Dynamic properties of an SARS-CoV-2 epidemic model via stochastic PINNs

This paper introduces a novel stochastic SEIRV model for investigating the spread of the SARS-CoV-2 epidemic using stochastic physics-informed neural networks (S-PINNs). We first prove the global positivity of solutions via Lyapunov functions and Itô's formula. Then, persistence and extinction properties are analyzed by a threshold. The S-PINNs algorithm integrates noise into the loss function for seamless data-driven and physics-based learning. Finally, the algorithm based on the SEIRV model is applied to SARS-CoV-2 data from Austria, Switzerland, and Belgium, and it outperforms PINNs, LSTMs, and Logistic models, especially on noisy data.