Model overview

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The COVID-19 Simulator uses a validated system dynamics (compartment) model to simulate the trajectory of COVID-19 at the state level from March 15, 2020 onwards in the United States. Utilizing the most recent reported data 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 reproduction 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 count 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

In the current version of the COVID-19 Simulator, we evaluate the impact of different state-level non-pharmaceutical intervention strategies defined by varying intensity and timing as defined below:

  1. Minimal restrictions: This strategy assumes that there is minimal social distancing in place to reduce the spread of COVID-19, but there is an assumed level of learned social awareness (handwashing, avoiding close contact when sick, etc.). We assume the of this intervention will be 1.68, which is 30% lower than the basic reproduction number.9
  2. Current intervention: This strategy captures the level of opening or closing that is currently happening in each state.13 We used the current value of the from the website rt.live to make future projections under this scenario.14 Each week, we update the projections of each states based on the current of the state.
  3. Stay-at-home orders: This strategy assumes a statewide stay-at-home order. We used rt.live to estimate the for the states who declared stay-at-home orders. For each state, we used the minimum value observed since the beginning of epidemic as the value of the stay-at-home orders for that state.14
  4. Lockdown: This strategy assumes 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 needs), as has been done in countries such as Italy, China, and India. We used the of 0.3, as estimated in Wuhan after the lockdown of the region.8

We simulate different combinations of two sequential interventions, each of which could last for 1–16 weeks. After the interventions, the effective reproduction number is changed to that of the public awareness only scenario (RE of 1.68).

Assumptions

First, due to uncertainty about the possibility of re-infection with COVID-19, we assumed that immediate re-infection of COVID-19 is not feasible within the time frame of this study (9 months), based on the opinions of several experts.3 Second, after each intervention, we check whether or not the epidemic is suppressed based on a pre-defined daily case count threshold. This threshold is defined as the number of daily COVID-19 cases in a given state falling below 1 new case per 100,000 people. If this threshold is met, we assume all cases can be isolated and therefore transmission of coronavirus in the community is stopped.

Model outcomes

For each state, the model generates the following outcomes from March 15, 2020 onwards:

  • Cumulative deaths from COVID-19 infection
  • Daily new cases of COVID-19 infection
  • Cumulative cases of COVID-19 infection
  • Active cases of COVID-19 infection
  • Number of hospital beds needed for COVID-19 patients
  • Number of ICU beds needed for COVID-19 patients

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).15 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 beds) 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.

Table 1. Key model parameters used in COVID-19 Simulator

Parameter

Value or range

Source

Basic reproduction number

2.4 cases per infections

5

Latent period duration

4.5–5.8 days

6

Infectiousness period duration

2.1–7 days

7

Effective reproduction number of Lockdown

0.3 case per infections

8

Effective reproduction number of Stay Home Orders

state specific

estimated

Effective reproduction number of Current Interventions

state specific

estimated

Effective reproduction number of Minimal Restriction

1.68 case per infections

9

Infection fatality rate

0.00769

16

Hospitalization rate upon diagnosis

state specific

10

Rate of hospitalization per death

state specific or 10.02

10 and 11

Number of patients in ICU per death

state specific or 3.15

10 and 11

Mean hospitalization (non-ICU) duration

8 days

12

Mean duration of stay in ICU

10 days

12

Mean duration between diagnosis and death

16 days

12

Threshold to suppress the epidemic

10 new cases per million inhabitants

assumption

 

References

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  2. Soetaert KE, Petzoldt T, Setzer RW. Solving differential equations in R: package deSolve. Journal of Statistical Software. 2010;33.
  3. Leung H. Can You Be Re-Infected After Recovering From Coronavirus? Here's What We Know About COVID-19 Immunity. Time. April 3, 2020. 2020.
  4. Xiang Y, Gubian S, Suomela B, Hoeng J. Generalized Simulated Annealing for Global Optimization: The GenSA Package. R Journal. 2013;5(1).
  5. Guan W-j, Ni Z-y, Hu Y, et al. Clinical Characteristics of Coronavirus Disease 2019 in China. New England Journal of Medicine. 2020.
  6. 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. Annals of Internal Medicine. 2020;172(9):577-582.
  7. 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.
  8. 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.
  9. 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.
  10. The COVID Tracking Project ( https://covidtracking.com/)
  11. 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.
  12. 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.
  13. Lee J, Mervosh S, Avila Y, Harvey B, Matthews A. See How All 50 States Are Reopening (and Closing Again). The New York Times2020.
  14. Systrom K, Vladek T, Krieger. M. Rt.live (2020). GitHub repository, https://github.com/rtcovidlive/covid-model (last accessed: Aug 12, 2020).
  15. Centers for Medicaid and Medicare Services. Cost Reports. In:2019.
  16. CDC COVID-19 Response Team. COVID-19 Pandemic Planning Scenarios. September 10, 2020. Accessed at: https://www.cdc.gov/coronavirus/2019-ncov/hcp/planning-scenarios.html