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Seasonality and critical community size for infectious diseases

Published online by Cambridge University Press:  17 February 2009

R. M. Cullen ,
A. Korobeinikov  and
W. J. Walker
R. M. Cullen
Affiliation:
Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand.
A. Korobeinikov
Affiliation:
Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24–29 St Giles', Oxford OX1 3LB, UK; e-mail: korobeinikov@math.ox.ac.uk.
W. J. Walker
Affiliation:
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.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 4 , April 2003 , pp. 501 - 512
Copyright
Copyright © Australian Mathematical Society 2003

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