A progressive ODE model of seasonal allergic rhinitis: from core Th2 axis to 21-dimensional multi- pathway integration with seasonal dynamics and directional assessment

Background Seasonal allergic rhinitis (SAR) affects approximately 400 million individuals worldwide, yet a quantitative framework integrating the complete immunological cascade from allergen exposure to clinical symptoms is lacking. Individual pathways (Th2/IgE, TLR4/NF-κB, Th17/Treg) have been characterized in isolation, but their interactions and relative contributions to symptom generation remain poorly understood. Methods We constructed a progressively extended ordinary differential equation (ODE) model evolving from a 10-dimensional core Th2/IgE/mast cell/eosinophil axis to a 21-dimensional system integrating TLR4/MyD88/NF-κB innate immunity and Th17/Treg imbalance with seasonal priming and tolerance dynamics. The model was calibrated against published cytokine data (Leaker 2016, Linton 2025) and validated against clinical trial drug efficacy (Corren 2021, Bauer 2023). Sobol global sensitivity analysis (5,888 samples, 21 parameters) was performed. A 2,000-patient virtual cohort was generated with lognormal parameter distributions (CV = 30%), and PCA-reduced K-means clustering (PC1–PC2 of six output metrics) identified virtual subtypes. Convergence was verified by doubling the base sample size to N = 512: all S1 and ST indices changed by less than 0.013, confirming adequate convergence at the original N = 256. Results The core model reproduces the biphasic symptom profile (immediate peak 7.0 at 1.9h, late plateau 3.4 at 12-24h) and reveals a mechanistic dichotomy: the immediate peak is governed by the mast cell-mediator axis while total burden is controlled by the eosinophil-resolution axis. The 19-dimensional extension shows that TLR4 and Th17/Treg pathways primarily modulate the late-phase response (11.3% AUC reduction via IL-10 suppression). Sobol analysis identifies the IL-10/Treg axis as the 3rd-4th most important determinant of total symptom burden. The seasonal extension captures immunological priming (IL-5 + 46.1%). Three virtual subtypes map to published AR phenotypes. The model predicts that the Th17/Treg ratio shows a stronger directional association with late-phase severity than IgE, consistent with published clinical data. Conclusion This progressive ODE model provides a quantitative framework for understanding SAR pathway interactions and generates five testable hypotheses for future experimental validation. The finding that 22% of simulated individuals in the virtual cohort exhibit a severe IL-17-high phenotype supports the hypothesis that Th17/Treg-targeted therapies may benefit a biologically defined subgroup of SAR patients, warranting validation in real patient cohorts.