The Incidence of Infectious Diseases under the Influence of Seasonal Fluctuations
- K. Dietz
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The present paper is concerned with the effect of seasonal variations of the contact rate on the incidence of infectious diseases. The regular oscillations of the number of cases around the average endemic level has attracted the attention of epidemiologists and mathematicians alike, In particular, the two-year period of measles in some large communities has been the object of many attempts of explanation in terms of deterministic and stochastic models, Soper’s  deterministic approach produced damped oscillations in contrast to the observations, Bartlett  suggested that a stochastic version of Soper’s model was more realistic, (See also Bailey , Chap, 7.) London and Yorke  however were able to obtain undamped oscillations with periods of one and two years using a deterministic model which includes a latent period between the time of infection and the beginning of the infectious period, From their simulations they conclude that the length of the latent period has to be within a small range for the occurrence of biennial outbreaks, Recently, Stirzaker  treated this problem from the point of view of the theory of nonlinear oscillations according to which the biennial cycles of measles epidemics could be understood as subharmonic parametric resonance.
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- BARTLETT, M.S, “Deterministic and stochastic models for recurrent epidemics”, Proc.Third Berkeley Symp. Math. Statists Prob., 4 (1956), 81–109.
- BAILEY, N.T.J, The Mathematical Theory of Infectious Diseases and its Applications, (2nd edn) Griffin, London and High Wycombe (1975).
- LONDON, W.P. and YORKE, J.A. “Recurrent outbreaks of measles, chickenpox and mumps. I: Seasonal variation in contact rates”, Amer.J.Epidem., 98 (1973) 453–468
- STIRZAKER, D.R. “A perturbation method for the stochastic recurrent epidemic”, J.Inst.Maths Applics. 15 (1975), 135–160. CrossRef
- DIETZ, K, “Transmission and control of arbovirus diseases”, in Proceedings of a SIMS Conference on Epidemiology, Ludwig, D. and Cooke, K.L., eds., SIAM, Philadelphia, (1975), 104–121.
- MUENCH, H, Catalytic Models in Epidemiology, Harvard Univ. Press (1959).
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- ANDERSON, G.W. “The principles of epidemiology as applied to infectious diseases” in Bacterial and Mycotic Infections of Man (4th edn), Dubos, R.J. and Hirsch, J.G. eds., Lippincott, Philadelphia (1965), 886–912.
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- BENENSON, A.S. (ed.), Control of Communicable Diseases in Man (11th edn) American Public Health Association, Washington, D.C. (1970).
- GRIFFITHS, D.A. “A catalytic model of infection for measles”, Appl.Startsist., 23, (1974). 330–339. CrossRef
- TAYLOR, I. and KNOWELDEN, J, Principles of Epidemiology, (2nd edn). Churchill, London (1964).
- The Incidence of Infectious Diseases under the Influence of Seasonal Fluctuations
- Book Title
- Mathematical Models in Medicine
- Book Subtitle
- Workshop, Mainz, March 1976
- Book Part
- pp 1-15
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Biomathematics
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
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- Editor Affiliations
- 1. Fakultät für Klinische Medizin Mannheim, Universität Heidelberg
- 2. Fachbereich Mathematik, Johannes Gutenberg Universität
- 3. Abt. Medizinische Statistik und Dokumentation
- 4. Institut für Dokumentation, Information und Statistik, Deutsches Krebsforschungszentrum
- K. Dietz (5)
- Author Affiliations
- 5. Health Statistical Methodology, World Health Organization, 1211, Geneva 27, Switzerland
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