Some bounds on estimates for reproductive ratios derived from the age-specific force of infection.

In this paper we shall look at estimation of reproductive ratios for common childhood infections such as chickenpox, measles, mumps, and hepatitis A with and without a vaccination program. The paper starts with a survey of previous work in this area. We suppose that we are given data in the form of an age-related serological profile with a given vaccination program. This is used to estimate the reproductive ratio and evaluate vaccination campaigns. The effect of different mixing patterns, such as homogeneous mixing, assortative mixing, proportional mixing, and symmetric mixing are discussed. R phi denotes the reproductive ratio when a steady-state vaccination campaign phi is used. Assortative mixing maximizes the reproductive ratio R phi. A mixing pattern which minimizes R phi and a lower bound for R phi for the important symmetric mixing case are found. The most usual situation is that we are given the age-serological profile with no vaccination so that we have bounds for the basic reproductive ratio R0. These results are illustrated with an application to vaccination against hepatitis A in Bulgaria. Numerical evaluations of the effect of different elimination vaccination strategies are examined.

[1]  S. D. Collins,et al.  Age Incidence of the Common Communicable Diseases of Children. A Study of Case Rates among all Children and among Children not previously attacked and of Death Rates and the Estimated Case Fatality. , 1929 .

[2]  R. Ross,et al.  Prevention of malaria. , 2012, BMJ.

[3]  D Greenhalgh,et al.  Vaccination campaigns for common childhood diseases. , 1990, Mathematical biosciences.

[4]  H. Ramlau-Hansen.  Smoothing Counting Process Intensities by Means of Kernel Functions , 1983 .

[5]  B Cvjetanović,et al.  Epidemiological models of poliomyelitis and measles and their application in the planning of immunization programmes. , 1982, Bulletin of the World Health Organization.

[6]  Roy M. Anderson,et al.  Endemic infections in growing populations , 1985 .

[7]  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.

[8]  C. Farrington.  Modelling forces of infection for measles, mumps and rubella. , 1990, Statistics in medicine.

[9]  J. Gillis,et al.  Matrix Iterative Analysis , 1961 .

[10]  B. Silverman.  Density estimation for statistics and data analysis , 1986 .

[11]  K Dietz,et al.  Evaluation of age-specific vaccination strategies. , 1984, Theoretical population biology.

[12]  O. Diekmann,et al.  On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations , 1990, Journal of mathematical biology.

[13]  Niels Keiding,et al.  Age‐Specific Incidence and Prevalence: A Statistical Perspective , 1991 .

[14]  H. Muench,et al.  Derivation of Rates from Summation Data by the Catalytic Curve , 1934 .

[15]  D. Griffiths,et al.  A Catalytic Model of Infection for Measles , 1974 .

[16]  K Dietz,et al.  Proportionate mixing models for age-dependent infection transmission , 1985, Journal of mathematical biology.

[17]  F. Black,et al.  Measles antibodies in the population of New Haven, Connecticut. , 1959, Journal of immunology.

[18]  H. Bang,et al.  Measles in virgin soil, Greenland 1951. , 1954, Danish medical bulletin.

[19]  R M May,et al.  Vaccination against rubella and measles: quantitative investigations of different policies , 1983, Journal of Hygiene.

[20]  E. Miller,et al.  Surveillance of antibody to measles, mumps, and rubella by age. , 1988, BMJ.

[21]  B T Grenfell,et al.  Quantitative investigations of different vaccination policies for the control of congenital rubella syndrome (CRS) in the United Kingdom , 1986, Journal of Hygiene.

[22]  D. Schenzle.  An age-structured model of pre- and post-vaccination measles transmission. , 1984, IMA journal of mathematics applied in medicine and biology.

[23]  R. May,et al.  Directly transmitted infections diseases: control by vaccination. , 1982, Science.

[24]  S. Iwarson,et al.  Antibody against hepatitis A in seven European countries. I. Comparison of prevalence data in different age groups. , 1979, American journal of epidemiology.

[25]  D. Schenzle,et al.  Control of Virus Transmission in Age-Structured Populations , 1985 .

[26]  Roy M. Anderson,et al.  Directly transmitted viral and bacterial infections of man , 1982 .

[27]  B T Grenfell,et al.  Oscillatory fluctuations in the incidence of infectious disease and the impact of vaccination: time series analysis , 1984, Journal of Hygiene.

[28]  G. Macdonald,et al.  The analysis of infection rates in diseases in which superinfection occurs. , 1950, Tropical diseases bulletin.

[29]  R M May,et al.  Spatial, temporal, and genetic heterogeneity in host populations and the design of immunization programmes. , 1984, IMA journal of mathematics applied in medicine and biology.

[30]  J. E. Swanson,et al.  Hepatitis A in day-care centers. A community-wide assessment. , 1980, The New England journal of medicine.

[31]  A. Benenson.  CONTROL OF COMMUNICABLE DISEASES IN MAN , 1966 .

[32]  H. Knolle.  The General Age‐Dependent Endemic with Age‐Specific Contact Rate , 1983 .

[33]  R. Anderson,et al.  Rubella epidemiology in South East England , 1986, Journal of Hygiene.

[34]  Klaus Dietz,et al.  Mathematical Models for Infectious Disease Statistics , 1985 .

[35]  J. Macgregor,et al.  Epidemic measles in Shetland during 1977 and 1978. , 1981, British medical journal.

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