The effect of seasonal host birth rates on population dynamics: the importance of resonance

Journal of Theoretical Biology
J M IrelandJ V Greenman

Abstract

Many of the simple mathematical models currently in use often fail to capture important biological factors. Here we extend current models of insect-pathogen interactions to include seasonality in the birth rate. In particular, we consider the SIR model with self-regulation when applied to specific cases--rabbit haemorrhagic disease and fox rabies. In this paper, we briefly summarize the results of the model with a constant time-independent birth rate, a, which we then replace with the time dependent birth rate a(t), to investigate how this effects the dynamics of the host population. We can split parameter space into an area in which the model without seasonality has no oscillations, in which case a simple averaging rule predicts the behaviour. Alternatively, in the area where oscillations to the equilibrium do occur in the non-seasonal model, disease persistence is more complicated and we get more complex dynamical behaviour in this case. We apply resonance techniques to discover the structure of the subharmonic modes of the SIR model with self-regulation. We then look at whether many biological systems are likely to display these "resonant" dynamics and find that we would expect them to be widespread.

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Citations

May 8, 2008·Journal of Mathematical Biology·Nicolas Bacaër, Xamxinur Abdurahman
Jun 1, 2012·Journal of Mathematical Biology·Suzanne M O'ReganDmitrii Rachinskii
Nov 10, 2012·Journal of Mathematical Biology·Rachel A TaylorAndrew White
Nov 30, 2012·Proceedings. Biological Sciences·R DonnellyM Boots
May 16, 2014·Proceedings. Biological Sciences·A J PeelO Restif
Oct 25, 2008·The American Naturalist·Luca BolzoniGiulio A De Leo
Jun 26, 2007·Theoretical Population Biology·Daihai He, David J D Earn
May 4, 2007·Journal of Theoretical Biology·J V Greenman, R A Norman
Apr 25, 2015·Trends in Ecology & Evolution·Micaela Martinez-Bakker, Barbara Helm
Nov 17, 2007·The Journal of Animal Ecology·Matthew J SmithXavier Lambin
Mar 15, 2011·Journal of Theoretical Biology·J V Greenman, V B Pasour
Jan 9, 2015·Journal of the Royal Society, Interface·Konstans WellsDamien A Fordham
Feb 6, 2020·Journal of Theoretical Biology·Alix M C SauveFrédéric Barraquand

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