Estimated Association of Construction Work With Risks of COVID-19 Infection and Hospitalization in Texas

Key Points Question Is construction work associated with increased community transmission of coronavirus disease 2019 (COVID-19) and disproportionate morbidity among construction workers in US cities? Findings This decision analytical model of COVID-19 found that resuming construction work during shelter-in-place orders was associated with increased hospitalization risks in the construction workforce and increase transmission in the surrounding community. Based on COVID-19 hospitalization data through August 20, 2020, construction workers had a nearly 5-fold increased risk of hospitalization in central Texas compared with other occupational categories. Meaning The findings of this study suggest that enacting workplace safety policies and providing paid sick leave could protect essential workers in high-contact industries and prevent further widening of disparities in COVID-19 morbidity and mortality.

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., 30 this ratio represents the prevalence in morbid obesity in children given the one observed in adults. From Morgan et al., 7 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 31 of the proportion of each age group with underlying high risk conditions (Table S2). 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 olds the high risk proportion is slightly higher than the national average. Figure S1. Demographic and risk composition of the Austin-Round Rock MSA. 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, 5 reported HIV prevalence, 6 and reported morbid obesity prevalence, 7,8 corrected for multiple conditions. The population of pregnant women is derived using the CDC's method combining fertility, abortion and fetal loss rates. [32][33][34] Table S1. 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 5 HIV/AIDS CDC HIV Surveillance report 6 Obesity CDC 500 cities, 5 Sturm and Hattori 8 Morgan et al. 7 Pregnancy National Vital Statistics Reports 32 and abortion data 33  35 and Hamer et al. 36 suggest that black race, lack of insurance, male sex, smoking, obesity, and physical inactivity increase risk.
In order to assess the adequacy of our model, we measured the correlation between the prevalence of high risk conditions assumed by our model and the prevalence of other COVID-19 high risk conditions, namely obesity, physical activity, insurance rates, and smoking rates across the cities included in the CDC 500 Cities's dataset. 5 We find a high degree of overlap, with uninsured rates having the lowest correlation ( Figure S2). Figure S2. Correlation between high risk proportions assumed in the model (y-axis) and other COVID-19 high-risk factors (x-axes): lack of health insurance, smoking, obesity, and physical inactivity prevalence. Each point corresponds to a city included in the CDC's 500 cities project. Numbers in plots are the Pearson correlation coefficients.

Structure
The model structure is diagrammed in Figure S3 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), pre-symptomatic infectious (P Y ), pre-asymptomatic infectious (P A ), symptomatic infectious (I Y ), asymptomatic infectious (I A ), symptomatic infectious that are hospitalized (I H ), recovered (R), and deceased (D). The symbols S, E, P Y , P A ,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 . The model for individuals in age group and risk group is given by: where A and K are all possible age and risk groups, , , , are the relative infectiousness of the , , , compartments, respectively, is transmission rate, , is the mixing rate between age group , ∈ , , , are the recovery rates for the , , compartments, respectively, is the exposed rate, , are the pre-(a)symptomatic rates, 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. We model stochastic transitions between compartments using the -leap method 2,3 with key parameters given in Table S3. 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: with and where denotes the force of infection for individuals in age group and risk group and is given by: Figure S3. Compartmental model of COVID-19 transmission Each subgroup (defined by age and risk) is modeled with a separate set of compartments. Upon infection, susceptible individuals (S) progress to exposed (E) and then to either pre-symptomatic infectious ( ) or preasymptomatic infectious ( ) from which they move to symptomatic infectious (I Y ) and asymptomatic infectious (I A ) respectively. All asymptomatic cases eventually progress to a recovered class where they remain protected from future infection (R); symptomatic cases are either hospitalized (I H ) or recover. Mortality (D) varies by age group and risk group and is assumed to be preceded by hospitalization.

