"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 I
will explain three: functorial semantics, model composition, and model
stratification. This is joint work with Xiaoyan Li, Sophie
Libkind, Nathaniel Osgood, Evan Patterson and Eric Redekopp.
You can see my slides here and watch my talk here:
You can get the code for Stockflow
here
and ModelCollab
here.
John Baez, Xiaoyan Li, Sophie Libkind, Nathaniel D. Osgood and Eric
Redekopp, A categorical framework
for modeling with stock and flow diagrams, in Mathematics of
Public Health: Mathematical Modelling from the Next Generation,
eds. Jummy David and Jianhong Wu, Springer, 2023, pp. 175-207.
John Baez, Xiaoyan Li, Sophie Libkind, Nathaniel Osgood and Evan Patterson,
Compositional modeling with
stock and flow diagrams, Proceedings Fifth International Conference
on Applied Category Theory, EPTCS380 (2022), 77-96.
