John C. Baez, Xiaoyan Li, Sophie Libkind et al.
Stock and flow diagrams are already an important tool in epidemiology, but category theory lets us go further and treat these diagrams as mathematical entities in their own right. In this chapter we use communicable disease models created with our software, StockFlow.jl, to explain the benefits of the categorical approach. We first explain the category of stock-flow diagrams and note the clear separation between the syntax of these diagrams and their semantics, demonstrating three examples of semantics already implemented in the software: ODEs, causal loop diagrams, and system structure diagrams. We then turn to two methods for building large stock-flow diagrams from smaller ones in a modular fashion: composition and stratification. Finally, we introduce the open-source ModelCollab software for diagram-based collaborative modeling. The graphical user interface of this web-based software lets modelers take advantage of the ideas discussed here without any knowledge of their categorical foundations.