INALBIO: An Absorbing Compartmental and Fairness-Constrained Bio-Inspired Modeling for Sepsis Mortality Prediction

Abstract

Sepsis mortality prediction requires a clear separation between clinical progression, numerical approximation, predictive error, model complexity, calibration, and subgroup disparity. This study presents INALBIO, an integrated framework combining a seven-state absorbing within-admission model, a ten-variable physiological differential system, numerical integration, bio-inspired featuresubset search, and augmented-Lagrangian fairness constraints. A retrospective descriptive analysis of MIMIC-IV identified 22,507 adult coded-sepsis admissions among 18,041 patients, with 4,395 inhospital deaths (19.5%). The first-admission cohort contained 18,041 admissions and 3,716 deaths (20.6%). Mortality was 28.2% among ICU-associated admissions and 4.8% among admissions without ICU involvement; it increased from 6.5% for sepsis without a severe-sepsis or shock modifier to 15.1% for severe sepsis and 35.2% for septic shock. The compartmental model preserves positivity and total augmented probability mass, has monotone absorbing outcomes, admits no positive endemic equilibrium, and converges to a terminal discharge–mortality equilibrium set under a recurrence threshold below one. Constructed software tests favored fourth-order Runge–Kutta (RK4) over Euler and narrowly over fourth-order Adams–Bashforth–Moulton (ABM4). A particle-swarm verification reduced 20 RK4-derived candidates to four features. In an artificial-group fairness test, the TPR disparity decreased from 0.417 to 0.056 and the maximum TPR/FPR disparity decreased from 0.421 to 0.056; however, log loss increased from 0.610 to 0.668, Brier score from 0.214 to 0.237, and AUROC decreased from 0.690 to 0.639. Thus, the constraint reduced constructed disparity at the cost of predictive performance. INALBIO provides a concise, auditable basis for future leakage-safe fitting and locked clinical evaluation.