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Modeling Infectious Disease Dynamics on Higher-order Networks: Pattern Formation and Parameter Identification
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DOI：10.1016/j.jfranklin.2026.108701.png)
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Abstract
En 中文
The reaction-diffusion model is commonly used to describe the spread of infectious diseases in networks. In this study, we extend the classical model by introducing third-order diffusion terms to investigate a disease transmission model with higher-order interactions. These interactions are modeled by using first-order and second-order Laplacian matrices, aiming to capture the spatial dynamics of disease spread. We have explored the conditions for Turing instability in both the Erdős–Rényi (ER) and triangular lattice networks. Numerical simulations indicate that, when comparing disease spread across the two networks, the ER network exhibits faster transmission and a more uniform distribution of infected individuals. Moreover, the coupling strength significantly affects pattern formation, and when it reaches a certain threshold, it may trigger an explosive spread. Finally, parameter identification for both networks is performed using the Projected Gradient (PG) algorithm, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm, and the Barzilai–Borwein (BB) algorithm, with a comparative analysis of their global convergence and efficiency.
Keywords:
reaction-diffusion model
higher-order interactions
Turing instability
network dynamics
parameter identification
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4.2
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812
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