The Incidence of Infectious Diseases under the Influence of Seasonal Fluctuations
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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.
KeywordsLatent Period Equilibrium Solution Reproduction Rate Periodic Pattern Contact Rate
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