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On periodic solutions of a delay integral equation modelling epidemics

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Summary

A delay-integral equation, proposed by Cooke and Kaplan in [1] as a model of epidemics, is studied. The focus of this work is on the qualitative behavior of solutions as a certain parameter is allowed to vary. It is shown that if a certain threshold is not exceeded then solutions tend to zero exponentially while if this threshold is exceeded, periodic solutions exist. Many features of the numerical studies in [1] are explained.

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References

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Authors and Affiliations

  1. The University of Iowa, 52242, Iowa City, IA, USA

    H. L. Smith

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  1. H. L. Smith
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Smith, H.L. On periodic solutions of a delay integral equation modelling epidemics. J. Math. Biology 4, 69–80 (1977). https://doi.org/10.1007/BF00276353

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  • DOI: https://doi.org/10.1007/BF00276353

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