## Abstract

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.

Original language | English |
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Pages (from-to) | 553-567 |

Number of pages | 15 |

Journal | Discrete and Continuous Dynamical Systems- Series A |

Issue number | Supplement 2011 |

DOIs | |

Publication status | Published - 1 Oct 2011 |

## Keywords

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