"Stock and flow diagrams" are widely used for modeling in epidemiology. Modelers often regard these diagrams as an informal step toward a mathematically rigorous formulation of a model in terms of ordinary differential equations. However, these diagrams have a precise syntax, which can be explicated using category theory. Although commercial tools already exist for drawing these diagrams and solving the differential equations they describe, my collaborators and I have created new software that overcomes some limitations of existing tools. Basing this software on categories has many advantages, but here I explain two: functorial semantics, and model composition. This is joint work with Xiaoyan Li, Sophie Libkind, Nathaniel Osgood, Evan Patterson and Eric Redekopp. I gave this talk on Friday December 8, 2023 at the the Edinburgh Mathematical Society. Slides of some similar talks and links to the software are here: https://math.ucr.edu/home/baez/compos...