# Products of Compartmental Models in Epidemiology

## TL;DR

This paper introduces a product-based framework for structured epidemic models, enabling systematic development, analysis, and extension to complex features like multi-strain dynamics, thereby enhancing understanding and sensitivity analysis.

## Contribution

It presents a novel product structure approach for epidemic models, facilitating model refinement, extension, and systematic analysis of complex epidemiological features.

## Key findings

- Product structures derived from directed graphs effectively model geographic and demographic heterogeneity.
- The framework supports extension to multi-strain pathogen dynamics.
- Systematic use of products aids in model development and sensitivity analysis.

## Abstract

In this paper, we show that many structured epidemic models may be described using a straightforward product structure. Such products, derived from products of directed graphs, may represent useful refinements including geographic and demographic structure, age structure, gender, risk groups, or immunity status. Extension to multi-strain dynamics, i.e. pathogen heterogeneity, is also shown to be feasible in this framework. Systematic use of such products may aid in model development and exploration, can yield insight, and could form the basis of a systematic approach to numerical structural sensitivity analysis.