A Lyapunov–PINN framework for global stability of an SEIR epidemic model with educational interventions

In this work, the global dynamical behavior of an extended SEIR-type disease model is studied using Physics-Informed Neural Networks (PINNs). To capture the impact of educational interventions on disease transmission, the model includes two infectious classes, $$I_1$$ and $$I_2$$, representing individuals with and without education, respectively. The basic reproduction number, $$R_0$$, is derived to determine the existence and stability of disease-free and endemic equilibrium states. A Lyapunov-based loss function is incorporated into the PINN framework, allowing the network to enforce stability constraints while learning the system dynamics. The proposed framework utilizes structural symmetry within the compartmental dynamics to enhance the learning of Lyapunov functions and improve stability verification. This hybrid approach enables PINNs to validate global stability properties in a physics-consistent and data-efficient manner, in addition to approximating the solution trajectories of the disease model. The proposed framework builds upon conventional analytical methods in epidemiological modeling, highlighting the capability of Physics-Informed Neural Networks to accurately represent and analyze complex epidemic dynamics.