Bulletin of Mathematical Biology

, Volume 73, Issue 7, pp 1583–1602 | Cite as

A Mathematical Framework for Agent Based Models of Complex Biological Networks

  • Franziska Hinkelmann
  • David Murrugarra
  • Abdul Salam Jarrah
  • Reinhard LaubenbacherEmail author
Original Article


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.


Agent based models Algebraic models 


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Copyright information

© Society for Mathematical Biology 2010

Authors and Affiliations

  • Franziska Hinkelmann
    • 1
    • 2
  • David Murrugarra
    • 1
    • 2
  • Abdul Salam Jarrah
    • 2
    • 3
  • Reinhard Laubenbacher
    • 1
    • 2
    Email author
  1. 1.Department of MathematicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA
  2. 2.Virginia Bioinformatics InstituteVirginia Polytechnic Institute and State UniversityBlacksburgUSA
  3. 3.Department of Mathematics and StatisticsAmerican University of SharjahSharjahUnited Arab Emirates

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