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Diffusion-Driven Pattern Formation in a Network-Based Tuberculosis Model with Higher-Order Transmission
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DOI：10.1007/s13538-026-02058-y.png)
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Abstract
En 中文
Tuberculosis (TB) transmission dynamics are significantly impacted by social clustering, prolonged exposure, and heterogeneous population mobility in a network of connected populations, which cannot be effectively captured by classical homogeneous mixing (HM) frameworks. The current study proposes and analyzes a network-based reaction-diffusion model of tuberculosis that incorporates demographic processes, disease progression, treatment, and relapse, along with heterogeneous population mobility on a complex contact network. The model of tuberculosis transmission in this study incorporates both first-order (two-person-based) and higher-order (group-based) contacts, enabling simultaneous exposure to multiple infected individuals. Using a diffusion framework based on the Laplacian operator, an explicit expression for the basic reproduction number is derived, showing that the threshold for disease invasion is determined by the spectral radius of the underlying contact network. Key analytical properties of the model are established, including existence, non-negativity, and boundedness of solutions, as well as local stability of the disease-free equilibrium. Linearization and Laplacian mode decomposition reveal that, while higher-order transmission has no impact on the disease invasion threshold, heterogeneous diffusion can induce instabilities in an otherwise stable homogeneous equilibrium state. Numerical simulations on random, scale-free, and small-world networks validate the analytical findings and demonstrate the emergence of persistent spatial heterogeneity and localized endemic hotspots. In particular, network structure and mobility heterogeneity are shown to influence the spatial patterns of infection beyond the initial outbreak phase. A mechanistic explanation for diffusion-driven pattern formation in the network-based tuberculosis model is presented, highlighting the importance of incorporating mobility and network structure in the formulation of TB control strategies.
Keywords:
Tuberculosis model
Turing patterns
Reaction-diffusion systems
Complex networks
Higher-order transmission
Diffusion-driven instability
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