Hybrid FSIR Model with Parameter Embedding via Machine Learning

Abstract

Epidemiological model parameters vary in realworld conditions due to seasonality, interventions, and behavioral factors, making static parameterization insufficient. This paper proposes a hybrid FSIR (Fractional SusceptibleInfected-Recovered) model that combines a Caputo fractional derivative core with adaptive data-driven parameter embedding via neural networks. Unlike approaches that apply PINN solely to fractional systems [6], the proposed strategy employs MLP for fast pre-training and PINN for fine-tuning with physical consistency. On synthetic tests, MLP recovers time-varying parameters with error below 0.4%, while the hybrid approach ensures both approximation accuracy and physical correctness of predictions.