Modeling leptospirosis incidence in the northeast of Brazil using probability distributions and climatic factors: Insights for public health

• Robust methodological approach applying various probability distribution functions. • Leptospirosis incidence in nine capital cities of Brazil between 2001 and 2022. • Integration of statistical modeling with climatic variables. • Relationship between extreme weather events and leptospirosis outbreaks. This study aimed to model the incidence of leptospirosis as a function of climatic variables—precipitation (Pcp, mm) and temperature (T,°C)—using different probability distribution functions (PDF). Monthly time series of leptospirosis cases and climate data from nine cities in Northeast Brazil (NEB) (2001–2022) were analyzed using gamma, normal, lognormal, and Weibull distributions, combined with correlation analyses to assess relationships between environmental factors and disease incidence. Our findings indicated that all distributions successfully modeled the observed data, but the Normal distribution provided the best fit across most cities, as confirmed by the Kolmogorov–Smirnov (KS) test (average KS statistic of normal: 0.284; lognormal: 0.444; gamma: 0.442; Weibull: 0.432 to p -value > 0.05). In conclusion, this study emphasizes the value of applying continuous probability distributions to understand leptospirosis patterns in low-incidence contexts and underscores the influence of climatic conditions on disease occurrence. Future studies incorporating additional environmental and social parameters may enhance predictive accuracy and inform public health strategies to reduce leptospirosis outbreaks in vulnerable flood-prone areas.