Software for Compositional Modeling in Epidemiology

Here is the video of my talk at Applied Category Theory 2023. While it has ‘epidemiology’ in the title, it’s mostly about general ways to use category theory to build flexible, adaptable models:

Here are the slides:

• Software for compositional modeling in epidemiology.

Abstract. Mathematical models of disease are important and widely used, but building and working with these models at scale is challenging. Many epidemiologists use “stock and flow diagrams” to describe ordinary differential equation (ODE) models of disease dynamics. In this talk we describe and demonstrate two software tools for working with such models. The first, called StockFlow, is based on category theory and written in AlgebraicJulia. The second, called ModelCollab, runs on a web browser and serves as a graphical user interface for StockFlow. Modelers often regard diagrams as an informal step toward a mathematically rigorous formulation of a model in terms of ODEs. However, stock and flow diagrams have a precise mathematical syntax. Formulating this syntax using category theory has many advantages for software, but in this talk we explain three: functorial semantics, model composition, and model stratification.

You can get the code for Stockflow here and ModelCollab here.

For more, read these:

• John Baez, Xiaoyan Li, Sophie Libkind, Nathaniel Osgood and Evan Patterson, Compositional modeling with stock and flow diagrams.

• John Baez, Xiaoyan Li, Sophie Libkind, Nathaniel D. Osgood, Long Pham and Eric Redekopp, A categorical framework for modeling with stock and flow diagrams.

• Andrew Baas, James Fairbanks, Micah Halter, Sophie Libkind and Evan Patterson, An algebraic framework for structured epidemic modeling.

• Sophie Libkind, Andrew Baas, Evan Patterson and James Fairbanks,
Operadic modeling of dynamical systems: mathematics and computation.