Mathematical modeling of infectious disease at scale is important, but
challenging. Some of these difficulties can be alleviated by an approach that
takes diagrams seriously as mathematical formalisms in their own right. Stock &
flow diagrams are widely used as broadly accessible building blocks for
infectious disease modeling. In this chapter, rather than focusing on the
underlying mathematics, we informally use communicable disease examples created
by the implemented software of StockFlow.jl to explain the basics,
characteristics, and benefits of the categorical framework. We first
characterize categorical stock & flow diagrams, and note the clear separation
between the syntax of stock & flow diagrams and their semantics, demonstrating
three examples of semantics already implemented in the software: ODEs, causal
loop diagrams, and system structure diagrams. We then establish composition and
stratification frameworks and examples for stock & flow diagrams. Applying
category theory, these frameworks can build large diagrams from smaller ones in
a modular fashion. Finally, we introduce the open-source ModelCollab software
for diagram-centric real-time collaborative modeling. Using the graphical user
interface, this web-based software allows the user to undertake the types of
categorically-rooted operations discussed above, but without any knowledge of
their categorical foundations