A simple influenza model with complicated dynamics

Roberts, M.G., Hickson, R.I., Mccaw, J.M., and Talarmain, L. (2019) A simple influenza model with complicated dynamics. Journal of Mathematical Biology, 78. pp. 607-624.

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Abstract

We propose and analyse a model for the dynamics of a single strain of an influenza-like infection. The model incorporates waning acquired immunity to infection and punctuated antigenic drift of the virus, employing a set of differential equations within a season and a discrete map between seasons. We show that the between-season map displays a variety of qualitatively different dynamics: fixed points, periodic solutions, or more complicated behaviour suggestive of chaos. For some example parameters we demonstrate the existence of two distinct basins of attraction, that is the initial conditions determine the long term dynamics. Our results suggest that there is no reason to expect influenza dynamics to be regular, or to expect past epidemics to give a clear indication of future seasons' behaviour.

Item ID: 64029
Item Type: Article (Research - C1)
ISSN: 1432-1416
Keywords: Seasonal influenza, Transmission model, Discrete dynamics, Dynamical systems
Copyright Information: © Springer-Verlag GmbH Germany, part of Springer Nature 2018
Date Deposited: 13 Aug 2020 01:55
FoR Codes: 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010202 Biological Mathematics @ 34%
01 MATHEMATICAL SCIENCES > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations @ 33%
11 MEDICAL AND HEALTH SCIENCES > 1117 Public Health and Health Services > 111706 Epidemiology @ 33%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970101 Expanding Knowledge in the Mathematical Sciences @ 50%
92 HEALTH > 9204 Public Health (excl. Specific Population Health) > 920404 Disease Distribution and Transmission (incl. Surveillance and Response) @ 50%
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