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System Dynamics & Pressure

The operational layer of the NHRA Game maps strategic choices and demand shocks to hospital performance.

1. Pressure Index

The System Pressure Index (\(P\)) is a non-dimensional metric of operational strain:

\[ P = 0.8 + 0.2 \left( \frac{W_{wait}}{60} \right) + 0.5 \left( \frac{O - 0.8}{0.1} \right) \]

Where:

  • \(O\): Occupancy rate.
  • \(W_{wait}\): Queue wait time.

2. Capacity Lags

Capacity does not adjust instantaneously. We model operational inertia using expansion/contraction lags:

\[ C_{t+1} = C_t + \lambda (C_{target} - C_t) \]

Where:

  • \(\lambda\): Lag coefficient (Expansion \(\lambda_{exp}\) < Contraction \(\lambda_{con}\)).

3. System Modes

The model operates as a state machine with four modes:

  • Normal: Pressure < 1.25
  • Stress: 1.25 < Pressure < 1.50
  • Crisis: Pressure > 1.50
  • Recovery: Transitioning back to Normal.

4. Evidence Grounding

  • Occupancy: AIHW 88% efficient threshold.
  • Lags: Stylised based on hiring and infrastructure cycles.