Abstract
For many infectious diseases, immunity wanes over time. The majority of SIRS models assume that this loss of immunity takes place at a constant rate. We study temporary immunity within a SIRS model structure if the rate of loss of immunity can depend on the time since recovery from disease. We determine the conditions under which the endemic steady state becomes unstable and periodic oscillations set in, showing that a fairly rapid change between slow and rapid immunity loss is necessary to produce oscillations.
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Acknowledgements
Thanks to members of the sLaM and eκoSystems groups for discussion and comments. This work was supported by a 21st Century Science Initiative Grant from the James S. McDonnell Foundation.
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Bhattacharya, S., Adler, F.R. A Time Since Recovery Model with Varying Rates of Loss of Immunity. Bull Math Biol 74, 2810–2819 (2012). https://doi.org/10.1007/s11538-012-9780-7
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DOI: https://doi.org/10.1007/s11538-012-9780-7