### Abstract

Language | English |
---|---|

Pages | 136-149 |

Number of pages | 14 |

Journal | Mathematical Biosciences |

Volume | 221 |

Issue number | 2 |

DOIs | |

Publication status | Published - Oct 2009 |

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### Keywords

- epidemic models
- equilibrium and stability analysis
- basic reproduction number
- backward bifurcation
- stochastic model
- core group model

### Cite this

*Mathematical Biosciences*,

*221*(2), 136-149. https://doi.org/10.1016/j.mbs.2009.08.003

}

*Mathematical Biosciences*, vol. 221, no. 2, pp. 136-149. https://doi.org/10.1016/j.mbs.2009.08.003

**Dynamic phenomena arising from an extended Core Group model.** / Greenhalgh, David; Griffiths, Martin.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Dynamic phenomena arising from an extended Core Group model

AU - Greenhalgh, David

AU - Griffiths, Martin

PY - 2009/10

Y1 - 2009/10

N2 - In order to obtain a reasonably accurate model for the spread of a particular infectious disease through a population, it may be necessary for this model to possess some degree of structural complexity. Many such models have, in recent years, been found to exhibit a phenomenon known as backward bifurcation, which generally implies the existence of two subcritical endemic equilibria. It is often possible to refine these models yet further, and we investigate here the influence such a refinement may have on the dynamic behaviour of a system in the region of the parameter space near R0 = 1. We consider a natural extension to a so-called core group model for the spread of a sexually transmitted disease, arguing that this may in fact give rise to a more realistic model. From the deterministic viewpoint we study the possible shapes of the resulting bifurcation diagrams and the associated stability patterns. Stochastic versions of both the original and the extended models are also developed so that the probability of extinction and time to extinction may be examined, allowing us to gain further insights into the complex system dynamics near R0 = 1. A number of interesting phenomena are observed, for which heuristic explanations are provided.

AB - In order to obtain a reasonably accurate model for the spread of a particular infectious disease through a population, it may be necessary for this model to possess some degree of structural complexity. Many such models have, in recent years, been found to exhibit a phenomenon known as backward bifurcation, which generally implies the existence of two subcritical endemic equilibria. It is often possible to refine these models yet further, and we investigate here the influence such a refinement may have on the dynamic behaviour of a system in the region of the parameter space near R0 = 1. We consider a natural extension to a so-called core group model for the spread of a sexually transmitted disease, arguing that this may in fact give rise to a more realistic model. From the deterministic viewpoint we study the possible shapes of the resulting bifurcation diagrams and the associated stability patterns. Stochastic versions of both the original and the extended models are also developed so that the probability of extinction and time to extinction may be examined, allowing us to gain further insights into the complex system dynamics near R0 = 1. A number of interesting phenomena are observed, for which heuristic explanations are provided.

KW - epidemic models

KW - equilibrium and stability analysis

KW - basic reproduction number

KW - backward bifurcation

KW - stochastic model

KW - core group model

UR - http://www.elsevier.com/wps/find/journaldescription.cws_home/505777/description#description

U2 - 10.1016/j.mbs.2009.08.003

DO - 10.1016/j.mbs.2009.08.003

M3 - Article

VL - 221

SP - 136

EP - 149

JO - Mathematical Biosciences

T2 - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 2

ER -