Parameters
Individuals were initially separated into five age groups: 0-4, 5-7, 18-49, 50-64, and 65+ years old based on population data for the five-county Austin-Round Rock Metropolitan Area from the 2017 American Community Survey. 4 Each age group was divided into a low-risk and high-risk group, based on the prevalence of chronic conditions estimated for the Austin population (Fig. S2). 5- 8 We also estimated the proportion of pregnant women in each age group as a special risk class. 9 All individuals were assumed to be susceptible to the disease.
There are an estimated 50,000 construction workers in the Austin metropolitan area representing over 4% of the labor force, 10 not accounting for undocumented workers. We assumed all construction workers to be in the 18-49 group for simplicity, with the same low/high-risk distribution, and we modeled them as a 6 th separate group with specific contacts, adding an extra row and an extra column to the contact matrices specifically for construction workers so as to be able to model their specific contact patterns as intended. All details on the construction of the adjusted contact matrices as well as the derived matrices are provided in sections 2.3-2.5. In order to keep the total population constant, we reduced the number of individuals in the 18-49 group according to the number of construction workers.
Infected individuals were modeled to enter an incubation period where they were symptom-free and not yet infectious. They then enter a pre-(a)symptomatic compartment where they do not present symptoms yet but they already transmit the disease, 11 with distinction between asymptomatic and symptomatic starting in this compartment. Individuals then progressed accordingly to either a symptomatic or asymptomatic compartment. Asymptomatic individuals were assumed to have the same pre-symptomatic and infectious period as symptomatic individuals but lower infectiousness. 12 The rates at which symptomatic cases were moved to a hospitalized compartment and died depended on both age and risk group. Recovered individuals were considered fully immune.
All model parameters are provided in Tables S3-S5 and were based on published estimates from COVID-19 studies as well as input from the US CDC and City of Austin. Age-specific contact rates were estimated using contact matrices published by Prem et al. and are adjusted to model school closures and various levels of social distancing. 13 The pre-symptomatic period was sampled from a triangular distribution from 1.9 days to 3.9 days with mean of 2.9 days 11,14 and the infectious period was sampled from a triangular distribution from 3 days to 5 days with mean of 4 days, 11 with a mean generation interval estimated at 5.8 days. 14 We assumed the asymptomatic ratio to be 43% 15 with 44% of infections arising from pre-symptomatic transmission during the incubation period. 11 Following the CDC's planning scenarios and observed data from the 2009 H1N1 pandemic in the United States, we assumed that the infection hospitalization rate and infection fatality rate was ten times higher in high-risk than low-risk individuals, within each age group. The average length of stay of 11 days in the hospital for people who survive and recover and 7.8 days for people who die is estimated using arrival and departure data from the Seton system in Austin. 16,17 We estimate and simultaneously using a nonlinear least squares fitting procedure in the SciPy/Python package 18 For a given pair of and , we run a deterministic simulation of our model assuming central values for each parameter. Using a trust region method, the algorithm finds values of and that minimize the sum of squared daily differences between the simulated ( ) and actual ( ) daily hospitalizations from March 13, 2020 through May 3, 2020: . We calculated 95% confidence intervals for the social distancing parameter indirectly by running 500 stochastic simulations for each of the following possible values of : 0.0, 0.05, ...., 0.95, 1.0. For each value of , we conducted the following analysis to determine if lies inside the 95% confidence interval for .
• For all simulations, we calculate the day-to-day difference in hospitalizations (i.e., heads in beds) during the period following the Stay Home-Work Safe order: . We do the same for the actual data: .
• We compute the 95% prediction interval for across all 500 stochastic simulations for for each day .
• We then conduct a test of the null hypothesis . Under this null hypothesis, we would expect roughly 95% of the observed data ( ) to fall within the 95% prediction band for that we constructed from our simulations. By analyzing the day-to-day difference in hospitalizations rather than daily hospitalizations, we can assume that the data are independent from one day to the next. Then the expected number of observed values contained in the 95% prediction band is given by the binomial expression: where is the number of data points contained within the 95% prediction band and is the total number of data points (i.e., days).
• If the binomial probability of is less than 0.05, we reject the null hypothesis .
To construct a 95% confidence interval for we take the minimum and maximum for which we did not reject the null hypothesis .
In order to obtain 95% confidence intervals for the basic reproductive number and the doubling time we calculated the 95% confidence interval for the transmission rate using the same methodology as that used for the social distancing parameter . We fixed the social distancing parameter at its best estimated value and ran 500 stochastic simulations for each of the possible values of : , , ... , with our best estimate for the transmission rate. We then conducted the same analysis as that described above and the 95% confidence interval for is obtained by taking the minimum and maximum for which we did not reject the null hypothesis .
The confidence intervals for and the doubling time are then obtained by using the confidence interval bounds of as input to the system's Next Generation Matrix.

