Evaluating public health intervention techniques is essential to manage dengue successfully. This study proposes an epidemic model that includes two essential therapeutic interventions: vaccination and treating infected individuals to better understand dengue transmission dynamics. We introduce a seven-state model and investigate the model's endemic and disease-free equilibria. Results show that when vaccination efficacy is low, therapy is a more effective strategy for lowering dengue cases, whereas a highly effective vaccine significantly reduces dengue cases. The study also formulates an optimal control problem, suggesting that combined strategies are more effective in mitigating the disease spread.