Application of Physics-Informed Neural Networks (PINN) in the Kermack-McKendrick Approach to Epidemiological Models

This work proposes the use of Physics-Informed Neural Networks (PINNs) to solve an inverse problem in the Kermack-McKendrick epidemiological model, fitting the parameters of the theoretical curve to the weekly mortality data from the Black Death epidemic in Bombay (1905-1906). The original model was revisited using PINNs, which integrate differential equations and machine learning to estimate parameters, minimizing the original mean squared error (MSE) on the data. Compared to the original fit (MSE ≈ 4273.42) and the Least Squares Method (MSE ≈ 3208.53), the PINN achieved an MSE of approximately 3204.00, reducing the error by about 25 % compared to the classical model. The implementation combined data normalization, hyperparameter optimization, and automatic differentiation, enabling greater numerical stability and accuracy in parameter estimation. The results highlight the potential of PINNs in epidemic modeling, with potential future applications to COVID-19 data in Brazil.