Deep learning aided surrogate modeling of the epidemiological models

The study of disease spread often relies on compartmental models based on nonlinear differential equations, which typically require computationally intensive numerical algorithms, especially for parameter estimation. This paper introduces a deep neural network-based surrogate modeling (DNN-SM) approach, engineered to accurately replicate the behavior of epidemiological models while significantly reducing computational demands. This approach adeptly handles the complexities inherent in nonlinear models and optimizes parameter estimation efficiency. We demonstrate the efficacy of the DNN-SM through its application to various disease models, including the Susceptible–Infected–Recovered (SIR), Susceptible–Exposed–Infected–Recovered (SEIR), and the more complex Susceptible–Exposed–Presymptomatic–Asymptomatic–Symptomatic–Reported (SEPADR) models. The results reveal that our DNN-SM not only forecasts solution trajectories with high accuracy but also operates approximately ten times faster than traditional ODE solvers for forward problems. By comparing the parameter estimation results of the DNN-SM and ODE solvers, we show that the DNN-SM produces highly accurate results with much less computational costs. The DNN-SM has been validated using both short-term and long-term COVID-19 data from several European countries. The results demonstrate that the DNN-SM provides accurate trajectories with significantly lower computational cost compared to traditional numerical methods.