Reproducible Materials

All code and data needed to reproduce our results can be found in our public GitHub repository: https://github.com/CEIDatUGA/COVID-GA-model.


Introduction

The epidemiology of SARS-CoV-2 is poorly understood. Here we develop a model for the transmission of SARS-CoV-2 from March 2020 through May 2020 in Georgia, USA. This model is being used for inference, forecasting, and scenario analysis.

Key features of this model include:

  1. Stochastic transmission process. Stochastic models are models with a realistic level of random variation. Stochastic models are essential for proper modeling of systems that start with a small number of infections.
  2. Realistic interval distributions for presymptomatic and symptomatic periods.
  3. Transmission is allowed at different rates for asymptomatic, presymptomatic, and symptomatic individuals.
  4. Time varying rates of case detection, isolation, and case notification.
  5. Realistic intervention scenarios.
  6. Affect of human mobility on transmission (i.e., social distancing).
  7. A latent process that allows transmission to vary over time due to environmental factors and other behavioral measures that can reduce transmission but are difficult to include with data (e.g., wearing face masks).

This model contains both fixed and fitted parameter values. Fixed parameters were defined using clinical outcome reports. Fitted parameters values were found by calibration to incident case and death reports, as described in more detail below. The pandemic of SARS-CoV-2 is still evolving and information that was used in the construction of this model may be incomplete or contain errors. Accordingly, these results are preliminary, provisional, and subject to change. These results have not been peer-reviewed, but have been prepared to a professional standard with the intention of providing useful interpretation of a rapidly developing event.

Methods

Data

We fit the model to incident case and death reports for Georgia, as collated by The COVID Tracking Project.

In addition, we include a covariate that describes human mobility. These data come from Unacast. We smooth the raw data from Unacast using a spline fit, resulting in the trajectory of human movement shown below. This covariate is used to reduce baseline transmission.

The Model

The model comprises susceptible, pre-symptomatic, asymptomatic, symptomatic, diagnosed, hospitalized, deceased, and recovered persons. The following compartments are included:

  • \(\boldsymbol{S}\) - Uninfected and susceptible individuals. Susceptible individuals can become infected by individuals in the \(L\), \(I_a\), \(I_{su}\), \(I_{sd}\), \(C\), and \(H\) stages. Rates of transmission from these stages can be adjusted individually.
  • \(\boldsymbol{L}\) - Individuals with latent infections who do not yet show symptoms. Those individuals can be infectious. At the end of the \(L\) stage, a fraction moves into the \(I_a\) stage, another fraction moves into the \(I_{su}\) stage, and the remainder into the \(I_{sd}\) stage.
  • \(\boldsymbol{I_a}\) - Individuals who are infected and asymptomatic. Those individuals are likely infectious, but the model allows to adjust this.
  • \(\boldsymbol{I_{su}}\) - Individuals who are infected and symptomatic, but are undetected. Those individuals are likely infectious. Individuals in this compartment never get diagnosed, and are assumed to recover.
  • \(\boldsymbol{I_{sd}}\) - Individuals who are infected and symptomatic, and are detected. Those individuals are likely infectious. Individuals in this compartment will be diagnosed and move to \(C\).
  • \(\boldsymbol{C}\) - Individuals who have been diagnosed as cases. Those individuals are likely isolated and not infectious, but the model allows to adjust this. A fraction of individuals in the \(C\) stage will naturally recover, without the need for hospitalization. The remainder moves into the \(H\) stage.
  • \(\boldsymbol{H}\) - Individuals who have been hospitalized. Those individuals are likely isolated and not infectious, but the model allows to adjust this. A fraction of individuals in the \(H\) stage will recover, the remainder will die.
  • \(\boldsymbol{R}\) - Recovered/removed individuals. Those individuals have recovered and are immune.
  • \(\boldsymbol{D}\) - Individuals who died from the infection.

To allow more realistic distributions of movement through compartments, several of these compartments are internally split into multiple stages using the linear chain trick.5

  • \(\boldsymbol{L}\) - 4 compartments
  • \(\boldsymbol{I_a}\) - 4 compartments
  • \(\boldsymbol{I_{su}}\) - 4 compartments
  • \(\boldsymbol{I_{sd}}\) - 4 compartments
  • \(\boldsymbol{C}\) - 4 compartments
  • \(\boldsymbol{H}\) - 4 compartments

The flow diagram for this model shown below.