A mathematical framework for agent based models of complex biological networks.

TitleA mathematical framework for agent based models of complex biological networks.
Publication TypeJournal Article
Year of Publication2011
JournalBulletin of mathematical biology
Volume73
Issue7
Pagination1583-602
ISSN0092-8240
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. This mathematical framework can also accommodate other model types such as Boolean networks and the more general logical models, as well as Petri nets.

URLhttps://dx.doi.org/10.1007/s11538-010-9582-8
DOI10.1007/s11538-010-9582-8
Short TitleBull Math Biol
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