Abstract / Summary
Abstract Depression is a major public-health burden whose population dynamics reflect interacting social, behavioral, clinical, and treatment-related processes. Mathematical models can provide a useful framework for evaluating population-level interventions; however, model parameters are inherently uncertain, and real-world systems may be affected by unexpected disturbances. Intervention strategies optimized for a fixed nominal model may therefore lose performance when actual dynamics differ from those assumed during controller design. Robust nonlinear feedback control provides an alternative framework in which interventions adapt continuously to changes in the system state. Here, we extend a seven-compartment nonlinear depression model by developing a sliding mode control (SMC) strategy for the secondary-depression compartment and compare it with a Pontryagin maximum principle (PMP) optimal-control benchmark. To separate robustness from differences in intervention intensity, the controllers were evaluated under matched nominal integrated quadratic control effort. PMP achieved better nominal performance, whereas SMC showed substantially greater resilience when the system departed from nominal assumptions. Under ± 20% parameter uncertainty, median degradation in cumulative depression burden was 0.23% with SMC compared with 3.98% with PMP. This robustness advantage persisted across generic uncertainty levels from ± 5% to ± 30% and in an additional analysis using parameter ranges derived from the published confidence intervals of the empirical model calibration. SMC also substantially attenuated externally imposed disturbances across variations in shock magnitude, timing, and duration. Lyapunov analysis established the reaching condition for the unsaturated SMC law, while numerical evaluation characterized the effects of intervention constraints on the implemented closed-loop dynamics. These findings reveal a nominal-performance–robustness trade-off between optimal and robust feedback control and demonstrate the potential value of explicitly accounting for uncertainty and disturbances when designing intervention strategies for nonlinear population-level depression models.