Parametric Bootstrap Capture Recapture
I did a little research and I think it works like that:


Collect a dataset of $n$ observations.
Fit a parametric model to your data. If you want to model the recaptures, I would suggest a Poisson-GLM. You can also estimate the parameter directly from your data and simply parametrize a Poisson distribution. However, this approach would not model the random variation in your data.
Use the fitted model to draw a sample of size $n$
Calculate your desired metric based on the sample. I guess in your case this would be human population size (calculated as ${N} = \frac{nM}{m}$?)
Repeat steps 3 and 4 many times (1000+)
There you go! Now you can easily assess the variability in population size based on the estimates from your bootstrap samples.