A mathematical model for the spread of Strepotococcus pneumoniae with transmission dependent on serotype
Greenhalgh, David and Lamb, Karen Elaine and Robertson, Christopher (2012) A mathematical model for the spread of Strepotococcus pneumoniae with transmission dependent on serotype. Journal of Biological Dynamics, 6 (Supple). pp. 72-87. ISSN 1751-3758 (https://doi.org/10.1080/17513758.2011.592548)
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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.
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Item type: Article ID code: 37074 Dates: DateEvent2012Published30 April 2012Published OnlineSubjects: Science > Mathematics > Probabilities. Mathematical statistics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 25 Jan 2012 15:41 Last modified: 08 Apr 2024 19:46 URI: https://strathprints.strath.ac.uk/id/eprint/37074