<p>Burnout among healthcare providers is a pressing mental health challenge that contributes to increased staff turnover and significant personal and professional consequences. In this study, we develop a compartmental mathematical model that captures the progression of burnout through distinct psychological states, reflecting real-world dynamics observed in healthcare settings. Our analysis establishes the existence and global stability of an endemic equilibrium, indicating that, without effective intervention, burnout is likely to persist within the workforce. To address this, we incorporate optimal control theory to design and evaluate time-dependent intervention strategies, such as workload regulation and therapeutic support. These controls aim to minimize burnout prevalence while balancing the associated implementation costs. By providing a rigorous analytical framework, this research offers actionable insights for healthcare policymakers and administrators to systematically identify and implement the most effective measures to mitigate burnout. Ultimately, this work bridges mathematical modeling with practical mental health solutions, contributing valuable tools for sustaining healthcare workforce well-being.</p>