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Abstract The effectiveness of non-pharmaceutical interventions (NPIs) during a pandemic is challenging to assess due to the multifaceted interactions between interventions and population dynamics. Significant difficulty arises from the overlapping effects of various NPIs applied to different subgroups within a population. To address this, we propose a new mathematical model that incorporates various intervention strategies, including total and partial lockdowns, school closures, and reduced interactions among specific subgroups, such as the elderly. Our model extends previous work by explicitly accounting for the quadratic nature of control costs and the interplay between overlapping controls targeting the same population segments. Using optimal control theory, we identify intervention policies that effectively mitigate disease transmission while balancing economic and societal costs. To demonstrate the utility of our approach, we apply the model to real-world data from the COVID-19 pandemic in the State of New Jersey. Our results provide insights into the trade-offs and synergies of different NPIs and the importance of accurately capturing the relationship between a policy and the population affected.