Hospital-capacity prediction
Epidemic models can be connected to hospital demand by translating infections or symptomatic cases into admissions, occupancy and critical-care requirements.
Occupancy dynamics
If \(A(t)\) is the admission rate and patients leave at per-capita rate \(\delta\), a simple occupancy model is
\[\frac{dH}{dt}=A(t)-\delta H(t).\]For capacity \(C\), the decision-relevant event is
\[H(t)>C.\]Uncertain demand
When epidemic trajectories or clinical parameters are uncertain, the probability of exceeding capacity can be more informative than one projected occupancy curve:
\[P\left(\max_{0\le t\le T}H(t)>C\right).\]Use
Such models can compare intervention timings, staffing requirements and surge-capacity scenarios.
Key idea. Capacity planning is naturally an exceedance-risk problem when future epidemic and hospital demand are uncertain.