The uses of epidemic models.

This paper is concerned with models formulated to describe the spread of infectious diseases through a community. Some standard epidemic models are introduced and an overview of their uses is provided. The paper includes a discussion of the advantages of simple models over complex ones and the advantages of stochastic models over deterministic ones. The role that epidemic models can play in helping us to understand the spread of diseases and to plan control policies for diseases is explained. The paper also contains a review of some major insights gained from a study of epidemic models and from statistical analyses of disease data using epidemic models. Some explicit suggestions for future research projects are made.

[1]  N. Becker,et al.  Vaccination programmes for rare infectious diseases , 1972 .

[2]  K. Wickwire.  Mathematical models for the control of pests and infectious diseases: a survey. , 1977, Theoretical population biology.

[3]  D. Stirzaker,et al.  A Perturbation Method for the Stochastic Recurrent Epidemic , 1975 .

[4]  N. Becker,et al.  Estimation for an epidemic model. , 1976, Biometrics.

[5]  M R Klauber,et al.  Variola minor in Bragança Paulista county, 1956. Attack rates in various population units of the two schools including most students with the disease. , 1976, American journal of epidemiology.

[6]  J J Angulo,et al.  Variola minor in Bragança Paulista County, 1956: overall description of the epidemic and of its study. , 1976, International journal of epidemiology.

[7]  T. Kurtz.  Solutions of ordinary differential equations as limits of pure jump markov processes , 1970, Journal of Applied Probability.

[8]  R. Bartoszynski.  On a certain model of an epidemic , 1972 .

[9]  Nathan Mantel,et al.  Evaluation of Response-Time Data Involving Transient States: An Illustration Using Heart-Transplant Data , 1974 .

[10]  V. P. Godambe.  An Optimum Property of Regular Maximum Likelihood Estimation , 1960 .

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

[12]  N. Becker,et al.  Estimation for discrete time branching processes with application to epidemics. , 1977, Biometrics.

[13]  Denis Mollison,et al.  Spatial Contact Models for Ecological and Epidemic Spread , 1977 .

[14]  D. Tyrrell,et al.  A mathematical model of common-cold epidemics on Tristan da Cunha , 1971, Journal of Hygiene.

[15]  D. A. Griffiths,et al.  The Effect of Measles Vaccination on the Incidence of Measles in the Community , 1973 .

[16]  P. Whittle.  THE OUTCOME OF A STOCHASTIC EPIDEMIC—A NOTE ON BAILEY'S PAPER , 1955 .

[17]  R. Otter.  The Multiplicative Process , 1949 .

[18]  K. Gough.  The estimation of latent and infectious periods , 1977 .

[19]  Andrew D. Barbour,et al.  On a functional central limit theorem for Markov population processes , 1974, Advances in Applied Probability.

[20]  D. McLeish.  Dependent Central Limit Theorems and Invariance Principles , 1974 .

[21]  M. S. Bartlett,et al.  Monte Carlo Studies in Ecology and Epidemiology , 1961 .

[22]  H. E. Lewis,et al.  Common colds on Tristan da Cunha , 1971, Journal of Hygiene.

[23]  M. S. Bartlett,et al.  Some Evolutionary Stochastic Processes , 1949 .

[24]  Dennis V. Lindley,et al.  Empirical Bayes Methods , 1974 .

[25]  J. Mantle,et al.  An epidemic of influenza on Tristan da Cunha , 1973, Journal of Hygiene.

[26]  T. Kurtz.  Limit theorems for sequences of jump Markov processes approximating ordinary differential processes , 1971, Journal of Applied Probability.