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A simple influenza model with complicated dynamics |
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| Authors: | Roberts M. G. Hickson R. I. McCaw J. M. Talarmain L. |
| Affiliation: | 1.Institute of Natural and Mathematical Sciences, New Zealand Institute for Advanced Study and the Infectious Disease Research Centre, Massey University, Private Bag 102 904, North Shore Mail Centre, Auckland, New Zealand ;2.IBM Research Australia, Level 22, W Tower, 60 City Rd, Southgate, Melbourne, VIC, 3006, Australia ;3.School of Mathematics and Statistics, Faculty of Science, The University of Melbourne, Melbourne, VIC, 3010, Australia ;4.Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, Faculty of Medicine, Dentistry and Health Sciences, The University of Melbourne, Melbourne, VIC, 3010, Australia ;5.Institut National des Sciences Appliquées Lyon, Lyon, France ; |
| 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. |
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