A Categorical Framework for Modeling with Stock and Flow Diagrams

TL;DR

This paper introduces a categorical framework for modeling with stock and flow diagrams, enhancing epidemiological modeling through mathematical rigor, modular construction, and collaborative tools, demonstrated via software implementations.

Contribution

It formalizes stock-flow diagrams categorically, enabling modular composition, stratification, and integration with software tools like StockFlow.jl and ModelCollab.

Findings

Categorical formalization of stock-flow diagrams.

Development of modular composition and stratification methods.

Introduction of user-friendly collaborative modeling software.

Abstract

Stock and flow diagrams are already an important tool in epidemiology, but category theory lets us go further and treat these diagrams as mathematical entities in their own right. In this chapter we use communicable disease models created with our software, StockFlow.jl, to explain the benefits of the categorical approach. We first explain the category of stock-flow diagrams and note the clear separation between the syntax of these diagrams and their semantics, demonstrating three examples of semantics already implemented in the software: ODEs, causal loop diagrams, and system structure diagrams. We then turn to two methods for building large stock-flow diagrams from smaller ones in a modular fashion: composition and stratification. Finally, we introduce the open-source ModelCollab software for diagram-based collaborative modeling. The graphical user interface of this web-based software lets modelers take advantage of the ideas discussed here without any knowledge of their categorical foundations.