Mathematical Formalization of Indian Medical Heritage: A Novel TB Model with ¯ Ayurveda-Inspired Behavioral Adoption Dynamics

Résumé

Tuberculosis remains a critical public health challenge in India, where traditional knowledge systems offer culturally embedded preventive practices. Formal integration of such knowledge into epidemiological models can enhance intervention strategies. We develop a novel deterministic compartmental model incorporating principles from Indian Knowledge Systems (IKS). The model extends classical TB epidemiology with dual latent compartments, reinfection, treatment staging, and a behavioral adoption component representing IKS practice uptake. Mathematical analysis includes well-posedness proofs, derivation of the basic reproduction number R₀, equilibrium characterization, stability analysis, and sensitivity assessment. The model exhibits backward bifurcation at R₀ = 1, with the disease-free equilibrium being globally asymptotically stable when R₀ < 1 and the endemic equilibrium globally stable when R₀ > 1. Sensitivity analysis identifies IKS efficacy (εS) and adoption parameters (μa, κa) as key factors reducing R₀. Numerical simulations demonstrate that IKS adoption flattens infection curves and modifies long-term disease dynamics. This study provides the first mathematical formalization of IKS principles in epidemiological modeling, offering a culturally contextualized framework for TB control policy and establishing a methodology for integrating traditional knowledge systems into computational public health.