A Mathematical Framework for Agent Based Models of Complex Biological Networks

Franziska Hinkelmann, David Murrugarra, Abdul Salam Jarrah, Reinhard Laubenbacher

Research output: Contribution to journalArticlepeer-review

63 Scopus citations


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.

Original languageEnglish
Pages (from-to)1583-1602
Number of pages20
JournalBulletin of Mathematical Biology
Issue number7
StatePublished - Jul 2011

Bibliographical note

Funding Information:
This work was supported by a grant from the US Army Research Office. The authors are grateful to the National Institute for Mathematical and Biological Synthesis, which is sponsored by the National Science Foundation, the US Department of Homeland Security, and the US Department of Agriculture through NSF Award #EF-0832858, with additional support from The University of Tennessee, Knoxville. We have benefited greatly from the workshop “Investigative Workshop on Optimal Control and Optimization for Individual-based and Agent-based Models” held there in December 2009. The authors are grateful to all the participants of this workshop for stimulating discussions and insights. In particular, the authors thank Volker Grimm, Virginia Pasour, and Grigoriy Blekherman for helpful comments on an earlier draft of the manuscript.


  • Agent based models
  • Algebraic models

ASJC Scopus subject areas

  • Neuroscience (all)
  • Immunology
  • Mathematics (all)
  • Biochemistry, Genetics and Molecular Biology (all)
  • Environmental Science (all)
  • Pharmacology
  • Agricultural and Biological Sciences (all)
  • Computational Theory and Mathematics


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