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A simple mathematical model for genetic effects in pneumococcal carriage and transmission. (English) Zbl 1207.92025
Summary: Streptococcus pneumoniae (S. pneumoniae) is a bacterium commonly found in the throat of young children. Pneumococcal serotypes can cause a variety of invasive and non-invasive diseases such as meningitis and pneumonia. In 2000 a vaccine was introduced in the USA that not only prevents vaccine type disease but has also been shown to eliminate carriage of the vaccine serotypes. One key problem with the vaccine is that it has been observed that the same sequence types (genetic material found in the serotypes) are able to manifest in more than one serotype. This is a potential problem if sequence types associated with invasive disease may express themselves in multiple serotypes.
We present a basic differential equation mathematical model for exploring the relationship between sequence types and serotypes where a sequence type is able to manifest itself in one vaccine serotype and one non-vaccine serotype. An expression for the effective reproduction number is found and an equilibrium and then a global stability analysis carried out. We illustrate our analytical results by using simulations with realistic parameter values.

MSC:
92C50 Medical applications (general)
92C60 Medical epidemiology
34D23 Global stability of solutions to ordinary differential equations
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[1] McChlery, S.M.; Scott, K.J.; Clarke, S.C., Clonal analysis of invasive pneumococcal isolates in Scotland and coverage of serotypes by the licensed conjugate polysaccharide pneumococcal vaccine: possible implications for UK vaccine policy, Eur. J. clin. microbiol. infect. dis., 24, 262-267, (2005)
[2] Lipsitch, M., Vaccination against colonizing bacteria with multiple sero-types, Proc. natl. acad. sci., 94, 6571-6576, (1997)
[3] Diekmann, O.; Heesterbeek, J.A.P., Mathematical epidemiology of infectious disease, (2000), John Wiley · Zbl 0997.92505
[4] Birkhoff, G.; Rota, G.C., Ordinary differential equations, (1982), Ginn Boston · Zbl 0183.35601
[5] A. Weir, Modelling the impact of vaccination and competition on pneumococcal carriage and disease in Scotland, Unpublished Ph.D. Thesis, University of Strathclyde, Glasgow, Scotland, 2009.
[6] P. Farrington, What is the reproduction number for pneumococcal infection, and does it matter? in: 4th International Symposium on Pneumococci and Pneumococcal Diseases, May 9-13 2004 at Marina Congress Center, Helsinki, Finland, 2004.
[7] Zhang, Q.; Arnaoutakis, K.; Murdoch, C.; Lakshman, R.; Race, G.; Burkinshaw, R.; Finn, A., Mucosal immune responses to capsular pneumococcal polysaccharides in immunized preschool children and controls with similar nasal pneumococcal colonization rates, Pediatr. infect. dis. J., 23, 307-313, (2004)
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