The UVA Patchsim Model

The model places the people of each county or city into four compartments: susceptible to the disease (S), exposed but not yet infectious (E), infectious (I), and recovered (R). It then uses a series of differential equations to predict the “flow” of people from one compartment to the next. The assumption being that infectious individuals may infect susceptibles who then follow the chain to recovered which includes those who died).

The models also place individuals into one of four tiers of immunity and assume that immunity begins to wane after four months. As there are 133 counties and cities in Virginia, four compartments per county, and four tiers of immunity for each, there are 2,128 total compartments in this model. The movement of infected individuals from county to county was included based on US Census commuter flow data, but proved unnecessary for a good model fit and was discontinued.

Once the compartments are set, the models are then calibrated to historic case, hospitalization, and death data from VDH. This is done by varying a few key parameters to achieve the best possible fit to historic data. These parameters are as follows:

  • Duration of incubation (between 5-9 days)
  • Duration of Infectiousness (between 3-7 days) 
  • Undocumented case rate (between 1:1 to 7:1) 
  • Detection delay: exposure to confirmation (between 4-12 days)  

The ranges of these parameters are derived from scientific literature. This approach captures uncertainty, but allows the model to precisely track the full trajectory of the outbreak.

Once these parameters are set, the model can be run into the future giving projections of future case rates and outcomes. The hospitalization rate and death rate from the last month of historic data are then used, in conjunction with projections of future case rates, to estimate future hospitalizations and death. Currently the models assume that 6.8% of cases will be hospitalized within three days of case confirmation, and 1.45% will die within 11 days of confirmation.