ANZIAM J.
44 (2003), 501-512
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Seasonality and critical community size for infectious diseases
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R. M. Cullen
Department of Mathematics
University of Auckland
Private Bag 92019
Auckland
New Zealand
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A. Korobeinikov
Centre for Mathematical Biology
Mathematical Institute
University of Oxford
24--29 St Giles'
Oxford OX1 3LB
UK
korobeinikov@math.ox.ac.uk
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W. J. Walker
Department of Mathematics
University of Auckland
Private Bag 92019
Auckland
New Zealand
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Abstract
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The endemicity of infectious diseases is
investigated from a deterministic viewpoint.
Sustained oscillation of infectives is often due
to seasonal effects which may be related to
climatic changes. For example the transmission of
the measles virus by droplets is enhanced in
cooler, more humid seasons. In many countries the
onset of cooler, more humid weather coincides
with the increased aggregation of people and the
seasonal effect can be exacerbated. In this
paper we consider non-autonomous compartmental
epidemiological models and demonstrate that the
critical community size phenomenon may be
associated with the seasonal variation in the
disease propagation. This approach is applicable
to both the prevaccination phenomenon of critical
community size and the current goal of worldwide
elimination of measles by vaccination.
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