Comparative study of PINNs and numerical methods in infectious disease reaction-diffusion models

Lingxi Xia; Bangsheng Han; Lingxi Xia; Bangsheng Han

doi:10.3934/bdia.2025012

Big Data and Information Analytics

2025, Volume 9, 265-284. doi: 10.3934/bdia.2025012

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Research article

Comparative study of PINNs and numerical methods in infectious disease reaction-diffusion models

Lingxi Xia ,
Bangsheng Han ^,

School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China

Received: 28 October 2025 Revised: 21 November 2025 Accepted: 24 November 2025 Published: 28 November 2025

This study employed physics-informed neural networks (PINNs) and numerical methods to solve a two-dimensional spatial susceptible-infectious (SI) epidemic model incorporating nonlinear propagation terms and diffusion processes. By integrating governing equations, initial and boundary conditions, and sparse reference solution data, PINNs define a multi-objective loss function, forming a supervised learning framework grounded in physical mechanisms. The results demonstrated that PINNs can accurately capture the spatiotemporal evolution patterns and spatial distribution characteristics of the density field in the model. In terms of solution accuracy, the long time predictions of PINNs significantly outperformed those of the Euler method and the second-order Runge-Kutta method (RK2), showing strong agreement with the fourth-order Runge-Kutta method (RK4) benchmark solutions. This validates the effectiveness of PINNs in solving complex reaction-diffusion systems, offering an innovative approach for modeling the spatial dynamics of infectious diseases.
- physics-informed neural networks,
- reaction-diffusion equations,
- infectious disease models,
- Runge-Kutta methods,
- supervised learning
Citation: Lingxi Xia, Bangsheng Han. Comparative study of PINNs and numerical methods in infectious disease reaction-diffusion models[J]. Big Data and Information Analytics, 2025, 9: 265-284. doi: 10.3934/bdia.2025012

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Abstract

This study employed physics-informed neural networks (PINNs) and numerical methods to solve a two-dimensional spatial susceptible-infectious (SI) epidemic model incorporating nonlinear propagation terms and diffusion processes. By integrating governing equations, initial and boundary conditions, and sparse reference solution data, PINNs define a multi-objective loss function, forming a supervised learning framework grounded in physical mechanisms. The results demonstrated that PINNs can accurately capture the spatiotemporal evolution patterns and spatial distribution characteristics of the density field in the model. In terms of solution accuracy, the long time predictions of PINNs significantly outperformed those of the Euler method and the second-order Runge-Kutta method (RK2), showing strong agreement with the fourth-order Runge-Kutta method (RK4) benchmark solutions. This validates the effectiveness of PINNs in solving complex reaction-diffusion systems, offering an innovative approach for modeling the spatial dynamics of infectious diseases.

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