It is the case that some activities claiming to reside under the STEM umbrella do not, in fact, give participants the opportunity to engage in anything other than routine mathematics. With this in mind, we explore here the potential for developing and then delivering STEM activities based on the discipline of mathematical epidemiology. We argue that this field does indeed provide us with a rich source of such activities which, in addition to allowing students to encounter some interesting and demanding mathematics, encourages non-trivial forays into aspects of the biological sciences, computer technology, chemistry, medicine and statistics. Projects may be tailored to the needs of both secondary-school pupils and undergraduates. The examples presented here will, as well as providing ideas for use in the classroom or lecture theatre, be utilized in order to highlight a number of the key issues associated with the STEM agenda.