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Model Overview

The COVID-19 Simulator uses a validated mathematical (compartment) model to simulate the trajectory of COVID-19 at the state level from March 15, 2020 to August 31, 2020 in the United States. Utilizing the most recent data reported by the Johns Hopkins University for each state, the COVID-19 Simulator considers state-specific disease spread dynamics. Specifically, to reproduce the observed trends and project future cases of COVID-19, time-varying and state-specific effective reproductive numbers are estimated using curve fitting algorithms and fed as inputs into a compartment model. The compartment model is defined using Susceptible, Exposed, Infectious, and Recovered compartments (i.e., SEIR model) with continuous time progression. Model programming and analysis were performed in R (version 3.6.2), and the package deSolve was used to solve the ordinary differential equation system.

The COVID-19 Simulator evaluates the impact of different non-pharmaceutical intervention strategies to reduce the spread of COVID-19 under varying intensity and timing at the state and national level. For each selected strategy, the model projects and visualizes the total number of deaths from COVID-19, daily counts of cases, cumulative number of cases, number of active cases, and the number of hospital beds and intensive care unit (ICU) beds needed for COVID-19 patients.

Intervention Strategies

We simulate model outcomes until August 31, 2020 under different levels and duration of social-distancing interventions, as defined below:

  1. Minimal restrictions: This strategy assumes that there is minimal social distancing in place to reduce the spread of COVID-19, with an assumed level of learned social awareness (handwashing, avoiding close contact when sick, etc.). We assume the RE of this intervention will be 1.68, which is 30% lower than the basic reproduction number, R0, of COVID-19.
  2. Current intervention in each state: This strategy mimics the current intervention taking place in the state. For most states this is a stay-at-home order, where people are advised to stay at home except for essential needs such as grocery shopping and picking up prescriptions. The New York Times provides an updated list of the current interventions in each state. Considering the current level of interventions and rising public awareness, we assumed that the transmission rate (controlled by the RE parameter) will decrease over time. To estimate the reduction in the transmission rate, we first estimated RE values of the last 10 days for each state based on the daily count of COVID-19 cases using the R package EpiEstim.1 Because the effects of social distancing interventions are changing over time, we captured future time-trends in RE values by fitting exponential regression models for each state. We assumed that the projected RE values would not go below 0.3 under the current intervention.2 For a state where we observed an upward trend of RE values, we conservatively assumed that the latest value of the fitted RE values will control the transmission rate of the epidemic in that state. The estimation and the projection of the RE values are dynamically updated with new data to better reflect the intervention dynamics in each state. Download the current RE values (using data up to June 28, 2020).
  3. Lockdown: This strategy assumes that there is a complete ban on travel, including cancelling flights and closing inter-state travel and local travel (except for limited time for essential needs such as grocery shopping and picking up prescriptions), as has been done in countries such as Italy, China, and India. We used the RE of 0.3, as estimated in Wuhan after the lockdown of the region.2

 

Suppression of transmission

We assumed that once the number of active COVID-19 cases (infectious and not recovered) in a given state reaches below a threshold of 10 active cases per 1,000,000 people, all cases can be isolated, which will stop the transmission of coronavirus in the community.

 

Case fatality rate

Since the true prevalence of COVID-19 is not known, mortality in the model is determined using the observed case fatality rate (CFR), i.e., the ratio of the confirmed deaths to the reported COVID-19 cases. To account for the duration between diagnosis and death, we considered a lag time of 16 days between the diagnosis of cases and the reported deaths. 3 Furthermore, because the COVID-19 testing rate is increasing over time, which affects the diagnosis rate, we captured time-varying changes in CFR by fitting state-specific CFR curves. Download state-specific CFR projections based on most recent data.

 

Hospital beds capacity

Data on hospital beds and capacity were extracted from the annual cost reports (fiscal years 2016 through 2019) that hospitals file to the Centers for Medicare & Medicaid Services (CMS). The data from these reports is then made available through CMS’s Healthcare Cost Report Information System (HCRIS). Data were analyzed over a period of years to allow for corrections of both missing and inaccurate data. Hospitals that were deemed unlikely to be able to assist greatly in a pandemic were not counted in this analysis (alcohol and drug treatment hospitals, psychiatric hospitals, community mental health hospitals, hospice, religious non-medical hospitals, and skilled nursing facilities and homecare). For Intensive Care Unit (ICU) beds, we also included beds in similar units that could be repurposed as general intensive care in the event of a pandemic (cardiac critical care, burn ICU, and surgical ICU units).

To get the estimated number of beds available to COVID-19 patients, we calculated the average number of available beds (hospital beds or ICU) in each hospital on a single day. This was done using reported bed days and reported inpatient days for each type of bed. If the hospital reported bed numbers but did not report bed utilization numbers, we used the state average occupancy rate (calculated from all states that provided this data) to calculate the estimated number of beds available to coronavirus patients.

 

Key model parameters used in COVID-19 Simulator

Parameter

Value or Range

Source

Basic reproductive number (R0)

2.4

4

Latent period duration

4.5-5.8

5

Infectiousness period duration

2.1-7

5

Effective reproduction number of Current Intervention

state specific

estimated

Effective reproduction number of Public Awareness

1.68

6

Effective reproduction number of Lockdown

0.3

2

Hospitalization rate upon diagnosis

state-specific

The COVID Tracking Project

Rate of critical care after hospitalization

23.9%

The COVID Tracking Project

Mean hospitalization duration for non-critical care patients

8 days

8

Mean hospitalization duration for critical care patient

16 days

8

Time until hospitalization

5 days

8

Case fatality rate reduction factor

95.1%

estimated

Threshold to suppress the epidemic

10 active cases per 1 million

assumption

 


References

  1. Cori A, Ferguson NM, Fraser C, Cauchemez S. A new framework and software to estimate time-varying reproduction numbers during epidemics. Am J Epidemiol. 2013;178(9):1505-1512.
  2. Pan A, Liu L, Wang C, et al. Association of Public Health Interventions With the Epidemiology of the COVID-19 Outbreak in Wuhan, China. JAMA. 2020.
  3. Baud D, Qi X, Nielsen-Saines K, Musso D, Pomar L, Favre G. Real estimates of mortality following COVID-19 infection. The Lancet Infectious Diseases.
  4. Li Q, Guan X, Wu P, et al. Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus–Infected Pneumonia. New England Journal of Medicine. 2020;382(13):1199-1207.
  5. Lauer SA, Grantz KH, Bi Q, et al. The Incubation Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application. Ann Intern Med. 2020;172:577–582. [Epub ahead of print 10 March 2020]. doi: https://doi.org/10.7326/M20-0504
  6. Anderson RM, Heesterbeek H, Klinkenberg D, Hollingsworth TD. How will country-based mitigation measures influence the course of the COVID-19 epidemic? The Lancet. 2020;395(10228):931-934.
  7. CDC COVID-19 Response Team. Severe outcomes among patients with coronavirus disease 2019 (COVID-19)—United States, February 12–March 16, 2020. MMWR Morb Mortal Wkly Rep. 2020;69(12):343-346.
  8. Ferguson N, Laydon D, Nedjati-Gilani G, et al. Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand. Imperial College COVID-19 Response Team. Preprint at Spiral https://doi.org/10.25561/77482 (2020). In:2020.