Current Forecasts

Info column

Updated May 11, 2020 at 09:40 EDT

Data is shown as circles and grey shaded regions indicate uncertainty bounds for the best fit 95% across 1000 simulations. Hover over plots to see data values and interactive menu, and scroll down to see additional plots.

Current Summary

Model forecast for cumulative lab-confirmed cases:
Date Uncertainty lower bound Best-fit Uncertainty upper bound
May 16 (1 week) 44458 49169 52055
May 30 (3 weeks) 44542 50333 53425

Additionally, the current best fit across model simulations projects (for uncertainty ranges, please see plots):

  • May 16, 2020 (1 week): roughly 1000 COVID+ hospitalized patients (beds needed) with roughly 250 in ICU
  • May 30, 2020 (3 weeks): roughly 400 COVID+ hospitalized patients (beds needed) with roughly 90 in ICU

Note that the model is a work in progress and being updated as the epidemic progresses. Because we are still making improvements and including new data in the model, these results are highly preliminary and uncertain. The forecasts shown here also do not account for the ongoing changes in social distancing occurring over the coming weeks. For more on social distancing, see the ‘Scenarios’ tab.

For more information about the transmission model and methods, please see the ‘About’ tab.

Plot Column

1-week forecast of cumulative COVID-19 cases in Michigan

3-week forecast of cumulative COVID-19 deaths in Michigan

3-week forecast of COVID-19 ICU occupancy (i.e. beds needed)

3-week forecast of current COVID-19 patients needing O\(_2\) support

Plot Column

3-week forecast of cumulative COVID-19 cases in Michigan

3-week forecast of COVID-19 hospitalized patients (i.e. beds needed)

3-week forecast of current COVID-19 patients needing ventilators

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Social Distancing Scenarios

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Summary

  • Early in the growth phase, social distancing efforts tend to delay the epidemic peak further, while efforts later in the growth phase nearer the peak tend to reduce the epidemic peak more.
  • Start efforts before the peak of the epidemic: social distancing is generally more effective when it is started during the growth phase of the epidemic—once the peak has already occurred the impact of social distancing is often much less.
  • Continue efforts until after the peak of the epidemic: to avoid a rebound in cases after social distancing efforts stop, social distancing efforts tend to work best if they continue past the peak of the epidemic. This means it will be important to consider how to make social distancing efforts sustainable.

Limitations

  • While in the growth phase of the epidemic, projecting the height and timing of the peak or overall duration of the epidemic is highly uncertain. Thus, these simulations should be used to explore potential scenarios and general patterns regarding the impact of social distancing, rather than for prediction of specific numbers.
  • This model represents just one simulation from the range of realistic parameter values used for forecasting (given in the ‘About’ tab).
  • This model does not account for stochasticity, i.e. the effects of randomness in contact patterns and the disease transmission process. This means that the model will not be able to capture the potential for random extinction of the epidemic during long periods with very few cases.

About

Model description is in-progress, to be updated soon!

Overview

This transmission model has been developed to assist in understanding and forecasting epidemic spread and hospital resource needs, and to explore and examine alternative scenarios (see scenarios tab). The model is calibrated based on Michigan data on COVID-19 testing and demographics, as well as Michigan and other literature data on disease progression, severity, mortality, etc.

Model description


Figure 1. Diagram for the basic transmission model used in this analysis.

The spread of infectious disease in a population can be modeled as a dynamical system, where the number of infections changes over time accordingly to a host of complex and interrelated processes. The two fundamental disease processes are transmission and recovery, but sociobehavioral processes or other aspects of the natural history of infection can also be included to model a specific disease outbreak.

We have tested several different models based on more complex versions of what is known as an SIR model, or susceptible (S), infectious (I), recovered (R) model. This class of models tracks the fraction of the population in different disease stages.

A diagram of the simplest form of our model is shown in Figure 1. In this model of COVID19 disease, we track people who are susceptible (\(S\)), have mild disease but have not sought care (\(I_1\)), have mild disease and have sought care (\(I_{1,c}\)), have recovered (\(R\)), have severe disease (\(I_2\)), have been hospitalized (\(H\)), and have died (\(D\)). We have also tested similar models accounting for superspreading, alternative distributions of the latent and infectious period, and asymptomatic transmission, with similar results, so we opted for the simplest version of the model in this analysis. From the model, we estimated the number of people who need intensive care, ventilators, or oxygen support as a fraction of hospitalized patients.

