Journal of Mathematical Biology

, Volume 9, Issue 1, pp 37–47

Integral equation models for endemic infectious diseases

  • Herbert W. Hethcote
  • David W. Tudor

DOI: 10.1007/BF00276034

Cite this article as:
Hethcote, H.W. & Tudor, D.W. J. Math. Biology (1980) 9: 37. doi:10.1007/BF00276034


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.

Key words

Epidemiology Endemic infectious diseases Deterministic models Thresholds Distributed delays Stability 

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Herbert W. Hethcote
    • 1
  • David W. Tudor
    • 2
  1. 1.Department of MathematicsThe University of IowaIowa CityUSA
  2. 2.Department of MathematicsThe College of CharlestonCharlestonUSA