Modeling Asthma Burden in India Using Physics-Informed Neural Networks with Time-Varying Parameters Driven by Pollution Dynamics

Asthma is a chronic respiratory condition exacerbated by environmental pollution, particularly in rapidly urbanizing regions such as India. Accurate modeling of asthma dynamics in response to pollution is challenging due to the presence of un-measured, time-varying parameters. In this study, we develop a seven-compartment asthma-pollution model incorporating susceptible, carrier, exposed, undiagnosed infected, diagnosed infected, recovered, and pollutant burden compartments. We employ a physics-informed neural network (PINN) framework to infer the hidden temporal profiles of key parameters, including the pollution-driven transmission rate ({xi}(t)), environmental progression rate ({lambda}1(t)), pollutant accumulation rate (A(t)), and pollutant depletion rate ({tau}t(t)), from synthetically generated noisy data. The PINN approach integrates the compartmental ODE system via a fourth-order Runge-Kutta solver and minimizes a combined loss function capturing both state fidelity and parameter consistency. Evaluation of model performance demonstrates excellent agreement with ground-truth trajectories, achieving mean squared errors below 10-4 for all compartments and sub-2% deviation for inferred parameters. These results highlight the utility of PINNs for reverse function discovery in complex epidemiological systems and provide a framework for quantitatively linking environmental pollution to asthma burden in settings with limited observational data.