Background Dengue is a major public health challenge, and predictive models are crucial for early warning systems. However, many current modeling practices rely exclusively on climatic factors or employ complex algorithms that lack the interpretability needed for informed public health decision-making. To address these shortcomings, we developed and validated a multidimensional, interpretable statistical model to predict monthly dengue incidence. Methodology/Principal Findings We used a Generalized Linear Mixed Model (GLMM) with a Negative Binomial distribution to analyze 14 years (2010-2023) of spatiotemporal data from 37 municipalities in Huila, Colombia, an endemic region. The model integrates non-linear and lagged effects of climatic, demographic, and socioeconomic factors. The final model underwent rigorous external validation on an independent test set (2021-2023). Our model demonstrated high predictive discrimination (R2 = 0.743, Spearman's {rho} = 0.657), accurately capturing the timing of epidemic outbreaks. Key findings include the identification of an optimal thermal window for transmission at 27-28{degrees}C, a threshold effect for precipitation above 800 mm, and a saturation dynamic in outbreak autocorrelation. Conclusions/Significance This mechanistically-informed statistical approach provides a robust and transparent tool for epidemiological surveillance, successfully balancing high predictive performance with the explanatory power needed for effective, data-driven public health interventions.