The Consortium for Mathematics and its Applications (COMAP), hosts an annual mathematical modeling contest for undergraduate students known as the Mathematical Challenge in Modeling (MCM). A list of problems and results can be found here.

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Modeling framework figure and PPT for how to use: A “Rule-of-Five” Framework for Models and Modeling to Unify Mathematicians and Biologists and Improve Student Learning, published here
https://www.tandfonline.com/doi/full/10.1080/10511970.2018.1489318

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This classroom modeling project applies mathematical techniques to solve a problem related to drug dosage patterns. Suitable for high school or undergraduate students. Prerequisite: Calculus I.