Effects of Cocooning on Coronavirus Disease Rates after Relaxing Social Distancing

As coronavirus disease spreads throughout the United States, policymakers are contemplating reinstatement and relaxation of shelter-in-place orders. By using a model capturing high-risk populations and transmission rates estimated from hospitalization data, we found that postponing relaxation will only delay future disease waves. Cocooning vulnerable populations can prevent overwhelming medical surges.


Parameter Estimation using Austin Hospitalization Data
The city of Austin provided the total number of heads in beds for confirmed  patients in hospitals in Austin-Round Rock MSA from March 13 to April 24, 2020 (Appendix Table 2). Let H(t) be the observed and Ĥ(t) be the predicted hospitalization totals on day t, where predictions are made from the deterministic model formulation. We conducted least-squares fitting to estimate β,κ,t0, corresponding to the baseline transmission rate, the reduction in contacts following Austin's Stay Home-Work Safe Order, and the initial seed date of the epidemic respectively.
We calculated 95% confidence intervals for κ � by comparing prediction intervals from stochastic simulations with the hospitalization data. We ran 500 stochastic simulations for each of the following possible values of κ′: 0.0, 0.05, ...., 0.95, 1.0. For each value of κ′, we conducted the following analysis to determine if κ′ lies inside the 95% confidence interval for κ′.
• We compute the 95% prediction interval for ̂ across all 500 stochastic simulations for κ′ for each day t.
• We then conduct a test of the null hypothesis 0 : κ ′ = κ. 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 Nobserved is the number of data points contained within the 95% prediction band and Npoints is the total number of data points (i.e., days).
• We calculate Ncontained, the actual number of data points contained within the 95% prediction band, and compute a p-value by identifying the probability that one would observe Ncontained or more extreme results under the null distribution. If p<0.05, we reject the null hypothesis 0 : κ ′ = κ.

Model Parameters
Model parameters are provided in Appendix Tables 3-9.

Section 3. Sensitivity Analyses Sensitivity Analysis with Respect to Age-Specific Contact Rates
We conducted a sensitivity analysis in which we modeled the same 4 scenarios but without any age-specific contact rates. That is, we removed the contact matrices altogether and assume that transmission rates are homogeneous across the population. Under these conditions, we would expect cocooning to have an even larger beneficial effect (Appendix Figure 3).
Specifically, 9% of the 200 simulations exceed hospital capacity with cocooning assuming homogeneous contact rates, where the number is 19% with contact matrices. The reduction in peak hospitalization with cocooning is also higher when assuming homogeneous mixing. This likely stems from our primary model (with contact matrices) assuming that persons >65 years of age have fewer contacts on average than younger adults and children. In a sense, they are naturally cocooned by their baseline behavior. In the homogeneous contact model, this large high-risk group is more exposed, and thus even moderate cocooning has a large protective effect.

Sensitivity Analysis with Respect to Cocooning of High-Risk Persons <65 Years of Age
In the cocooned population, 34% are >65 years of age and 66% are younger persons with >1 chronic condition, as described in Appendix Section 4. When we restrict cocooning in our model to protect only persons >65 years of age, the projected epidemiologic effects are reduced (Appendix Figure 4). Not only does this reduce protection to only 34% of the vulnerable population, but it targets the subset of the high-risk population with the lowest contact rates. The younger high-risk populations who remain exposed are more likely to become infected and infect others because of their higher rates of daily contacts.

COVID-19 Complications
We estimated age-specific proportions of the population at high risk for complications from COVID-19 based on data for Austin, TX and Round-Rock, TX from the 500 Cities Project by the US Centers for Disease Control and Prevention (CDC) (16; Appendix Figure 5).
We assumed 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 (23). The estimates were obtained from the 2015-2016 Behavioral Risk Factor Surveillance System (BRFSS, https://www.cdc.gov/brfss/index.html) data by using a small-area estimation methodology called multilevel regression and poststratification (11,12), which links geocoded health surveys to high spatial resolution population demographic and socioeconomic data (12).

Estimating High-Risk Proportions for Adults
To estimate the proportion of adults at high risk for complications, we used CDC's 500 cities data, as well as data on the prevalence of HIV/AIDS, obesity, and pregnancy among adults (Appendix Table 10).
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 (24) gives United States estimates for the proportion of the adult population with 0, 1, or >2 chronic conditions, per age group. By 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 10) putting them at high-risk for complications from influenza.

HIV
We used the data from Table 20a in CDC HIV surveillance report (17) to estimate the population in each risk group living with HIV in the United States (last column, 2015 data).
Assuming independence between HIV and other chronic conditions, we increased the proportion of the population at high risk for influenza to account for persons with HIV but no other underlying conditions.

Morbid Obesity
A body mass index (BMI) >40 kg/m 2 indicates morbid obesity and is considered high risk for influenza. The 500 Cities Project reports the prevalence of obese persons in each city with BMI >30 kg/m 2 (not necessarily morbid obesity). We use the data from Table 1 in Sturm and Hattori (18) to estimate the proportion of persons with BMI >30 kg/m 2 that actually have BMI >40 kg/m 2 across the United States; we then apply this to the 500 cities obesity data to estimate the proportion of persons who are morbidly obese in each city. Table 1 of Morgan et al. (19) 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 estimated the number of pregnant women in each age group and each city, following the methodology in CDC reproductive health report (25). 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 took a different approach to estimating the proportion of children at high risk for severe influenza. The For asthma, we assumed that variation among cities would be similar for children and adults.
Thus, we used 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 (27).
We first estimated the proportion of children having either asthma, diabetes, cancer, or HIV, assuming no overlap in these conditions. We estimated city-level morbid obesity in children by using the estimated morbid obesity in adults multiplied by a national constant ratio

Resulting Estimates
We compared our estimates for the Austin-Round Rock MSA to published national-level estimates (29) of the proportion of each age group with underlying high-risk conditions (Appendix Table 11). The biggest difference was observed in older adults, with Austin having a lower proportion at risk for complications from COVID-19 than the national average; for persons 25-39 years of age, the high-risk proportion was slightly higher than the national average (Appendix Figure 5). (1 -) × (home + other) *We assume the age-specific contact rates given in (4), which takes the contact numbers estimated through diary-based POLYMOD study in Europe (5) and extrapolates to the United States. The values in Appendix Tables 6-9 are the assumed daily contacts between each pair of age groups at home, school, work, and all other places, respectively. For example, the value of 2.0 in Table A6 row 1 column 2 means that 1 person in the 0-4 age group is estimated to contact 2 people daily in the 18-64 age group at home. These contact matrices are used to adjust the transmission rate between age groups. The accuracy of the contact matrices is limited by the following: possible biases with the original diary-based study (5); assumptions made when projecting the original study to the United States (4); and impacts of coronavirus disease policies and perceptions on daily contact patterns.