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The COVID-19 pandemic highlighted the need to quickly respond, via public policy, to the onset of an infectious disease breakout. Deciding the type and level of interventions a population must consider to mitigate risk and keep the disease under control could mean saving thousands of lives. Many models were quickly introduced highlighting lockdowns, testing, contact tracing, travel policies, later on vaccination, and other intervention strategies along with costs of implementation. Here, we provided a framework for capturing population heterogeneity whose consideration may be crucial when developing a mitigation strategy based on non-pharmaceutical interventions. Precisely, we used age-stratified data to segment our population into groups with unique interactions that policy can affect such as school children or the oldest of the population, and formulated a corresponding optimal control problem considering the economic cost of lockdowns and deaths. We applied our model and numerical methods to census data for the state of New Jersey and determined the most important factors contributing to the cost and the optimal strategies to contained the pandemic impact.