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

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Abstract

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.

Original languageEnglish
Pages (from-to)72-87
Number of pages16
JournalJournal of Biological Dynamics
Volume6
Issue numberSupplelment 1
Early online date30 Apr 2012
DOIs
Publication statusPublished - 2012

Keywords

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

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