How to extract parameters for epidemic model from data-fitting?

Jul 3, 2020
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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
formula.jpg
directly from the epidemic curves. In particular, they fit a curve to the cumulative mortality using the least-squares method (figure below, on the left) to estimate γ.
query_epidemiology.jpg
I also fit a curve on the data (on the right; in this case, the cumulative COVID-19 mortality rate for China) using the Gomperz function
gomp.jpg
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?
Thank you
 

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