In this paper, we considered a partitioned epidemic model with reaction-diffusion behavior, analyzed the dynamics of populations in various compartments, and explored the significance of spreading parameters. Unlike traditional approaches, we proposed a novel paradigm for addressing the dynamics of epidemic models: Inferring model dynamics and, more importantly, parameter inversion to analyze disease spread using Reaction-Diffusion Disease Information Neural Networks (RD-DINN). This method leverages the principles of hidden disease spread to overcome the black-box mechanism of neural networks relying on large datasets. Through an embedded deep neural network incorporating disease information, the RD-DINN approximates the dynamics of the model while predicting unknown parameters. To demonstrate the robustness of the RD-DINN method, we conducted an analysis based on two disease models with reaction-diffusion terms. Additionally, we systematically investigated the impact of the number of training points and noise data on the performance of the RD-DINN method. Our results indicated that the RD-DINN method exhibits relative errors less than $ 1\% $ in parameter inversion with $ 10\% $ noise data. In terms of dynamic predictions, the absolute error at any spatiotemporal point does not exceed $ 5\% $. In summary, we present a novel deep learning framework RD-DINN, which has been shown to be effective for reaction-diffusion disease modeling, providing an advanced computational tool for dynamic and parametric prediction of epidemic spread. The data and code used can be found at https://github.com/yuanfanglila/RD-DINN.
Citation: Xiao Chen, Fuxiang Li, Hairong Lian, Peiguang Wang. A deep learning framework for predicting the spread of diffusion diseases[J]. Electronic Research Archive, 2025, 33(4): 2475-2502. doi: 10.3934/era.2025110
In this paper, we considered a partitioned epidemic model with reaction-diffusion behavior, analyzed the dynamics of populations in various compartments, and explored the significance of spreading parameters. Unlike traditional approaches, we proposed a novel paradigm for addressing the dynamics of epidemic models: Inferring model dynamics and, more importantly, parameter inversion to analyze disease spread using Reaction-Diffusion Disease Information Neural Networks (RD-DINN). This method leverages the principles of hidden disease spread to overcome the black-box mechanism of neural networks relying on large datasets. Through an embedded deep neural network incorporating disease information, the RD-DINN approximates the dynamics of the model while predicting unknown parameters. To demonstrate the robustness of the RD-DINN method, we conducted an analysis based on two disease models with reaction-diffusion terms. Additionally, we systematically investigated the impact of the number of training points and noise data on the performance of the RD-DINN method. Our results indicated that the RD-DINN method exhibits relative errors less than $ 1\% $ in parameter inversion with $ 10\% $ noise data. In terms of dynamic predictions, the absolute error at any spatiotemporal point does not exceed $ 5\% $. In summary, we present a novel deep learning framework RD-DINN, which has been shown to be effective for reaction-diffusion disease modeling, providing an advanced computational tool for dynamic and parametric prediction of epidemic spread. The data and code used can be found at https://github.com/yuanfanglila/RD-DINN.
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Xiao Chen, Fuxiang Li, Hairong Lian, Peiguang Wang. A deep learning framework for predicting the spread of diffusion diseases[J]. Electronic Research Archive, 2025, 33(4): 2475-2502. doi: 10.3934/era.2025110
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