Correlation-Weighted Communicability Curvature as a Structural Driver of Dengue Spread: A Bayesian Spatial Analysis of Recife (2015-2024)

TL;DR

This study addresses dengue diffusion in Recife by linking urban road-network structure to incidence patterns through correlation-weighted communicability curvature. It develops a graph-theoretic framework where edges reflect both structural connectivity via the matrix exponential $C_{ij}(\beta)$ and temporal synchrony via weights $w_{ij}$ to form $\kappa_{ij} = C_{ij}(\beta) w_{ij}$. Across Negative Binomial, fixed-effects, SAR/SAC, and INLA/BYM2 models, curvature consistently exhibits the strongest, most stable negative association with dengue incidence, and in BYM2 the structured spatial component collapses ($\phi \approx 0$), showing that functional urban connectivity explains spatial dependence previously attributed to adjacency. These findings imply that dengue spread in dense cities is governed more by network-mediated flows than by geographic contiguity, with practical implications for targeted surveillance and control that leverage structural connectivity and high-resolution risk mapping. The work integrates network metrics, spectral graph theory, and Bayesian hierarchical modeling to produce robust, actionable insights for urban epidemiology and arboviral surveillance, and suggests future SPDE-based extensions for continuous risk surfaces.

Abstract

We investigate whether the structural connectivity of urban road networks helps explain dengue incidence in Recife, Brazil (2015--2024). For each neighborhood, we compute the average \emph{communicability curvature}, a graph-theoretic measure capturing the ability of a locality to influence others through multiple network paths. We integrate this metric into Negative Binomial models, fixed-effects regressions, SAR/SAC spatial models, and a hierarchical INLA/BYM2 specification. Across all frameworks, curvature is the strongest and most stable predictor of dengue risk. In the BYM2 model, the structured spatial component collapses ($φ\approx 0$), indicating that functional network connectivity explains nearly all spatial dependence typically attributed to adjacency-based CAR terms. The results show that dengue spread in Recife is driven less by geographic contiguity and more by network-mediated structural flows.

Figures (4)

• Figure 1: Street-level functional connectivity graph for Recife. Nodes represent geocoded dengue case locations, and edges denote correlated local incidence time series. The graph is superimposed on the geographic map to reveal the underlying transmission topology, highlighting structural pathways and spatial constraints that shape diffusive spread.
• Figure 2: Mean communicability curvature by neighborhood in 2015.
• Figure 3: Mean communicability curvature by neighborhood in 2019.
• Figure 4: Mean communicability curvature by neighborhood in 2024.

Theorems & Definitions (16)

• Proposition 1: Monotonicity of Communicability
• proof
• Theorem 1: Communicability as a Diffusion Approximation
• proof
• Proposition 2: Percolation Threshold Maximizes Mean Communicability
• Lemma 1: Spectral Representation of Communicability
• proof
• Lemma 2: Spectral Growth at the Percolation Threshold
• proof
• Lemma 3: Path Diversity at the Critical Threshold