JOINT COMPUTATIONAL STUDY OF GLOBAL STABILITY AND PARAMETER ESTIMATION IN SEIR MODELS USING A PHYSICS-INFORMED NEURAL NETWORK

This study presents a Physics-Informed Neural Network (PINN) framework for simulating disease dynamics governed by the Susceptible-Exposed-Infectious-Recovered (SEIR) model. Utilizing a fully connected neural network implemented in PyTorch, the approach employs automatic differentiation to enforce initial conditions and solve the system of ordinary differential equations (ODEs) associated with the SEIR model. The PINN is trained using a composite loss function that integrates boundary conditions with physics-based constraints, allowing for accurate modeling of the temporal evolution of all SEIR compartments. Beyond forward simulation, this work addresses the inverse problem of parameter estimation specifically, identifying the time-dependent contact rate using temporal epidemiological data. By training the network on observed data for the susceptible, exposed, infectious, and recovered populations, the model approximates the solution vector and simultaneously minimizes a loss that combines data fidelity with the residual of the SEIR system. A key contribution of this study is the numerical demonstration of the SEIR system's global stability without assuming a constant population size, achieved via a generalized Lyapunov theorem. Additionally, physical constraints embedded directly into the learning process enhance the model's ability to inform control strategies and ensure long-term system stabilization. This machine learning-based framework offers a robust and flexible tool for both understanding disease spread and conducting real-time epidemiological inference. It highlights the potential of PINNs for solving complex inverse problems, improving predictive accuracy, and supporting data-driven decision-making in public health. The code can be downloaded fromhttps://github.com/shahbaz1982/SEIR.