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kaitejohnson committed Nov 26, 2024
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Expand Up @@ -62,10 +62,10 @@ We model infection dynamics in these subpopulations hierarchically: subpopulatio
#### Subpopulation definition
The total population consists of $K_\mathrm{total}$ subpopulations $k$ with corresponding population sizes $n_k$. We associate one subpopulation to each of the $K_\mathrm{sites}$ wastewater sampling sites in the jurisdiction and assign that subpopulation a population size $n_k$ equal to the population size reported for that wastewater catchment area.

Whenever the sum of the wastewater catchment population sizes $\sum\nolimits_{k=1}^{K_\mathrm{sites}} n_k$ is less than the total population size $n$, we use an additional subpopulation of size $n - \sum\nolimits_{k=1}^{K_\mathrm{sites}} n_k$ to model individuals in the population who are not covered by wastewater sampling.
In this case, we refer to the subpopulation not covered by wastewater as the reference subpopulation, denoted by $k=0$.
Whenever the sum of the wastewater catchment population sizes $\sum\nolimits_{k=1}^{K_\mathrm{sites}} n_k$ is less than the total population size $n$, we use an additional subpopulation of size $n - \sum\nolimits_{k=1}^{K_\mathrm{sites}} n_k$ to model individuals in the population who are not covered by wastewater sampling.
In this case, we refer to the subpopulation not covered by wastewater as the reference subpopulation, denoted by $k=0$.

The total number of subpopulations is then $K_\mathrm{total} = K_\mathrm{sites} + 1$: the subpopulation to account for individuals not covered by wastewater sampling plus the $K_\mathrm{sites}$ subpopulations with sampled wastewater.
The total number of subpopulations is then $K_\mathrm{total} = K_\mathrm{sites} + 1$: the subpopulation to account for individuals not covered by wastewater sampling plus the $K_\mathrm{sites}$ subpopulations with sampled wastewater.

The model without wastewater (hospital admissions only model) is therefore a special case of the model where $K_\mathrm{sites} = 0$ and $K_\mathrm{total} = 1$, with subpopulation size $n_k = n$, the total population.

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