Dynamics and forecasting of an age-structured stochastic SIR model with Lévy perturbations via physics-informed neural networks

Understanding and predicting real-world epidemic dynamics has consistently posed a formidable challenge. This study addresses an age-structured stochastic SIR model incorporating a general incidence rate, high-order white noise, and Lévy jump perturbations. By employing Lyapunov function method, we establish the existence and uniqueness of a global positive solution. Furthermore, we derive a stochastic threshold that delineates the conditions for disease persistence and extinction. Moreover, the existence and uniqueness of a stationary distribution are proven by applying an improved version of Hasminskii's theory. Numerical simulations based on the positivity- and boundedness-preserving Euler-Maruyama scheme corroborate the theoretical results, showing that reducing the amplitude of higher-order noise amplifies the infection burden, whereas increasing the age-structure parameters <i>ϑ</i> and <i>ς</i> markedly suppresses transmission. Finally, the efficacy of physics-informed neural network based on stochastic SIR model (PINN-SIR), is demonstrated through its application to the fitting and forecasting of COVID-19 case in Zhejiang, China. The method shows promise for extension to more complex dynamical systems and diseases.