Topological Fuzzy Analytic Hierarchy Process (ToF-AHP) for geospatial assessment of malaria vulnerability in Nigeria

Malaria remains a persistent public health challenge in Nigeria, where structural inequalities in socioeconomic, gender, and health service factors amplify transmission risk. This study develops a Topological Fuzzy Analytic Hierarchy Process (ToF-AHP) framework to assess malaria vulnerability from social and spatial perspectives. The approach integrates fuzzy pairwise comparisons with topological data analysis to capture higher-order structural patterns among vulnerability determinants. Five indicators, ITN usage, maternal education, socioeconomic status, antenatal care (ANC) non-attendance, and distance to health facilities, were used to construct a composite vulnerability index and generate a spatially explicit national map. Results show pronounced north-south disparities, with the Northeast and Northwest exhibiting high to very high vulnerability, driven largely by low maternal education, poverty, limited ANC attendance, and ITN non-use. Maternal and gender-linked socioeconomic factors account for 34.63% of overall vulnerability, highlighting how women's education, maternal healthcare access, and household conditions structurally shape malaria risk environments. In southern Nigeria, vulnerability is generally low to moderate, with localized hotspots in coastal areas of the South-South and parts of the Southwest, reflecting persistent accessibility constraints. Comparative analysis shows that ToF-AHP produces more stable priority weights than conventional fuzzy AHP. Sensitivity analyses indicate generally robust spatial patterns under ±20% one-at-a-time weight perturbations and across classification schemes, with strongest agreement between Jenks and Quantile and lower agreement under Equal Interval. Conceptual spatial validation shows that approximately 62.52% of very high malaria incidence zones coincide with high and very high vulnerability areas, supporting the model's potential to guide equity-oriented, spatially targeted malaria interventions.