An age-structured model for pertussis transmission.

The vaccination program for pertussis (whooping cough) in the United States consists of giving multiple doses of pertussis vaccine to young children. A demographic model with a steady-state age distribution is used as a basis for building an epidemiologic model for the transmission of pertussis. This age-structured model includes vaccination of infants and children for pertussis with waning of both infection-acquired and vaccine-induced immunity. Computer simulations of the mathematical model between 1940 and 2040 show the changes that took place during the implementation phase of the U.S. program and predict only minor future changes in the age distribution and incidence of pertussis if the vaccination program is maintained at the 1995 level. The sensitivities of these results to changes in demographic and epidemiologic parameters, vaccine efficacy, duration of protection, and levels of vaccination coverage are investigated.

[1]  Henry Nider,et al.  Report of the Committee on Infectious Diseases , 1989 .

[2]  S. Levin.  Lectu re Notes in Biomathematics , 1983 .

[3]  A. Galazka,et al.  The efficacy of DPT and oral poliomyelitis immunization schedules initiated from birth to 12 weeks of age. , 1985, Bulletin of the World Health Organization.

[4]  H. Lambert.  EPIDEMIOLOGY OF A SMALL PERTUSSIS OUTBREAK IN KENT COUNTY, MICHIGAN. , 1965, Public health reports.

[5]  A. Benenson.  Control of communicable diseases manual , 1995 .

[6]  R. W. Hiorns,et al.  The mathematical theory of the dynamics of biological populations : based on a conference organised by the Institute of Mathematics and Its Applications in association with the Institute of Biology , 1975 .

[7]  R. May,et al.  Infectious Diseases of Humans: Dynamics and Control , 1991, Annals of Internal Medicine.

[8]  H. Hethcote,et al.  Modeling HIV Transmission and AIDS in the United States , 1992 .

[9]  Steven J. Schwager,et al.  Statistical and mathematical approaches in HIV/AIDS modeling: a review , 1989 .

[10]  J. W. Bass,et al.  The return of pertussis , 1987, The Pediatric infectious disease journal.

[11]  H. Hethcote,et al.  A simulation model of AIDS in San Francisco: II. Simulations, therapy, and sensitivity analysis. , 1991, Mathematical biosciences.

[12]  J. Cherry,et al.  Pertussis in German adults. , 1995, Clinical infectious diseases : an official publication of the Infectious Diseases Society of America.

[13]  D. Jenkinson.  Duration of effectiveness of pertussis vaccine: evidence from a 10 year community study , 1988, British medical journal.

[14]  D Greco,et al.  A controlled trial of two acellular vaccines and one whole-cell vaccine against pertussis. Progetto Pertosse Working Group. , 1996, The New England journal of medicine.

[15]  P. Fine,et al.  Reflections on the efficacy of pertussis vaccines. , 1987, Reviews of infectious diseases.

[16]  E. Zell,et al.  Pertussis surveillance--United States, 1989-1991. , 1992, MMWR. CDC surveillance summaries : Morbidity and mortality weekly report. CDC surveillance summaries.

[17]  A. J. Lotka.  The Stability of the Normal Age Distribution. , 1922, Proceedings of the National Academy of Sciences of the United States of America.

[18]  J. Cherry.  Acellular pertussis vaccines--a solution to the pertussis problem. , 1993, The Journal of infectious diseases.

[19]  C. Farrington,et al.  Age-specific efficacy of pertussis vaccine during epidemic and non-epidemic periods , 1993, Epidemiology and Infection.

[20]  J. Yorke,et al.  Gonorrhea Transmission Dynamics and Control , 1984 .

[21]  J. Cherry,et al.  A Search for Bordetella pertussis Infection in University Students , 1992 .

[22]  H. Schmitt,et al.  Pertussis in adults: frequency of transmission after household exposure , 1995, The Lancet.

[23]  E. Hewlett,et al.  The past, present, and future of pertussis. The role of adults in epidemiology and future control. , 1989, The Western journal of medicine.

[24]  Herbert W. Hethcote,et al.  Optimal ages of vaccination for measles , 1988 .

[25]  Herbert W. Hethcote,et al.  Epidemiological models for heterogeneous populations: proportionate mixing, parameter estimation, and immunization programs , 1987 .

[26]  D J Nokes,et al.  Predicting the impact of measles vaccination in England and Wales: model validation and analysis of policy options , 1995, Epidemiology and Infection.

[27]  D. Mollison.  Epidemic models : their structure and relation to data , 1996 .

[28]  H. Hethcote,et al.  An immunization model for a heterogeneous population. , 1978, Theoretical population biology.

[29]  H. Shannon,et al.  A model basis for the control of whooping cough. , 1986, International journal of epidemiology.

[30]  H. Hethcote.  Models for Infectious Human Diseases: Modeling heterogeneous mixing in infectious disease dynamics , 1996 .

