comorbidity estimates to determine overlap. Reference about chronic conditions (17) gives US estimates for the proportion of the adult population with 0, 1 or >2 chronic conditions, per age group. Using this and the 500 cities data we can estimate the proportion of the population pHR in each age group in each city with >1 chronic condition listed in the CDC 500 cities data (Appendix Table 2) putting them at high risk for flu complications.

HIV
We use the data from Table 20 in a CDC HIV surveillance report (18) to estimate the population in each risk group living with HIV in the U.S. (last column, 2015 data). Assuming independence between HIV and other chronic conditions, we increase the proportion of the population at high-risk for influenza to account for individuals with HIV but no other underlying conditions.

Morbid Obesity
A BMI >40 kg/m 2 indicates morbid obesity and is considered high risk for influenza. The 500 Cities Project reports the prevalence of obese people in each city with BMI > 30 kg/m 2 (not necessarily morbid obesity). We use the data from Table 1 in Sturm and Hattori (19) to estimate the proportion of people with a BMI >30 that actually have a BMI >40 (across the United States); we then apply this to the 500 Cities obesity data to estimate the proportion of people who are morbidly obese in each city. Table 1 of Morgan et al. (20) suggests that 51.2% of morbidly obese adults have >1 other high risk chronic condition, and update our high-risk population estimates accordingly to account for overlap.

Pregnancy
We separately estimate the number of pregnant women in each age group and each city, following the methods in the CDC reproductive health report (21). We assume independence between any of the high-risk factors and pregnancy, and further assume that half the population are women.

Estimating High-Risk Proportions for Children
Since the 500 Cities Project only reports data for adults >18 years of age, we take a different approach to estimating the proportion of children at high risk for severe influenza. The 2 most prevalent risk factors for children are asthma and obesity; we also account for childhood diabetes, HIV and cancer.
From Miller et al. (22), we obtain national estimates of chronic conditions in children. For asthma, we assume that variation among cities will be similar for children and adults. Thus, we use the relative prevalence of asthma in adults to scale our estimates for children in each city. The prevalence of HIV and cancer in children are taken from CDC HIV surveillance report (18) and cancer research report (23), respectively.
We first estimate the proportion of children having either asthma, diabetes, cancer or HIV (assuming no overlap in these conditions). We estimate city-level morbid obesity in children using the estimated morbid obesity in adults multiplied by a national constant ratio for each age group estimated from Hales et al. (24), this ratio represents the prevalence in morbid obesity in children given the one observed in adults. From Morgan et al. (20), we estimate that 25% of morbidly obese children have another high-risk condition and adjust our final estimates accordingly.

Resulting Estimates
We compare our estimates for the Austin-Round Rock Metropolitan Area to published national-level estimates (25) of the proportion of each age group with underlying high risk conditions (Appendix Table 9). The biggest difference is observed in older adults, with Austin having a lower proportion at risk for complications for COVID-19 than the national average; for [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] year-old the high risk proportion is slightly higher than the national average.

Appendix Figure 2. Demographic and risk composition of the Austin-Round Rock population. Bars
indicate age-specific population sizes, separated by low risk, high risk, and pregnant. High risk is defined as individuals with cancer, chronic kidney disease, COPD, heart disease, stroke, asthma, diabetes, HIV/AIDS, and morbid obesity, as estimated from the CDC 500 Cities Project (15), reported HIV prevalence (18) and reported morbid obesity prevalence (19,20), corrected for multiple conditions. The population of pregnant women is derived using the CDC's method combining fertility, abortion and fetal loss rates (26)(27)(28).
Appendix Table 8. High-risk conditions for influenza and data sources for prevalence estimation Condition Data source Cancer (except skin), chronic kidney disease, COPD, coronary heart disease, stroke, asthma, diabetes CDC 500 cities (29) HIV/AIDS CDC HIV Surveillance report (

Section 3. Sensitivity Analysis with Respect to R0
Our base scenarios assume a basic reproductive number (R0) of 2.

Section 4. Sensitivity Analysis with Respect to Healthcare Durations
With the assumption that the healthcare system is likely to perform less effectively under the highly stressed condition, patient discharge might take longer in the surge setting. As sensitivity analysis, we analyzed longer duration hospital, ICU and ventilator treatment (Appendix Table 10). The results are summarized in Appendix Tables 11, 12 and Appendix Figure 5.

Section 5. Impact of 2-Week and 4-Week Delays in Implementation of Social
Distancing Interventions, 2020.
We also modeled intermediate delays of 2 weeks (March 28) and 4 weeks (April 11). Even 2-week delays undermine the efficacy of the interventions with respect to reducing healthcare demand below local capacity (Appendix Figure 6, Appendix Table 13).