tetano
Editor, Senior Moderator
J Math Biol. 2018 Aug 28. doi: 10.1007/s00285-018-1285-z. [Epub ahead of print]
[h=1]A simple influenza model with complicated dynamics.[/h] Roberts MG[SUP]1[/SUP], Hickson RI[SUP]2,[/SUP][SUP]3[/SUP], McCaw JM[SUP]3,[/SUP][SUP]4[/SUP], Talarmain L[SUP]5,[/SUP][SUP]6[/SUP].
[h=3]Author information[/h]
[h=3]Abstract[/h] 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.
[h=4]KEYWORDS:[/h] Discrete dynamics; Dynamical systems; Seasonal influenza; Transmission model
PMID: 30155777 DOI: 10.1007/s00285-018-1285-z
[h=1]A simple influenza model with complicated dynamics.[/h] Roberts MG[SUP]1[/SUP], Hickson RI[SUP]2,[/SUP][SUP]3[/SUP], McCaw JM[SUP]3,[/SUP][SUP]4[/SUP], Talarmain L[SUP]5,[/SUP][SUP]6[/SUP].
[h=3]Author information[/h]
[h=3]Abstract[/h] 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.
[h=4]KEYWORDS:[/h] Discrete dynamics; Dynamical systems; Seasonal influenza; Transmission model
PMID: 30155777 DOI: 10.1007/s00285-018-1285-z