### Abstract

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

Pages (from-to) | 72-87 |

Number of pages | 16 |

Journal | Journal of Biological Dynamics |

Volume | 6 |

Issue number | Supplelment 1 |

Early online date | 30 Apr 2012 |

DOIs | |

Publication status | Published - 2012 |

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### Keywords

- Steptococcus pneumoniae; equilibrium; global stability analysis; effective reproduction number; serotype
- serotype
- mathematical analysis

### Cite this

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*Journal of Biological Dynamics*, vol. 6, no. Supplelment 1, pp. 72-87. https://doi.org/10.1080/17513758.2011.592548

**A mathematical model for the spread of Strepotococcus pneumoniae with transmission dependent on serotype.** / Greenhalgh, David; Lamb, Karen Elaine; Robertson, Christopher.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A mathematical model for the spread of Strepotococcus pneumoniae with transmission dependent on serotype

AU - Greenhalgh, David

AU - Lamb, Karen Elaine

AU - Robertson, Christopher

PY - 2012

Y1 - 2012

N2 - We examine a mathematical model for the transmission of Streptococcus Pneumoniae amongst young children when the carriage transmission coefficient depends on the serotype. Carriage means pneumococcal colonization. There are two sequence types (STs) spreading in a population each of which can be expressed as one of two serotypes. We derive the differential equation model for the carriage spread and perform an equilibrium and global stability analysis on it. A key parameter is the effective reproduction number R e. For R e ≤ 1, there is only the carriage-free equilibrium (CFE) and the carriage will die out whatever be the starting values. For R e > 1, unless the effective reproduction numbers of the two STs are equal, in addition to the CFE there are two carriage equilibria, one for each ST. If the ST with the largest effective reproduction number is initially present, then in the long-term the carriage will tend to the corresponding equilibrium.

AB - We examine a mathematical model for the transmission of Streptococcus Pneumoniae amongst young children when the carriage transmission coefficient depends on the serotype. Carriage means pneumococcal colonization. There are two sequence types (STs) spreading in a population each of which can be expressed as one of two serotypes. We derive the differential equation model for the carriage spread and perform an equilibrium and global stability analysis on it. A key parameter is the effective reproduction number R e. For R e ≤ 1, there is only the carriage-free equilibrium (CFE) and the carriage will die out whatever be the starting values. For R e > 1, unless the effective reproduction numbers of the two STs are equal, in addition to the CFE there are two carriage equilibria, one for each ST. If the ST with the largest effective reproduction number is initially present, then in the long-term the carriage will tend to the corresponding equilibrium.

KW - Steptococcus pneumoniae; equilibrium; global stability analysis; effective reproduction number; serotype

KW - serotype

KW - mathematical analysis

U2 - 10.1080/17513758.2011.592548

DO - 10.1080/17513758.2011.592548

M3 - Article

VL - 6

SP - 72

EP - 87

JO - Journal of Biological Dynamics

JF - Journal of Biological Dynamics

SN - 1751-3758

IS - Supplelment 1

ER -