Balancing Human Mobility and Health Care Coverage in Sentinel Surveillance of Brazilian Indigenous Areas: Mathematical Optimization Approach.

Background: Optimizing sentinel surveillance site allocation for early pathogen detection remains a challenge, particularly in ensuring coverage of vulnerable and underserved populations. Objective: This study evaluates the current respiratory pathogen surveillance network in Brazil and proposes an optimized sentinel site distribution that balances Indigenous population coverage and national human mobility patterns. Methods: We compiled Indigenous Special Health District (Portuguese: Distrito Sanitário Especial Indígena [DSEI]) locations from the Brazilian Ministry of Health and estimated national mobility routes by using the Ford-Fulkerson algorithm, incorporating air, road, and water transportation data. To optimize sentinel site selection, we implemented a linear optimization algorithm that maximizes (1) Indigenous region representation and (2) human mobility coverage. We validated our approach by comparing results with Brazil's current influenza sentinel network and analyzing the health attraction index from the Brazilian Institute of Geography and Statistics to assess the feasibility and potential benefits of our optimized surveillance network. Results: The current Brazilian network includes 199 municipalities, representing 3.6% (199/5570) of the country's cities. The optimized sentinel site design, while keeping the same number of municipalities, ensures 100% coverage of all 34 DSEI regions while rearranging 108 (54.3%) of the 199 cities from the existing flu sentinel system. This would result in a more representative sentinel network, addressing gaps in 9 of 34 previously uncovered DSEI regions, which span 750,515 km² and have a population of 1.11 million. Mobility coverage would improve by 16.8 percentage points, from 52.4% (4,598,416 paths out of 8,780,046 total paths) to 69.2% (6,078,747 paths out of 8,780,046 total paths). Additionally, all newly selected cities serve as hubs for medium- or high-complexity health care, ensuring feasibility for pathogen surveillance. Conclusions: The proposed framework optimizes sentinel site allocation to enhance disease surveillance and early detection. By maximizing DSEI coverage and integrating human mobility patterns, this approach provides a more effective and equitable surveillance network, which would particularly benefit underserved Indigenous regions.