Benchmark Models

Models for Benchmarking

A. The LEMMA Model

I. Model Description

LEMMA (Local Epidemic Modeling for Management & Action) “allows for a range of user-specified parameterizations (including on the model structure) and is fit using case series data of COVID-19 hospitalizations.”. The COVID-19 case series used are recoded for both confirmed cases and persons under investigation (PUI) and are as follows: • Hospitalizations (including ICU) • ICU • Cumulative Deaths (deaths to date) • Cumulative Hospitalizations (total admits to date)

Thus, the model is fit using a total of 8 data series.

II. Methodology

The LEMMA model is based on a SEIR (Susceptible, Exposed, Infectious, and Recovered) model that uses Hamiltonian MCMC for parameter estimation: “The Santa Cruz County (SCZ) COVID-19 model is a time-discrete, stochastic SEIR model that uses Bayesian statistical methods, such as Hamiltonian Markov Chain Monte Carlo (MCMC) simulations, to forecast the COVID-19 pandemic in Santa Cruz County, California” Using such a stochastic (random) framework results in realistic forecasts as opposed to using an ordinary differential equations (ODEs). The model is implemented in Stan and briefly, the implementation of Hamiltonian MCMC in Stan is as follows: “The Hamiltonian Monte Carlo algorithm starts at a specified initial set of parameters θ; in Stan, this value is either user-specified or generated randomly. Then, for a given number of iterations, a new momentum vector is sampled and the current value of the parameter θ is updated using the leapfrog integrator with discretization time ϵ and number of steps L according to the Hamiltonian dynamics. Then a Metropolis acceptance step is applied, and a decision is made whether to update to the new state (θ∗,ρ∗)(θ∗,ρ∗) or keep the existing state (own emphasis).” The LEMMA model allows for the user-specification of the following initial parameter distribution (priors - mean and standard deviation) which are drawn from a normal distribution:

• Basic reproductive number R0 before Intervention1

• Number of Days from Infection to Becoming Infectious (Latent Period)

• Duration of infectiousness (days)

• Time from onset of infectiousness to hospitalization (days)

• Average Hospital Length of Stay for Patients not in ICU (Days)

• Average Hospital Length of Stay for Patients in ICU (Days)

• Percent of Infected that are Hospitalized

• Percent of Hospitalized COVID-19 Patients That are Currently in the ICU

• Mortality Rate among ICU COVID-19 Patients

• Intervention Date

• Re Multiplier

• Days to reach new Re

Other model parameters that require initialization using a single valued and not a distribution are:

• Number of people in the area of interest

• Specify the starting

• Final date of projections

Apart from the model parameter initializations, the model requires the 8 aforementioned data series and a set of initializations for model reproducibility and presentation.

III. Model Output

The model returns short and long term forecasts of the 0th to 100th percentiles (at a distance of 5 percentiles) for:

• Hospitalizations (including ICU)

• ICU

• Number of Deaths

• Cumulative Hospitalizations (total admits to date)

• Retransmission rate

IV. Benchmarking Against Transformer Model

IV.I Comparison Methodology

IV.II Results