Uncertainty and limitations

(In progress—more details to be added soon.)

Current Model Limitations

  • Tested fraction of cases: For any disease, most surveillence data detects only a fraction of the true total cases. For this outbreak, this fraction is changing over time as testing capacity ramps up. For now, we are estimating an average fraction of cases reported. Our predictions will be highly uncertain early in the outbreak before testing capacity and the reporting fraction stabilize.

  • Prediction during the exponential growth phase of an epidemic: It is notoriously difficult to predict important quantities such as the time or size of the peak number of cases while early on in an outbreak—or even just to forecast more than a couple weeks ahead with any accuracy. For example, we won’t know how much social distancing is impacting transmission rates until we start to see a change in the trajectory of cases (which, given the ramp up in testing and relatively long incubation period for this disease, may take days up to a couple of weeks after social distancing changes happen).

Parameter estimation

COVID19 disease is caused by the novel coronavirus SARS-Cov-2. Because it is so new, there is a lot of uncertainty about the natural history of the virus—how long the incubation period is, what the mortality rate is for different age groups, etc. This uncertainty surrounds almost every parameter in our model, and these parameters cannot be estimated from the epidemic curve alone (particularly early in the epidemic when few parameters are needed to replicate the epidemic growth rate).

Because we can make reasonable guesses as to sensible bounds for each parameter, we can take hundreds and thousands of combinations of reasonable values of the model parameters (currently, we use Sobol sampling). For each of these combination of parameters, we estimate the value of the reporting rates for cases and deaths that best explain the trajectory of the data. Altogether, these thousands of trajectories represent our best guess as to what the true epidemic curve has been—and what it will be shortly.

Parameter values and ranges for sampling

(To be updated with sources)
Parameter Default Lower Upper Definition Units
MIPop 9883635.00 9883635.000 9883635.000 Total population of Michigan People
fReport 0.10 0.001 0.200 Fraction of symptomatic individuals who are laboratory-confirmed Unitless
R0 3.00 2.000 5.000 Basic reproduction number People
IncPer 5.00 4.000 8.000 Incubation period Days
InfAsympPer 1.00 0.500 2.500 Duration of asymptomatic infectiousness Days
InfPer 7.00 4.000 16.000 Infectious period Days
fMort 0.01 0.005 0.030 Mortality fraction among infected individuals Unitless
TimetoDeath 18.50 15.000 22.000 Time from symptom onset to death Days
fAsymp 0.18 0.100 0.400 Fraction who are asymptomatic or only experience mild symptoms Unitless
fSuper 0.03 0.025 0.052 Fraction who are superspreaders Unitless
RelInfSuper 3.50 2.000 10.000 Relative infectiousness of superspreaders vs regular symptomatic individuals Unitless
RelInfAsymp 0.10 0.010 0.200 Relative infectiousness of early infectious but asymptomatic to symptomatic Unitless
fDocVisit 0.50 0.300 0.700 Fraction of symptomatic who will visit the doctor Unitless
TimetoSeekCare 2.50 1.000 7.000 Time to visit doctor (non-hospital) Days
fHosp 0.20 0.150 0.250 Fraction of symptomatic who will be hospitalized Unitless
fO2 0.20 0.100 0.250 Fraction of hospital admits who will need O2 Unitless
fVent 0.10 0.040 0.200 Fraction of hospital admits who will need a ventilator Unitless
fICU 0.20 0.110 0.300 Fraction of hospital admits who will be admitted to the ICU Unitless
fECMO 0.02 0.005 0.050 Fraction of hospital admits who will need ECMO (non-transfers) Unitless
TimetoHosp 11.00 3.000 14.000 Time from symptom onset to hospitalization Days
StayLengthHosp 11.00 7.000 14.000 Duration of hospital stay Days
RelativeDeathRep 2.00 1.250 3.000 Relative reporting of deaths vs cases Unitless

Team

The University of Michigan Epimath COVID-19 Modeling group is comprised of:

Questions? Please contact Marisa Eisenberg (marisae@umich.edu), Andrew Brouwer (brouweaf@umich.edu), and Josh Petrie (jpetrie@umich.edu) for more information.