### Abstract

It is well understood that populations cannot grow without bound and that it is competition between individuals for resources which restricts growth. Despite centuries of interest, the question of how best to model density dependent population growth still has no definitive answer. We address this question here through a number of individual based models of populations expressed using the process algebra WSCCS. The advantage of these models is that they can be explicitly based on observations of individual interactions. From our probabilistic models we derive equations expressing overall population dynamics, using a formal and rigorous rewriting based method. These equations are easily compared with the traditionally used deterministic Ordinary Differential Equation models and allow evaluation of those ODE models, challenging their assumptions about system dynamics. Further, the approach is applied to epidemiology, combining population growth with disease spread.

Original language | English |
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Title of host publication | Algebraic Biology |

Subtitle of host publication | Third International Conference, AB 2008, Castle of Hagenberg, Austria, July 31-August 2, 2008 Proceedings |

Editors | Katsuhisa Horimoto, Georg Regensburger , Markus Rosenkranz, Hiroshi Yoshida |

Publisher | Springer |

Pages | 139-155 |

Number of pages | 17 |

ISBN (Print) | 978-3-540-85100-4 |

DOIs | |

Publication status | Published - 2008 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Volume | 5147 |

ISSN (Print) | 0302-9743 |

### Keywords

- process algebra
- population dynamics
- epidemiology

## Cite this

McCaig, C., Norman, R., & Shankland, C. (2008). Process algebra models of population dynamics. In K. Horimoto, G. Regensburger , M. Rosenkranz, & H. Yoshida (Eds.),

*Algebraic Biology: Third International Conference, AB 2008, Castle of Hagenberg, Austria, July 31-August 2, 2008 Proceedings*(pp. 139-155). (Lecture Notes in Computer Science; Vol. 5147). Springer. https://doi.org/10.1007/978-3-540-85101-1_11