### Abstract

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

Pages | 553-567 |

Number of pages | 15 |

Journal | Discrete and Continuous Dynamical Systems - Supplement |

Volume | 2011 |

Issue number | Special Issue |

DOIs | |

Publication status | Published - Oct 2011 |

### Fingerprint

### Keywords

- streptococcus pneumoniae
- pneumoniae
- pneumococcal colonization
- mathematical analysis
- simulation
- global stability
- equilibrium and stability analysis
- basic reproduction number
- serotype
- multi-locus sequence type

### Cite this

}

*Discrete and Continuous Dynamical Systems - Supplement*, vol. 2011, no. Special Issue, pp. 553-567. https://doi.org/10.3934/proc.2011.2011.553

**A mathematical model for the spread of Streptococus Pneumoniae with transmission due to sequence type.** / Greenhalgh, David; Lamb, Karen Elaine; Robertson, Christopher.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A mathematical model for the spread of Streptococus Pneumoniae with transmission due to sequence type

AU - Greenhalgh, David

AU - Lamb, Karen Elaine

AU - Robertson, Christopher

PY - 2011/10

Y1 - 2011/10

N2 - This paper discusses a simple mathematical model to describe the spread of Streptococcus pneumoniae. We suppose that the transmission of the bacterium is determined by multi-locus sequence type. The model includes vaccination and is designed to examine what happens in a vaccinated population if MLSTs can exist as both vaccine and non vaccine serotypes with capsular switching possible from the former to the latter. We start off with a discussion of Streptococcus pneumoniae and a review of previous work. We propose a simple mathematical model with two sequence types and then perform an equilibrium and (global) stability analysis on the model. We show that in general there are only three equilibria, the carriage-free equilibrium and two carriage equilibria. If the effective reproduction number [R_e] is less than or equal to one, then the carriage will die out. If [R_e] > 1, then the carriage will tend to the carriage equilibrium corresponding to the multi-locus sequence type with the largest transmission parameter. In the case where both multi-locus sequence types have the same transmission parameter then there is a line of carriage equilibria. Provided that carriage is initially present then as time progresses the carriage will approach a point on this line. The results generalize to many competing sequence types. Simulations with realistic parameter values confirm the analytical results.

AB - This paper discusses a simple mathematical model to describe the spread of Streptococcus pneumoniae. We suppose that the transmission of the bacterium is determined by multi-locus sequence type. The model includes vaccination and is designed to examine what happens in a vaccinated population if MLSTs can exist as both vaccine and non vaccine serotypes with capsular switching possible from the former to the latter. We start off with a discussion of Streptococcus pneumoniae and a review of previous work. We propose a simple mathematical model with two sequence types and then perform an equilibrium and (global) stability analysis on the model. We show that in general there are only three equilibria, the carriage-free equilibrium and two carriage equilibria. If the effective reproduction number [R_e] is less than or equal to one, then the carriage will die out. If [R_e] > 1, then the carriage will tend to the carriage equilibrium corresponding to the multi-locus sequence type with the largest transmission parameter. In the case where both multi-locus sequence types have the same transmission parameter then there is a line of carriage equilibria. Provided that carriage is initially present then as time progresses the carriage will approach a point on this line. The results generalize to many competing sequence types. Simulations with realistic parameter values confirm the analytical results.

KW - streptococcus pneumoniae

KW - pneumoniae

KW - pneumococcal colonization

KW - mathematical analysis

KW - simulation

KW - global stability

KW - equilibrium and stability analysis

KW - basic reproduction number

KW - serotype

KW - multi-locus sequence type

UR - http://aimsciences.org/journals/displayArticles.jsp?paperID=7033

U2 - 10.3934/proc.2011.2011.553

DO - 10.3934/proc.2011.2011.553

M3 - Article

VL - 2011

SP - 553

EP - 567

JO - Discrete and Continuous Dynamical Systems - Series A

T2 - Discrete and Continuous Dynamical Systems - Series A

JF - Discrete and Continuous Dynamical Systems - Series A

SN - 1078-0947

IS - Special Issue

ER -