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.

翻译：我们运用统计物理学和拓扑数据分析工具，研究了2015年至2024年巴西累西腓市登革热病例的空间组织结构。将报告病例建模为度量空间中的点云，并通过Vietoris-Rips滤过和零维持续同调分析其空间连通性，该方法捕捉了不同空间尺度下连通分量的涌现与坍缩。通过使用经验距离分布的百分位数对滤过进行参数化，我们识别出与最大连通分量突然增长相关的临界渗流阈值。这些阈值定义了从碎片化空间模式到高度集中、渗流结构的不同几何状态。值得注意的是，发病率水平相近的年份表现出性质不同的渗流行为，表明仅凭病例数量无法决定传播的空间组织。我们的分析进一步揭示了登革热传播渗流特性存在显著的时间异质性，包括2020年出现的以空间渗流延迟或缺失为特征的结构性断裂。这些发现凸显了基于渗流的拓扑可观测量作为城市疫情结构的物理可解释且灵敏的描述符，为传统的空间与流行病学分析提供了补充视角。