Projecting hospital utilization during the COVID-19 outbreaks in the United States

Significance Our results highlight that the growing coronavirus disease 2019 (COVID-19) outbreak in the United States could gravely challenge the critical care capacity, thereby exacerbating case fatality rates. In the absence of a preventive vaccine, efforts to contain the outbreak, such as improving self-isolation rates and encouraging better hygiene practices, can alleviate some of the pressures faced by the healthcare system during an outbreak. Both emergency expansion of hospital facilities to treat COVID-19 and government appropriations to facilitate voluntary case isolation are urgently needed.

symptomatic cases develop a mild form of illness, while the remaining exhibit more severe and critical illness.
For the severe and critical cases, we assumed a proportion of patients immediately self-isolate themselves (based on the knowledge of having contacts with infectious cases) within their home ( ) and the remaining proportion continues to follow normal activity in the general population ( ). Of these severe cases who did not self-isolate directly upon symptom onset, a fraction will practice self-isolation after diagnosis during symptomatic disease (corresponding to an average of days after symptom onset).
A proportion, , of severe and critical symptomatic patients will recover without the need for hospitalization or critical care. The remaining proportion will require hospitalization (and/ For the cases experiencing mild illness ( ), we assumed that they do not immediately self-isolate upon symptom onset. Rather, a proportion of these mild cases practice self-isolation after days from symptom onset (a parameter that was varied in our simulations). In addition, these cases exhibiting mild symptoms do not require hospitalization or admission to the ICU. We also assumed that the relative infectivity of mild illness compared to severe and critical illness is reduced by 50%.
The dynamics of infection and control measures described here are schematically illustrated in Figure A1, and presented by equations (A1)-(A10) in the model. This model was used to investigate the effect of timely identification of symptomatic cases, self-isolation, and determine the hospital surge capacity required for treatment of severely and critically ill patients.

Mortality
We define the probability of mortality in the hospital to be . The mortality rate is denoted by , the rate to recovery in the hospital is denoted by , and model weight of mortality in the hospital is denoted by . Therefore, the probability of mortality in the hospital is expressed as Thus, the weight assigned to the mortality rate is

Contact Matrix
We used an estimated contact structure for the US that was based on contact surveys and demographic data (1). This structure was based on age classes spanning five years, ranging from 0-4 to 75-79. We first aggregated the number of contacts for each of our age classes 0-19, 20-49, 50-64, and 65+, with the age stratification of contacts still at five year intervals. Since the contact structure went to age 79, we used the span of 65-79 demographics for the purpose of compressing the contact matrix from the demographic data (2). We then determined the average number of contacts for in individual class based on our age stratification and the demographics of the US: where is the number of individuals in age range to , is the maximum age for class , is the aggregated number of contacts in age rage to for age class . We then determined the symmetric contract matrix by evaluating the average number of contacts For non-isolated individuals, we used the contact matrix that specified all locations, while the home contact matrix was utilized for isolated individuals (1).

Infectious period (used as a proxy for time to recovery from onset of symptoms in nonhospitalized patients)
We used the average duration of the serial interval (7.5 days) and the average duration of the incubation period (5.2 days), to approximate the infectious period of cases that would not be hospitalized (5). Since infection is random, the infectious period is twice the difference of the average serial interval and average incubation period. Thus, we estimate the infectious period to be 4.6 days.

Calibration of transmission rate for Reproductive Number
To calibrate the transmission parameter for R0=2 and 2.5, we used the next generation method (5,6). For calibration, we considered that there is no self-isolation ( and ). Results for the incidence of Hospitalization at the outbreak peak