Hospital and critical-care models
Hospital models extend epidemic models from transmission to healthcare demand.
Additional states
Compartments may represent hospital admission, general ward occupancy, intensive or critical care, discharge and death. Transitions are determined by probabilities and rates estimated for the relevant population.
Occupancy
If \(A(t)\) is the admission rate and patients leave hospital at per-capita rate \(\delta\), a simple occupancy model is
\[\frac{dH}{dt}=A(t)-\delta H.\]Capacity
If available capacity is \(C\), then periods with
\[H(t)>C\]represent modelled demand exceeding capacity.
Key idea. Healthcare-demand models connect epidemic trajectories to clinically meaningful outcomes such as admissions, occupancy, peak demand and capacity exceedance.