Is the Gompertz function the function behind the standard "epi curve"? It appears from the CDC web site and other places that the epi curve is the standard way epidemics are modeled. The CDC even has a simple tutorial for creating them: https://www.cdc.gov/training/quicklearns/createepi/index.htm...
An epi curve is created from observations and shows new infections per day.
The Gompertz function is a mathematical formula and can be used to estimate total infections up to a date.
However, if you take the epi curve and plot the aggregate number of infections you'll find a curve that the Gompertz function approximates quite well.