Mathematical Modeling of NF-κB Inhibition and Biofilm Disruption in LPS-Induced PANS: A Systems Biology Approach

Pediatric Acute-onset Neuropsychiatric Syndrome (PANS) is a complex neuroinflammatory disorder frequently exacerbated by peripheral immune triggers via the microbiota-gut-brain axis. This analysis synthesizes the mathematical modeling of a clinical case involving LPS gut dysbiosis with structured biofilms, presenting with profound anxiety, depression, and irritability. Through an iterative ordinary differential equation (ODE) approach, we demonstrate how a dual-action phytotherapeutic strategy—utilizing fresh aqueous ginger extract and grapefruit seed extract—achieves total symptom remission over a 60-day period while bypassing traditional Jarisch-Herxheimer (die-off) neuroinflammatory spikes.