Mechanistic handling of observation error in ww scaling with contributing infections

[kaitejohnson]

Problem

The expected variability in the wastewater measurements is a function of the number of contributing infections. The model doesn't currently have any component to account for the population size/number of infections

Assuming we can write the infected individuals distribution of number of genomes shed over the course of infection as: $$g_i \sim \mathrm{Gamma}(\kappa, \theta)$$

Which has mean $\kappa\theta$.

Then the sum of the genomes in each infected individual should be:

 \sum_{i=1}^{I(t)} g_{it}\sim \mathrm{Gamma}(\kappa I(t) , \; \theta)$

with mean $I(t)\kappa\theta$, because the mean of a gamma is shape *scale

The original write-up in #57 has the scale parameter also scaling with $I(t)$.

Context: https://github.com/cdcent/cfa-forecast-renewal-ww/issues/57