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

Minghao Song; Hua Liu; Jingyan Ma; Kai Zhang; Qibin Zhang; Yumei Wei; Minghao Song; Hua Liu; Jingyan Ma; Kai Zhang; Qibin Zhang; Yumei Wei

doi:10.3934/nhm.2026066

Networks and Heterogeneous Media

2026, Volume 21, Issue 5: 1767-1799. doi: 10.3934/nhm.2026066

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Research Article

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

1.
School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China
2.
School of Preparatory Education, Northwest Minzu University, Lanzhou 730000, China
3.
Gansu High-Tech Innovation Service Center, Lanzhou 730000, China
4.
Experimental Teaching Department, Northwest Minzu University, Lanzhou 730000, China

Received: 07 April 2026 Revised: 10 July 2026 Accepted: 11 August 2026 Published: 20 August 2026

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 $ R_0 $, 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.
- media coverage,
- SIR model,
- infectious disease dynamics,
- PINN,
- residual network,
- highway network
Citation: Minghao Song, Hua Liu, Jingyan Ma, Kai Zhang, Qibin Zhang, Yumei Wei. Dynamical analysis of infectious disease models considering awareness factors and neural network numerical simulation[J]. Networks and Heterogeneous Media, 2026, 21(5): 1767-1799. doi: 10.3934/nhm.2026066

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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 $ R_0 $, 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.

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