A Mathematical Framework for Agent Based Models of Complex Biological Networks

TL;DR

This paper introduces a mathematical framework that extends the ODD protocol for agent-based models of biological networks, enabling their analysis as dynamical systems with algebraic structure.

Contribution

It proposes an extension to the ODD protocol to describe agent-based models as algebraic dynamical systems for better analysis.

Findings

Mathematical specification facilitates model analysis.

Examples demonstrate the utility of the framework.

Framework bridges simulation and mathematical analysis.

Abstract

Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models it is not always easy to use published models. Also, since model descriptions are not usually given in mathematical terms, it is difficult to bring mathematical analysis tools to bear, so that models are typically studied through simulation. In order to address this issue, Grimm et al. proposed a protocol for model specification, the so-called ODD protocol, which provides a standard way to describe models. This paper proposes an addition to the ODD protocol which allows the description of an agent-based model as a dynamical system, which provides access to computational and theoretical tools for its analysis. The mathematical framework is that of algebraic models, that is, time-discrete dynamical systems with algebraic structure. It is shown by way of several examples how this mathematical specification can help with model analysis.