Depression is a pervasive mental health disorder with significant personal, societal, and economic impacts. Its prevalence is influenced by neighbourhood characteristics (e.g. socioeconomic and environmental factors), which traditional modeling approaches often fail to capture. The incorporation of spatial dependencies offers a promising avenue for understanding depression prevalence, yet integrating deep learning with spatial modeling remains largely unexplored. This study introduces DepGCN, a novel framework combining Graph Convolutional Networks (GCNs) and Neural Networks (NNs) to model depression prevalence at the census tract level in New York State, US. The GCN block captures spatial dependencies and neighborhood effects by aggregating information from adjacent regions, while the NN block refines these features for accurate predictions. The study leverages a comprehensive dataset for 2022, comprising 121 variables across ten themes, including demographic characteristics, socioeconomic indicators, housing stability, environmental quality, and access to healthcare services. DepGCN outperforms state-of-the-art methods like KNN, SVR, and XGBoost, achieving a 5.68% higher R² and 32% lower mean squared error than SVR, as the best-competing method in our study. Feature importance analysis highlights demographic and socioeconomic factors, such as age distribution, poverty levels, and racial composition, as key predictors of depression prevalence. The findings emphasize the importance of spatial dependency and correlation in mental health modeling and the potential of deep learning to advance public health research. DepGCN provides actionable insights for policymakers, enabling targeted interventions and equitable resource allocation to improve mental health outcomes.