Topological and Nonlinear Dynamics in Computational Psychiatry: Modeling Hyperacute Behavioral Transitions in PANS

Pediatric Acute-onset Neuropsychiatric Syndrome (PANS) is clinically characterized by a profound, non-linear, hyper-acute onset of severe obsessive-compulsive disorder (OCD), restrictive eating behaviors, or tics. This study introduces a novel analytical baseline model designed to simulate the non-linear, abrupt onset of symptoms in PANS. Utilizing Thom's cusp catastrophe theory, the framework models neuropsychiatric symptom severity as a state variable governed by a cubic equilibrium equation. Rather than assuming linear pathways, we introduce a sigmoidal gating function where peripheral inflammation is modulated by blood-brain barrier (BBB) permeability. Under this coordinate transformation, BBB disruption acts as the critical bifurcation factor that forces the neuroimmune system into a bistable state. The primary value of this topological model lies in its ability to mathematically explain the hallmark "overnight" clinical onset and the phenomenon of hysteresis observed during recovery.