diff --git a/model_definition.md b/model_definition.md index 0c613a71..8798c02f 100644 --- a/model_definition.md +++ b/model_definition.md @@ -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.