Deakin University
Browse
lamb-mathematicalmodel-2011.pdf (2.21 MB)

A mathematical model for the spread of streptococcus pneumoniae with transmission due to sequence type

Download (2.21 MB)
journal contribution
posted on 2011-01-01, 00:00 authored by D Greenhalgh, Karen Lamb, C Robertson
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 Re is less than or equal to one, then the carriage will die out. If Re > 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.

History

Journal

Discrete and Continuous Dynamical Systems- Series A

Volume

2011

Issue

Special Issue

Pagination

553 - 567

Publisher

American Institute of Mathematical Sciences

Location

Springfield, MO

ISSN

1078-0947

Language

eng

Publication classification

C1.1 Refereed article in a scholarly journal

Copyright notice

2011, American Institute of Mathematical Sciences

Usage metrics

    Research Publications

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC