In the work of Cleo Anastassopoulou et al. "Data-based analysis, modeling and forecasting of the COVID-19 outbreak" (Plos One 15(3):e0230405), the authors extracted the parameters α, β, and γ needed for a SIRD model directly from the epidemic curves. In particular, they fit a curve to the cumulative mortality using the least-squares method (on the left) to estimate γ:
I also fit a curve on the data (on the right; in this case, the cumulative mortality rate for China) using the Gomperz function
where a is an asymptote, b sets the displacement along the x-axis, c sets the growth rate and e is the Euler's Number.
The question is: how can I extrapolate γ from the fitted Gomperz function?
Since I have obtained the optimized values for a, b, and c using the least square approach, can I use them for downstream analysis? Would c be the value I should use for γ?