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

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.

[1]  M. Lipsitch.  Bacterial vaccines and serotype replacement: lessons from Haemophilus influenzae and prospects for Streptococcus pneumoniae. , 1999, Emerging infectious diseases.

[2]  R. Douglas,et al.  IMMUNISATION WITH A POLYVALENT PNEUMOCOCCAL VACCINE Reduction of Adult Respiratory Mortality in a New Guinea Highlands Community , 1977, The Lancet.

[3]  D. Greenberg,et al.  Reduction of nasopharyngeal carriage of pneumococci during the second year of life by a heptavalent conjugate pneumococcal vaccine. , 1996, The Journal of infectious diseases.

[4]  O. Diekmann,et al.  Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation , 2000 .

[5]  B. Spratt,et al.  Prevention of pneumococcal disease by vaccination: does serotype replacement matter? , 2000, The Lancet.

[6]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[7]  C. Whitney,et al.  Pre- and Postvaccination Clonal Compositions of Invasive Pneumococcal Serotypes for Isolates Collected in the United States in 1999, 2001, and 2002 , 2006, Journal of Clinical Microbiology.

[8]  J. Zhou,et al.  Horizontal transfer of multiple penicillin‐binding protein genes, and capsular biosynthetic genes, in natural populations of Streptococcus pneumoniae , 1991, Molecular microbiology.

[9]  M. Lipsitch,et al.  Vaccination against colonizing bacteria with multiple serotypes. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[10]  S. Clarke,et al.  Genetic Analysis of Diverse Disease-Causing Pneumococci Indicates High Levels of Diversity within Serotypes and Capsule Switching , 2004, Journal of Clinical Microbiology.

[11]  A. Lindberg,et al.  Glycoprotein conjugate vaccines. , 1999, Vaccine.

[12]  W. Schaffner,et al.  Effectiveness of seven-valent pneumococcal conjugate vaccine against invasive pneumococcal disease: a matched case-control study , 2006, The Lancet.

[13]  R. Huebner,et al.  Immunogenicity and impact on nasopharyngeal carriage of a nonavalent pneumococcal conjugate vaccine. , 1999, The Journal of infectious diseases.

[14]  R. Dagan,et al.  Reduction of nasopharyngeal carriage of Streptococcus pneumoniae after administration of a 9-valent pneumococcal conjugate vaccine to toddlers attending day care centers. , 2002, The Journal of infectious diseases.

[15]  G Koki,et al.  Multiple colonization of the upper respiratory tract of Papua New Guinea children with Haemophilus influenzae and Streptococcus pneumoniae. , 1989, The Southeast Asian journal of tropical medicine and public health.

[16]  B. Spratt,et al.  A multilocus sequence typing scheme for Streptococcus pneumoniae: identification of clones associated with serious invasive disease. , 1998, Microbiology.

[17]  Susan S. Huang,et al.  Modeling community- and individual-level effects of child-care center attendance on pneumococcal carriage. , 2005, Clinical infectious diseases : an official publication of the Infectious Diseases Society of America.

[18]  D. Caugant,et al.  Impact of a Pneumococcal Conjugate Vaccination Program on Carriage among Children in Norway , 2010, Clinical and Vaccine Immunology.

[19]  K. Klugman.  Efficacy of pneumococcal conjugate vaccines and their effect on carriage and antimicrobial resistance. , 2001, The Lancet. Infectious diseases.

[20]  Marc Lipsitch,et al.  No coexistence for free: neutral null models for multistrain pathogens. , 2009, Epidemics.

[21]  L. Hammitt,et al.  Invasive pneumococcal disease caused by nonvaccine serotypes among alaska native children with high levels of 7-valent pneumococcal conjugate vaccine coverage. , 2007, JAMA.

[22]  D. Crook,et al.  Vaccine Escape Recombinants Emerge after Pneumococcal Vaccination in the United States , 2007, PLoS pathogens.

[23]  Carlos Castillo-Chavez,et al.  Estimation of invasive pneumococcal disease dynamics parameters and the impact of conjugate vaccination in Australia. , 2008, Mathematical biosciences and engineering : MBE.

[24]  David Greenhalgh,et al.  A simple mathematical model for genetic effects in pneumococcal carriage and transmission , 2011, J. Comput. Appl. Math..

[25]  Richard Platt,et al.  Post-PCV7 Changes in Colonizing Pneumococcal Serotypes in 16 Massachusetts Communities, 2001 and 2004 , 2004, Pediatrics.

[26]  Mario Recker,et al.  Role of selection in the emergence of lineages and the evolution of virulence in Neisseria meningitidis , 2008, Proceedings of the National Academy of Sciences.

[27]  K. Mühlemann,et al.  Detection of Streptococcus pneumoniae Strain Cocolonization in the Nasopharynx , 2009, Journal of Clinical Microbiology.

[28]  A. Roddam.  Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation O Diekmann and JAP Heesterbeek, 2000, Chichester: John Wiley pp. 303, £39.95. ISBN 0-471-49241-8 , 2001 .

[29]  B. Spratt,et al.  Clonal relationships between invasive and carriage Streptococcus pneumoniae and serotype- and clone-specific differences in invasive disease potential. , 2003, The Journal of infectious diseases.

[30]  P. Böelle,et al.  Short- and Long-Term Effects of Pneumococcal Conjugate Vaccination of Children on Penicillin Resistance , 2004, Antimicrobial Agents and Chemotherapy.

[31]  J. C. Burkill,et al.  Ordinary Differential Equations , 1964 .

[32]  A. Nold.  Heterogeneity in disease-transmission modeling , 1980 .

[33]  S. Clarke,et al.  Serotypes and Sequence Types of Pneumococci Causing Invasive Disease in Scotland Prior to the Introduction of Pneumococcal Conjugate Polysaccharide Vaccines , 2004, Journal of Clinical Microbiology.

[34]  A. Schuchat,et al.  Impact of Conjugate Vaccine on Transmission of Antimicrobial-Resistant Streptococcus pneumoniae Among Alaskan Children , 2008, The Pediatric infectious disease journal.

[35]  P. Boelle,et al.  Impact of Capsular Switch on Invasive Pneumococcal Disease Incidence in a Vaccinated Population , 2008, PloS one.

[36]  M. Farley,et al.  Changing characteristics of invasive pneumococcal disease in Metropolitan Atlanta, Georgia, after introduction of a 7-valent pneumococcal conjugate vaccine. , 2007, Clinical infectious diseases : an official publication of the Infectious Diseases Society of America.

[37]  S. Obaro,et al.  Carriage of pneumococci after pneumococcal vaccination , 1996, The Lancet.

[38]  B. Spratt,et al.  Recombinational exchanges at the capsular polysaccharide biosynthetic locus lead to frequent serotype changes among natural isolates of Streptococcus pneumoniae , 1998, Molecular microbiology.

[39]  S. Yeh,et al.  Heptavalent pneumococcal vaccine conjugated to outer membrane protein of Neisseria meningitidis serogroup b and nasopharyngeal carriage of Streptococcus pneumoniae in infants. , 2003, Vaccine.

[40]  B. Gray,et al.  Epidemiologic studies of Streptococcus pneumoniae in infants: acquisition, carriage, and infection during the first 24 months of life. , 1980, The Journal of infectious diseases.