The effect of seasonal host birth rates on disease persistence

In this paper, we add seasonality to the birth rate of an SIR model with density dependence in the death rate. We find that disease persistence can be explained by considering the average value of the seasonal term. If the basic reproductive ratio R 0 > 1 with this average value then the disease...

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Bibliographic Details
Published in:Mathematical biosciences 2007-03, Vol.206 (1), p.31-45
Main Authors: Ireland, J.M., Mestel, B.D., Norman, R.A.
Format: Article
Language:English
Subjects:
Algorithms
Animals
Arvicolinae
Birth Rate
Caliciviridae Infections - mortality
Caliciviridae Infections - transmission
Communicable Diseases - mortality
Communicable Diseases - transmission
Computer Simulation
Cowpox - mortality
Cowpox - transmission
Disease persistence threshold
Models, Biological
Population Density
Population Dynamics
Rabbits
Seasonal birth rate
Seasons
Survival Rate
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Summary:In this paper, we add seasonality to the birth rate of an SIR model with density dependence in the death rate. We find that disease persistence can be explained by considering the average value of the seasonal term. If the basic reproductive ratio R 0 > 1 with this average value then the disease will persist and if R 0 < 1 with this average value then the disease will die out. However, if the underlying non-seasonal model displays oscillations towards the equilibrium then the dynamics of the seasonal model can become more complex. In this case, the seasonality can interact with the underlying oscillations, resonate and the population can display a range of complex behaviours including chaos. We discuss these results in terms of two examples, Cowpox in bank voles and Rabbit Haemorrhagic disease in rabbits.
ISSN:0025-5564
1879-3134
DOI:10.1016/j.mbs.2006.08.028