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

Greenhalgh, David, Lamb, Karen E and Robertson, Chris 2011, A mathematical model for the spread of streptococcus pneumoniae with transmission due to sequence type, Discrete and Continuous Dynamical Systems- Series A, vol. 2011, no. Special Issue, pp. 553-567.

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Title A mathematical model for the spread of streptococcus pneumoniae with transmission due to sequence type
Author(s) Greenhalgh, David
Lamb, Karen EORCID iD for Lamb, Karen E orcid.org/0000-0001-9782-8450
Robertson, Chris
Journal name Discrete and Continuous Dynamical Systems- Series A
Volume number 2011
Issue number Special Issue
Start page 553
End page 567
Total pages 15
Publisher American Institute of Mathematical Sciences
Place of publication Springfield, MO
Publication date 2011
ISSN 1078-0947
Keyword(s) Streptococcus pneumoniae
Multi-locus sequence type
Serotype
Basic reproduction number
Equilibrium and stability analysis
Global stability
Simulation
Summary 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.
Language eng
Field of Research 119999 Medical and Health Sciences not elsewhere classified
Socio Economic Objective 970111 Expanding Knowledge in the Medical and Health Sciences
HERDC Research category C1.1 Refereed article in a scholarly journal
Copyright notice ©2011, American Institute of Mathematical Sciences
Free to Read? Yes
Persistent URL http://hdl.handle.net/10536/DRO/DU:30061316

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Every reasonable effort has been made to ensure that permission has been obtained for items included in DRO. If you believe that your rights have been infringed by this repository, please contact drosupport@deakin.edu.au.