The evolution of SARS-CoV-2 underscores the significance of immune escape and reinfection in the spread of epidemics. This study proposes a two-strain compartmental model of the Omicron and Delta variants of SARS-CoV-2 and combines it with the Physics-Informed Neural Network (PINN) method to estimate time-dependent epidemiological parameters using daily epidemiological and variant-specific COVID-19 data from the State of Tennessee. Furthermore, a methodical superiority of PINN has been revealed over traditional non-linear least squares methods. The model captures the dynamics of primary transmission among susceptible individuals and secondary transmission resulting from the reinfection of recovered individuals with the other variant, thereby providing a mechanistic understanding of partial cross-immunity.

The PINN assimilates the non-linear equations of the two-strain compartmental model into the learning process using automatic differentiation, thereby satisfying the equations with the observed infection and recovery data. Time normalization, scaling of the system states, and log parameterization are used to improve the stability of the optimization process and maintain the positivity of the estimated epidemiological parameters, which are hidden.

To quantify the effect of immune escape on the sustainability of the epidemic, we examine various reinfection cases, including no reinfection and bidirectional reinfection. The trained PINN is used to forecast epidemic trajectories over a 30-day horizon, capturing strain-specific dynamics, variant dominance, and the risk of resurgence. Overall, this work demonstrates that physics-informed neural networks provide a principled and interpretable framework for learning non-stationary multi-strain epidemic dynamics and enabling reliable short-term forecasting from real-world data.