### Abstract

Original language | English |
---|---|

Pages (from-to) | 535-556 |

Number of pages | 22 |

Journal | Mathematics in Computer Science |

Volume | 2 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Mar 2009 |

### Fingerprint

### Keywords

- process algebra
- population dynamics
- epidemiology
- mean field equations
- symbolic computation

### Cite this

*Mathematics in Computer Science*,

*2*(3), 535-556. https://doi.org/10.1007/s11786-008-0066-2

}

*Mathematics in Computer Science*, vol. 2, no. 3, pp. 535-556. https://doi.org/10.1007/s11786-008-0066-2

**From individuals to populations : a symbolic process algebra approach to epidemiology.** / McCaig, Chris; Norman, R.; Shankland, C.

Research output: Contribution to journal › Article

TY - JOUR

T1 - From individuals to populations

T2 - a symbolic process algebra approach to epidemiology.

AU - McCaig, Chris

AU - Norman, R.

AU - Shankland, C.

PY - 2009/3/1

Y1 - 2009/3/1

N2 - Is it possible to symbolically express and analyse an individual-based model of disease spread, including realistic population dynamics? This problem is addressed through the use of process algebra and a novel method for transforming process algebra into Mean Field Equations. A number of stochastic models of population growth are presented, exploring different representations based on alternative views of individual behaviour. The overall population dynamics in terms of mean field equations are derived 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. The utility of our approach for epidemiology is confirmed by constructing a model combining population growth with disease spread and fitting it to data on HIV in the UK population.

AB - Is it possible to symbolically express and analyse an individual-based model of disease spread, including realistic population dynamics? This problem is addressed through the use of process algebra and a novel method for transforming process algebra into Mean Field Equations. A number of stochastic models of population growth are presented, exploring different representations based on alternative views of individual behaviour. The overall population dynamics in terms of mean field equations are derived 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. The utility of our approach for epidemiology is confirmed by constructing a model combining population growth with disease spread and fitting it to data on HIV in the UK population.

KW - process algebra

KW - population dynamics

KW - epidemiology

KW - mean field equations

KW - symbolic computation

U2 - 10.1007/s11786-008-0066-2

DO - 10.1007/s11786-008-0066-2

M3 - Article

VL - 2

SP - 535

EP - 556

JO - Mathematics in Computer Science

JF - Mathematics in Computer Science

SN - 1661-8270

IS - 3

ER -