Abstract
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 [1] deterministic approach produced damped oscillations in contrast to the observations, Bartlett [2] suggested that a stochastic version of Soper’s model was more realistic, (See also Bailey [3], Chap, 7.) London and Yorke [4] 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 [5] 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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Soper, H.E. “Interpretation of periodicity in disease prevalence”, J.R.Statist.Soc., 92 (1929), 34–73.
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.
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).
BERGER, J. “Zur Infektionskinetik bei Toxoplasmose, Röteln, Mumps and Zytomegalie, Zbl.Bakt.Hyg., I Abt.Orig. A, 224 (1973), 503–522.
SMITH, C.E.G, “Prospects for the control of infectious disease”, Proc.roy. Soc. Med., 63 (1970), 1181–1190.
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.
SCHMIDT, G. Parametererregte -Schwingungen, VEB Deutscher Verlag der Wissenschaften, Berlin (1975).
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.
TAYLOR, I. and KNOWELDEN, J, Principles of Epidemiology, (2nd edn). Churchill, London (1964).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1976 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
Dietz, K. (1976). The Incidence of Infectious Diseases under the Influence of Seasonal Fluctuations. In: Berger, J., Bühler, W.J., Repges, R., Tautu, P. (eds) Mathematical Models in Medicine. Lecture Notes in Biomathematics, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93048-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-93048-5_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07802-9
Online ISBN: 978-3-642-93048-5
eBook Packages: Springer Book Archive