The Incidence of Infectious Diseases under the Influence of Seasonal Fluctuations

Conference paper
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 11)


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.


Latent Period Equilibrium Solution Reproduction Rate Periodic Pattern Contact Rate 
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  1. 1.
    Soper, H.E. “Interpretation of periodicity in disease prevalence”, J.R.Statist.Soc., 92 (1929), 34–73.CrossRefGoogle Scholar
  2. 2.
    BARTLETT, M.S, “Deterministic and stochastic models for recurrent epidemics”, Proc.Third Berkeley Symp. Math. Statists Prob., 4 (1956), 81–109.MathSciNetGoogle Scholar
  3. 3.
    BAILEY, N.T.J, The Mathematical Theory of Infectious Diseases and its Applications, (2nd edn) Griffin, London and High Wycombe (1975).zbMATHGoogle Scholar
  4. 4.
    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) 453–468Google Scholar
  5. 5.
    STIRZAKER, D.R. “A perturbation method for the stochastic recurrent epidemic”, J.Inst.Maths Applics. 15 (1975), 135–160.CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    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.Google Scholar
  7. 7.
    MUENCH, H, Catalytic Models in Epidemiology, Harvard Univ. Press (1959).Google Scholar
  8. 8.
    BERGER, J. “Zur Infektionskinetik bei Toxoplasmose, Röteln, Mumps and Zytomegalie, Zbl.Bakt.Hyg., I Abt.Orig. A, 224 (1973), 503–522.Google Scholar
  9. 9.
    SMITH, C.E.G, “Prospects for the control of infectious disease”, Proc.roy. Soc. Med., 63 (1970), 1181–1190.Google Scholar
  10. 10.
    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.Google Scholar
  11. 11.
    SCHMIDT, G. Parametererregte -Schwingungen, VEB Deutscher Verlag der Wissenschaften, Berlin (1975).zbMATHGoogle Scholar
  12. 12.
    BENENSON, A.S. (ed.), Control of Communicable Diseases in Man (11th edn) American Public Health Association, Washington, D.C. (1970).Google Scholar
  13. 13.
    GRIFFITHS, D.A. “A catalytic model of infection for measles”, Appl.Startsist., 23, (1974). 330–339.CrossRefGoogle Scholar
  14. 14.
    TAYLOR, I. and KNOWELDEN, J, Principles of Epidemiology, (2nd edn). Churchill, London (1964).Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1976

Authors and Affiliations

  1. 1.Health Statistical MethodologyWorld Health OrganizationGeneva 27Switzerland

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