John Baez

Edinburgh Mathematical Society, December 4, 2023

Categories in Epidemiology

"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.

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, to appear in Mathematics for Public Health, Springer.
• 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, EPTCS 380 (2022), 77-96.
• Sophie Libkind, Andrew Baas, Micah Halter, Evan Patterson and James Fairbanks, An algebraic framework for structured epidemic modeling, Phil. Trans. R. Soc. A. 380 (2022), 20210309.
• Evan Patterson and Micah Halter, Compositional epidemiological modeling using structured cospans.

home