Topological Percolation in Urban Dengue Transmission: A Multi-Scale Analysis of Spatial Connectivity

TL;DR

This study applies topological data analysis to model and understand the spatial connectivity and percolation thresholds of dengue transmission in Recife, revealing complex temporal and spatial patterns beyond case counts.

Contribution

It introduces a novel topological approach using persistent homology to analyze urban dengue spread, identifying critical percolation thresholds and spatial regimes.

Findings

Identification of critical percolation thresholds in dengue spread

Detection of distinct spatial regimes from fragmented to percolated patterns

Revealing temporal heterogeneity and structural rupture in 2020

Abstract

We investigate the spatial organization of dengue cases in the city of Recife, Brazil, from 2015 to 2024, using tools from statistical physics and topological data analysis. Reported cases are modeled as point clouds in a metric space, and their spatial connectivity is studied through Vietoris-Rips filtrations and zero-dimensional persistent homology, which captures the emergence and collapse of connected components across spatial scales. By parametrizing the filtration using percentiles of the empirical distance distribution, we identify critical percolation thresholds associated with abrupt growth of the largest connected component. These thresholds define distinct geometric regimes, ranging from fragmented spatial patterns to highly concentrated, percolated structures. Remarkably, years with similar incidence levels exhibit qualitatively different percolation behavior, demonstrating that case counts alone do not determine the spatial organization of transmission. Our analysis further reveals pronounced temporal heterogeneity in the percolation properties of dengue spread, including a structural rupture in 2020 characterized by delayed or absent spatial percolation. These findings highlight percolation-based topological observables as physically interpretable and sensitive descriptors of urban epidemic structure, offering a complementary perspective to traditional spatial and epidemiological analyses.