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Integral equation models for endemic infectious diseases

Journal of Mathematical Biology volume 9, pages 37–47 (1980)Cite this article

Summary

Endemic infectious diseases for which infection confers permanent immunity are described by a system of nonlinear Volterra integral equations of convolution type. These constant-parameter models include vital dynamics (births and deaths), immunization and distributed infectious period. The models are shown to be well posed, the threshold criteria are determined and the asymptotic behavior is analysed. It is concluded that distributed delays do not change the thresholds and the asymptotic behaviors of the models.

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Authors and Affiliations

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

    Herbert W. Hethcote

  2. Department of Mathematics, The College of Charleston, 29401, Charleston, South Carolina, USA

    David W. Tudor

Authors
  1. Herbert W. Hethcote
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  2. David W. Tudor
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Additional information

This work was partially supported by NIH Grant AI 13233.

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Hethcote, H.W., Tudor, D.W. Integral equation models for endemic infectious diseases. J. Math. Biology 9, 37–47 (1980). https://doi.org/10.1007/BF00276034

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  • DOI: https://doi.org/10.1007/BF00276034

Key words

  • Epidemiology
  • Endemic infectious diseases
  • Deterministic models
  • Thresholds
  • Distributed delays
  • Stability