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

Research output: Contribution to journalArticle

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.
LanguageEnglish
Pages553-567
Number of pages15
JournalDiscrete and Continuous Dynamical Systems - Supplement
Volume2011
Issue numberSpecial Issue
DOIs
Publication statusPublished - Oct 2011

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Vaccines
Mathematical Model
Mathematical models
Locus
Vaccine
Bacteria
Reproduction number
Vaccination
Line
Global Analysis
Less than or equal to
Global Stability
Stability Analysis
Die
Tend
Generalise
Model
Simulation

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

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title = "A mathematical model for the spread of Streptococus Pneumoniae with transmission due to sequence type",
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.",
keywords = "streptococcus pneumoniae, pneumoniae , pneumococcal colonization , mathematical analysis, simulation , global stability, equilibrium and stability analysis, basic reproduction number, serotype, multi-locus sequence type",
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A mathematical model for the spread of Streptococus Pneumoniae with transmission due to sequence type. / Greenhalgh, David; Lamb, Karen Elaine; Robertson, Christopher.

In: Discrete and Continuous Dynamical Systems - Supplement, Vol. 2011, No. Special Issue, 10.2011, p. 553-567.

Research output: Contribution to journalArticle

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