Regime-Adaptive Identification of Dengue Transmission Hubs Using Discrete Morse Theory in Brazil
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Background: Dengue fever represents a persistent public health challenge in Brazil. Traditional outbreak prediction models prioritize high-incidence areas, po- tentially overlooking municipalities that serve as critical transmission bridges. Methods: We analyzed dengue surveillance data from Brazil's SINAN across three epidemic regimes: 2023 (1.51M cases), 2024 (6.43M cases, hyperendemic), and partial 2025 (1.50M cases). We constructed transmission networks using doc- umented importation flows and temporal cross-correlations with regime-adaptive thresholds. Discrete Morse theory classified municipalities as transmission sources (maxima), bridges (saddles), or sinks (minima) based on composite risk scores in- corporating case counts, connectivity, and importation patterns. Results: Despite 4.3-fold case variation across years, network density remained stable (0.0024-0.0027), with edge counts scaling proportionally to municipality cov- erage. Critical point distributions varied systematically: 2023 had 449 critical nodes; hyperendemic 2024 showed only 274 despite highest case burden; partial 2025 re- vealed 414 critical nodes. Critical municipalities exhibited significantly higher hub scores (M=2.08-2.16) versus non-critical nodes (M=0.47-0.91, Cohen's d=4.2-6.8, p<0.001). Hub scores correlated modestly with case counts (ρ=0.35-0.42), confirm- ing structural criticality diverges from epidemic volume. Conclusions: Discrete Morse theory successfully identifies transmission-critical municipalities across varying epidemic intensities. The paradoxical reduction in crit- 1 ical points during hyperendemic transmission (274 vs. 449 in moderate years) sug- gests topological simplification rather than elaboration during peak transmission. Stable network density across 4.3-fold case variation indicates resilient transmission architecture where epidemic intensity affects volume rather than structure. This provides actionable surveillance tools for public health systems managing fluctuat- ing dengue transmission, suggesting authorities to prioritize action areas structure- based rather than volume-based. Keywords: Dengue fever; Brazil; Transmission networks; Discrete Morse the- ory; Topological data analysis; Network epidemiology; Disease surveillance; Critical infrastructure
