The COVID-19 pandemic is a rolling crisis that required policymakers around the world to take action to manage the pandemic spread. During the period where vaccination was not available, the pandemic spread management lied in Non-Pharmaceutical Interventions (NPIs). A large number of mathematical models have been proposed to predict the pandemic spread and analyze the influence of various NPIs on multiple scenarios, getting more accurate and sophisticated over time. In this work, we review the latest mathematical models for pandemic spread NPIs and their main shortages. Specifically, the usage of modeling a homogeneous population rather than a heterogeneous one.