This directed case study examines differences between the exponential and logistic growth models in biology and how they are applied to solve real life problems. The narrative follows a student returning to the United States as he tries to assess his possible exposure to Middle East Respiratory Syndrome (MERS). To better understand his risk, James needs to get up to speed on a variety of topics including the difference between infection, transmission, virulence, etc., and how these topics can be mathematically modeled not only in relation to MERS, but also with respect to Ebola and influenza. This case was designed for use in the second semester of a biocalculus course or a course involving ordinary differential equations, which are appropriate for second year undergraduate students majoring in biology, pre-med, and bio-mathematics. These students typically have completed a semester of calculus and one year of general biology. The case provides an opportunity for students to develop their understanding of differential equations and increase their appreciation of mathematics as it applies to solving a problem of biology.