Category theory provides a general framework for building models of
dynamical systems. We explain this framework and illustrate it with
the example of "stock and flow diagrams". These diagrams are widely
used for simulations in epidemiology. Although tools already exist for
drawing these diagrams and solving the systems of differential
equations they describe, we have created a new software package called
StockFlow which uses ideas from category theory to overcome some
limitations of existing software. We illustrate this with code in
StockFlow that implements a simplified version of a COVID-19 model
used in Canada. This is joint work with Xiaoyan Li, Sophie Libkind,
Nathaniel Osgood and Evan Patterson.
You can see the talk slides here and watch the video above.
For more, read these:
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.