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

Citation
Ireland JM, Norman R & Greenman J (2004) The effect of seasonal host birth rates on population dynamics: the importance of resonance, Journal of Theoretical Biology, 231 (2), pp. 229-238.

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.

Keywords
seasonality; resonance; mathematical model; infectious disease

StatusPublished
AuthorsIreland Jillian M, Norman Rachel, Greenman Jonathan
Publication date21/11/2004
Publication date online04/08/2004
URLhttp://www.sciencedirect.com/…0022519304002905
PublisherElsevier
ISSN 0022-5193
LanguageEnglish

Journal
Journal of Theoretical Biology: Volume 231, Issue 2 (NOV 21 2004)

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