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A TWO-STRAIN EPIDEMIC MODEL WITH UNCERTAINTY IN THE INTERACTION

Published online by Cambridge University Press:  21 February 2013

M. G. ROBERTS
M. G. ROBERTS*
Affiliation:
Institute of Natural & Mathematical Sciences, New Zealand Institute for Advanced Study and Infectious Disease Research Centre, Massey University, Private Bag 102 904, North Shore Mail Centre, Auckland, New Zealand
*
m.g.roberts@massey.ac.nz
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Abstract

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Annual epidemics of influenza A typically involve two subtypes, with a degree of cross-immunity. We present a model of an epidemic of two interacting viruses, where the degree of cross-immunity may be unknown. We treat the unknown as a second independent variable, and expand the dependent variables in orthogonal functions of this variable. The resulting set of differential equations is solved numerically. We show that if the population is initially more susceptible to one variant, if that variant invades earlier, or if it has a higher basic reproduction number than the other variant, then its dynamics are largely unaffected by cross-immunity. In contrast, the dynamics of the other variant may be considerably restricted.

Keywords

epidemicsinfluenzaSIR modelimmunity

MSC classification

Secondary: 92D30: Epidemiology
Type
Research Article
Information
The ANZIAM Journal , Volume 54 , Issue 1-2 , October 2012 , pp. 108 - 115
Copyright
Copyright ©2013 Australian Mathematical Society 

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