[31]  Lisa Sattenspiel,et al.  Modeling and analyzing HIV transmission: the effect of contact patterns , 1988 .

[32]  J. W. Bass.  Pertussis: current status of prevention and treatment. , 1985, Pediatric infectious disease.

[33]  I M Longini,et al.  A simulation model of AIDS in San Francisco: I. Model formulation and parameter estimation. , 1991, Mathematical biosciences.

[34]  R. Sutter,et al.  Pertussis hospitalizations and mortality in the United States, 1985-1988. Evaluation of the completeness of national reporting. , 1992, JAMA.

[35]  Hadi Dowlatabadi,et al.  Sensitivity and Uncertainty Analysis of Complex Models of Disease Transmission: an HIV Model, as an Example , 1994 .

[36]  J. Deen,et al.  Household contact study of Bordetella pertussis infections. , 1995, Clinical infectious diseases : an official publication of the Infectious Diseases Society of America.

[37]  B T Grenfell,et al.  The estimation of age-related rates of infection from case notifications and serological data , 1985, Journal of Hygiene.

[38]  Herbert W. Hethcote,et al.  Gonorrhea modeling: a comparison of control methods , 1982 .

[39]  F. C. Hoppensteadt.  Mathematical theories of populations : demographics, genetics and epidemics , 1975 .

[40]  S. Palmer.  Vaccine efficacy and control measures in pertussis. , 1991, Archives of disease in childhood.

[41]  D. Commerce.  Statistical abstract of the United States , 1978 .

[42]  K. Edwards,et al.  Pertussis infection in adults with persistent cough. , 1995, JAMA.

[43]  J. Gordon,et al.  Whooping cough and its epidemiological anomalies. , 1951, The American journal of the medical sciences.

[44]  C. Castillo-Chavez,et al.  Like-with-like preference and sexual mixing models. , 1989, Mathematical biosciences.

[45]  E. Zell,et al.  Epidemiological features of pertussis in the United States, 1980-1989. , 1992, Clinical infectious diseases : an official publication of the Infectious Diseases Society of America.

[46]  L. Herwaldt.  Pertussis in adults. What physicians need to know. , 1991, Archives of internal medicine.

[47]  Roy M. Anderson,et al.  Vaccination and herd immunity to infectious diseases , 1985, Nature.

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

[49]  A. M'Kendrick.  Applications of Mathematics to Medical Problems , 1925, Proceedings of the Edinburgh Mathematical Society.

[50]  H. Hethcote,et al.  Measles and rubella in the United States. , 1983, American journal of epidemiology.

[51]  Herbert W. Hethcote,et al.  Dynamic models of infectious diseases as regulators of population sizes , 1992, Journal of mathematical biology.

[52]  J. Mcgowan,et al.  Epidemiology of pertussis, Atlanta, 1977. , 1981, Jornal de Pediatria.

[53]  M E Halloran,et al.  Epidemiologic effects of vaccines with complex direct effects in an age-structured population. , 1994, Mathematical biosciences.

[54]  P. Fine,et al.  Distribution of immunity to pertussis in the population of England and Wales , 1984, Journal of Hygiene.

[55]  K. Edwards,et al.  Prevalence and incidence of adult pertussis in an urban population. , 1996, JAMA.

[56]  H. Hethcote.  PERIODICITY AND STABILITY IN EPIDEMIC MODELS: A SURVEY , 1981 .

[57]  N G Becker,et al.  Waning immunity and its effects on vaccination schedules. , 1994, Mathematical biosciences.

[58]  M K Viljanen,et al.  Outcomes of Bordetella pertussis infection in different age groups of an immunized population. , 1994, The Journal of infectious diseases.

[59]  B T Grenfell,et al.  Pertussis in England and Wales: an investigation of transmission dynamics and control by mass vaccination , 1989, Proceedings of the Royal Society of London. B. Biological Sciences.

[60]  J. Mezzatesta,et al.  Adult immunization with acellular pertussis vaccine. , 1993, JAMA.

[61]  R M May,et al.  Age-related changes in the rate of disease transmission: implications for the design of vaccination programmes , 1985, Journal of Hygiene.

[62]  I. Onorato,et al.  Efficacy of whole-cell pertussis vaccine in preschool children in the United States. , 1992, JAMA.

[63]  J. Cherry,et al.  Frequency of unrecognized Bordetella pertussis infections in adults. , 1995, Clinical infectious diseases : an official publication of the Infectious Diseases Society of America.

[64]  Ian C. Marschner,et al.  The effect of preferential mixing on the growth of an epidemic. , 1992, Mathematical biosciences.

[65]  Sally M. Blower,et al.  Imperfect vaccines and herd immunity to HIV , 1993, Proceedings of the Royal Society of London. Series B: Biological Sciences.