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<p>Cholera remains a major public health challenge in many regions of the world, and its dynamics are shaped by the complex interaction between human mobility, environmentally mediated transmission, and spatial heterogeneity. However, classical epidemic models often treat these factors independently, limiting their ability to capture the persistent spatial heterogeneity and localized endemicity observed in cholera outbreaks. In this paper, we introduce a network-based adaptive reaction–diffusion model of cholera transmission that incorporates human mobility, environmental transmission of Vibrio cholerae, and behavioral responses to infection risk. Human mobility across the network is modeled using a graph Laplacian framework, in which diffusion coefficients are dynamically regulated by local infection prevalence. Environmental transmission is represented through a localized bacterial compartment with spatially heterogeneous spillover. The well-posedness of the model is established by proving positivity, boundedness, and global existence of solutions. The disease-free equilibrium and the basic reproduction number are derived, and their stability properties are analyzed. Using spectral and operator-level analysis, we show that adaptive human mobility fundamentally alters diffusion processes on the network, enabling diffusion-driven instability even when the underlying reaction dynamics are stable. Numerical simulations confirm the analytical results and demonstrate the emergence of self-organized, long-lived endemic states characterized by strong spatial localization and heavy-tailed infection distributions. These patterns persist under stochastic perturbations and heterogeneous susceptibility, highlighting the robustness of the proposed framework. This study shows that adaptive human mobility, interacting with environmental transmission, can generate robust, self-organized cholera hotspots through diffusion-driven instability, even when local disease dynamics are stable. Overall, the model provides a mechanistic explanation for spatial heterogeneity in cholera epidemics and offers new insights into the role of adaptive human mobility in shaping cholera dynamics.</p>

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Diffusion-driven pattern formation in a network-based cholera model with environmental transmission and adaptive mobility

  • 期刊论文

  • 发表日期：

    2026年3月19日

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  • Olumuyiwa James Peter,
  • Azhar Iqbal Kashif Butt

摘要

Cholera remains a major public health challenge in many regions of the world, and its dynamics are shaped by the complex interaction between human mobility, environmentally mediated transmission, and spatial heterogeneity. However, classical epidemic models often treat these factors independently, limiting their ability to capture the persistent spatial heterogeneity and localized endemicity observed in cholera outbreaks. In this paper, we introduce a network-based adaptive reaction–diffusion model of cholera transmission that incorporates human mobility, environmental transmission of Vibrio cholerae, and behavioral responses to infection risk. Human mobility across the network is modeled using a graph Laplacian framework, in which diffusion coefficients are dynamically regulated by local infection prevalence. Environmental transmission is represented through a localized bacterial compartment with spatially heterogeneous spillover. The well-posedness of the model is established by proving positivity, boundedness, and global existence of solutions. The disease-free equilibrium and the basic reproduction number are derived, and their stability properties are analyzed. Using spectral and operator-level analysis, we show that adaptive human mobility fundamentally alters diffusion processes on the network, enabling diffusion-driven instability even when the underlying reaction dynamics are stable. Numerical simulations confirm the analytical results and demonstrate the emergence of self-organized, long-lived endemic states characterized by strong spatial localization and heavy-tailed infection distributions. These patterns persist under stochastic perturbations and heterogeneous susceptibility, highlighting the robustness of the proposed framework. This study shows that adaptive human mobility, interacting with environmental transmission, can generate robust, self-organized cholera hotspots through diffusion-driven instability, even when local disease dynamics are stable. Overall, the model provides a mechanistic explanation for spatial heterogeneity in cholera epidemics and offers new insights into the role of adaptive human mobility in shaping cholera dynamics.