Demand drivers

Base admissions set the everyday arrival rate. Respiratory activity follows the CDC five-level scale for acute respiratory illness (minimal, low, moderate, high, very high) and adds a surge that ramps in over several days. Elective share is the part of demand leaders can defer.

Length of stay is a demand driver too: every added day holds a bed that a new admission needed. Discharge delays for patients awaiting post-acute placement act exactly like longer stays.

Capacity drivers

Staffed beds, not licensed beds, set the ceiling. Staffing availability removes beds that cannot be safely covered, so an 85% staffing day on 252 staffed beds leaves 214. Planned patients per nurse converts nurses into beds, and agency or float nurses and overflow beds add capacity back.

National evidence points the same way: the post-pandemic rise in occupancy came from fewer staffed beds rather than more patients.

Same scenario, two policies

Bed strain compares census with the beds left open. Staff strain compares census with what the nurses on duty can safely cover. Keeping beds open lowers bed strain without changing staff strain: the days past the critical line do not disappear, they move from the bed count to the nursing assignment, where they are harder to see.

Patients per nurse and mortality

In Aiken and colleagues’ study of surgical patients, each additional patient per nurse was associated with 7% higher odds of death within 30 days (odds ratio 1.07, 95% CI 1.03 to 1.12). Moving from 4 to 6 patients implies about 14% higher odds, and from 4 to 8 about 31%.

This is an association from one surgical cohort, applied here to show direction and scale. It is not a causal estimate for your hospital.

What the evidence shows

In U.S. hospitals during 2020 and 2021, occupancy above 85% was associated with boarding beyond the 4-hour standard, with a median boarding time of 6.58 hours (Janke and colleagues, 2022).

Across 46.2 million hospitalizations from 2017 to 2024, boarding became steadily more common; at the January 2022 peak, 40.1% of admitted patients boarded more than 4 hours and 6.3% more than 24 hours (Janke and colleagues, 2025).

Formulas

Effective capacity (close beds)
  E = floor(min(L, a×S + g×r)) + O
Effective capacity (keep beds open)
  E = floor(min(L, max(S, a×S + g×r))) + O
Nurses on duty
  N = a×S/r + g + O/r

Admissions on day t
  u(t) = U × min(1, t/ramp)
  A(t) = λ×es×(1−d) + λ×(1−es+u(t))×(1−v×[critical yesterday])
Census
  C(t) = C(t−1) + A(t) − C(t−1)/(LOS×(1−x))

Bed strain      s(t) = C(t)/E
Staff strain    C(t)/(N×r)
Spread          σ(t) = √(k×C(t))
90% range       C(t) ± 1.645σ(t)
Overflow risk   1 − Φ((E + 0.5 − C)/σ)
Expected excess σ[φ(z) − z(1 − Φ(z))], z = (E − C)/σ
Patients/nurse  min(C, E)/N
Relative odds   1.07^max(0, peak ratio − r)

Safe occupancy at risk p
  √μ = (−z√k + √(z²k + 4(E + 0.5)))/2, z = Φ⁻¹(1 − p)

Limitations

• Census is treated as one pool. Units such as ICU, step-down and pediatrics fill separately, so a hospital-level forecast can look calm while one unit is full.
• The Poisson spread is exact only for steady arrivals to ample beds; real demand is often more variable, which the variability setting approximates.
• Length of stay is held constant; in practice it can rise under congestion.
• The surge uplift percentages and all financial inputs are assumptions, not published values.
• The staffing and mortality relationship is an association from one surgical cohort and is shown for direction and scale only.