Dynamical analysis of infectious disease models considering awareness factors and neural network numerical simulation

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Abstract

Media coverage plays a crucial role in the spread of infectious diseases. To investigate the influence of media intervention on epidemic transmission, we adopted a media-aware susceptible–infected–recovered (SIR) model based on media-intervention epidemic studies. Our primary focus was the systematic optimization of Physics-Informed Neural Network (PINN) architectures. The dynamic behavior of the epidemic system was investigated through equilibrium, stability, and bifurcation analyses. The theoretical analysis characterized the threshold dynamics of the model through the basic reproduction number R₀, while numerical simulations further indicated that media intervention can reduce the infection peak and delay its arrival. Based on this epidemic framework, PINNs were employed for numerical simulation, and three algorithm optimization approaches were systematically investigated: (1) Replacing Euler-generated synthetic reference trajectories with RK4-generated reference trajectories to examine the influence of numerical discretization accuracy on PINN training and evaluation; (2) increasing the network depth from three to five layers to enhance the approximation of nonlinear epidemic dynamics; and (3) introducing skip-connection architectures, including Residual, Highway, and an exploratory residual-integrated Highway (ResHighway) network. Comparative results showed that the Residual network achieved the best overall accuracy and stability. Although the proposed ResHighway architecture yielded marginal accuracy gains compared with the Highway network, it underperformed the lightweight Residual network. This observation implies that overcomplicating network architectures may not bring consistent performance improvements to PINNs applied in epidemic dynamic modeling.

Keywords

media coverage / SIR model / infectious disease dynamics / PINN / residual network / highway network

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