  Compartmental epidemic models have been widely used for predicting the course
of epidemics, from estimating the basic reproduction number to guiding
intervention policies. Studies commonly acknowledge these models' assumptions
but less often justify their validity in the specific context in which they are
being used. Our purpose is not to argue for specific alternatives or
modifications to compartmental models, but rather to show how assumptions can
constrain model outcomes to a narrow portion of the wide landscape of potential
epidemic behaviors. This concrete examination of well-known models also serves
to illustrate general principles of modeling that can be applied in other
contexts.