Model modification to incorporate construction workforce
We assume there are currently 50,000 construction workers in the Austin-Round Rock MSA, all in the 18-49 yearold age group. The proportion of construction workers at high-risk of complications from COVID-19 is the same as the overall 18-49y age group in the Austin-Round Rock MSA.
We extended our US COVID-19 Pandemic Model to include a separate population subgroup representing construction workers. We moved 50,000 individuals from the regular 18-49y low risk and high risk compartments into the corresponding construction compartments. We also extended the contact matrices 1 governing transmission between age groups to allow us to manipulate the number of construction workers and intensity of their contacts separately from the rest of the workforce. Initially, we set their contact rates equal to those of the entire 18-49y population, except that we assume that all work contacts take place within the subgroup of construction workers. Social distancing measures reduce home, work and other contacts for non-construction workers and home and other contacts for construction workers. Tables S6-S9 give the original contact matrices and Tables S10-S13 give the updated contact matrices assuming 50,000 construction workers.
Let ( ) , denote the average daily number of contacts that a person in group has with people in group at location . Let denote the proportion of construction workers in the 18-49y group.

Original 5-age groups contact matrices
Age-specific contact rates were estimated by adjusting contact matrices published by Prem et al. 13      We assume that, without construction work, the community-wide reproduction number is below one. Basic epidemiology tells us that if the average number of secondary infections from infected construction workers to other construction workers exceeds one, then the community-wide reproduction number will also rise above one. We use this approach to determine the level of worksite transmission risk above which construction work undermines community mitigation (i.e., raises R0 above one).
Let denote the average number of secondary infections from an infected construction worker. We decompose this quantity into where and represent the number of infections occurring at work and other locations, respectively. Our model assumes that construction workers only have contacts with other workers while at work, so that represents infections among workers. In general, indicates the proportional change in transmission risk on construction sites that would raise or lower to one.
Using our estimates for the population-wide reproduction number of COVID-19 in Austin (see eAppendix 2.2) and published estimates for workplace and other contact patterns (see eAppendix 2.4), we estimate for the Austin area construction workforce, as follows.
• We assume that, in the absence of COVID-19 mitigation measures, the basic reproduction number for construction workers is the same as the population-wide basic reproduction number ( ) and that the average number of workplace secondary infections for construction workers ( ) is equal to the average number of secondary infections at the average workplace for the population as a whole.
• Let , , and denote the contact matrices governing interactions at home, work, school and other locations, provided in ref. 1 . We then estimate the typical weekday and weekend contact matrices as: and . and the average weekly contact matrix as: .
Let n be vector giving the population proportions for each age group and be the vector of ones of the same dimension as n. Then the average number of weekly contacts in the population is given by .
Similarly the average number of weekly workplace contacts is given by .
• Let be a constant proportional to the transmission rate of the virus, such that and . This implies that .
• Given our estimate of for Austin in March 2020 (Table S4), we thereby estimate that the average number of workplace secondary infections for construction workers is . Given that , we estimate that a 14% increase in workplace transmission risks relative to average workplace risk would enable sustained transmission among the construction workforce and undermine community wide social distancing efforts.  In our main results, we assume that the high risk proportion among construction workers is the same as the general 18-49y population. Thus, the estimated excess risk of hospitalizations among construction workers stems solely from increased exposure at work. Given that the construction workforce may experience higher rates of high risk conditions 37,38 stemming from overlapping socioeconomic, racial, occupational and health vulnerabilities, we varied the high risk proportion for the construction workforce. Specifically, we held the overall high risk proportion constant (for the population as a whole) and adjusted the ratio between the construction high risk proportion and the general 18-49y high risk proportion. We considered eight different ratios ranging from 0.8 (high risk proportion 20% lower in construction workers) to 2.0 (proportion double in construction workers). Let and denote the proportion of high-risk individuals among construction workers and among 18-49y in the general population, respectively. We varied the number of high-risk construction workers and 18-49y such that: . The primary analysis presented in the manuscript assumes equal high risk proportions in the two groups and corresponds to . For each of these ratios, the corresponding numbers and proportions of high-risk construction workers and other adults in the 18-49 group are given in table S14.
Table S15. Numbers and proportions of high-risk individuals among construction workers and nonconstruction workers in the 18-49y age group for the eight different risk scenarios. The ratio of high risk proportions, given as column headings, equals the proportion in the second row divided by the proportion in the fourth row.  Figure S5 compares the estimated relative risk of hospitalizations for construction workers through August 17, 2020 across the eight different scenarios. As in Figure 3, we calculated the ratio of hospitalization rate among construction workers and the hospitalization rate among other 18-49y.