Statistical modelling of measles and influenza outbreaks

This paper reviews the application of statistical models to outbreaks of two common respiratory viral diseases, measles and influenza. For each disease, we look first at its epidemiological characteristics and assess the extent to which these either aid or hinder modelling. We then turn to the models that have been developed to simulate geographical spread. For measles, a distinction is drawn between process-based and time series models; for influenza, it is the scale of the communities (from small groups to global populations) which primarily determines modelling style. Applications are provided from work by the authors, largely using Icelandic data. Finally we consider the forecasting potential of the models described.

[1]  P. J. Diggle.  Towards the Dynamic Analysis of Spatial Systems , 1980 .

[2]  C. V. Chapin.  MEASLES IN PROVIDENCE, R. I., 1858–1923 , 1925 .

[3]  George Sugihara,et al.  Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series , 1990, Nature.

[4]  L. A. Rvachev,et al.  A mathematical model for the global spread of influenza , 1985 .

[5]  Norman T. J. Bailey,et al.  The Mathematical Theory of Infectious Diseases , 1975 .

[6]  Hope-Simpson Re,et al.  Epidemic mechanisms of type A influenza. , 1979 .

[7]  C. Spicer.  The mathematical modelling of influenza epidemics. , 1979, British medical bulletin.

[8]  J. Ord,et al.  Spatial Diffusion: An Historical Geography of Epidemics in an Island Community , 1981 .

[9]  R C Souza.  Forecasting the Progress of Epidemics by Means of a Bayesian-Entropy Framework , 1982 .

[10]  George W. Williams,et al.  Spatial Aspects of Influenza Epidemics. , 1988 .

[11]  I. Longini,et al.  An optimization model for influenza A epidemics , 1978 .

[12]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[13]  H. Abbey.  An examination of the Reed-Frost theory of epidemics. , 1952, Human biology.

[14]  H. E. Soper.  The Interpretation of Periodicity in Disease Prevalence , 1929 .

[15]  A. Langworthy,et al.  An influenza simulation model for immunization studies. , 1976, American journal of epidemiology.

[16]  A. Cliff,et al.  A stochastic model for measles epidemics in a multi-region setting , 1977 .

[17]  M Greenwood,et al.  On the Statistical Measure of Infectiousness , 1931, Journal of Hygiene.

[18]  Peter Haggett,et al.  Measles: an historical geography of a major human viral disease, from global expansion to local retreat, 1840-1990. , 1993 .

[19]  Mark Bartlett,et al.  Deterministic and Stochastic Models for Recurrent Epidemics , 1956 .

[20]  M. Bartlett.  Measles Periodicity and Community Size , 1957 .

[21]  E. D. Kilbourne,et al.  The molecular epidemiology of influenza. , 1973, The Journal of infectious diseases.

[22]  F. Dunn,et al.  Epidemiologic studies of Asian influenza in a Louisiana parish. , 1959, American journal of hygiene.

[23]  A. Hinman.  World eradication of measles. , 1982, Reviews of infectious diseases.

[24]  A. Semple.  Epidemiology of the Influenza Epidemic in Liverpool in 1950-51. , 1951 .

[25]  A. Evans.  Epidemiological Concepts and Methods , 1982 .

[26]  P. Haggett,et al.  The changing geographical coherence of measles morbidity in the United States, 1962-88. , 1992, Statistics in medicine.

[27]  P. Fine,et al.  Background paper: Applications of mathematical models to the epidemiology of influenza: a critique , 1982 .

[28]  F. Dunn,et al.  Community-wide epidemic of Asian strain influenza; clinical and subclinical illnesses among school children. , 1958, Journal of the American Medical Association.

[29]  J. Fox.  Herd immunity and measles. , 1983, Reviews of infectious diseases.

[30]  F. M. Davenport,et al.  Influenza: The Viruses and the Disease , 1977 .

[31]  E Ackerman,et al.  Herd immunity: basic concept and relevance to public health immunization practices. , 1971, American journal of epidemiology.