Integral equation models for endemic infectious diseases Article Received: 24 April 1979 Revised: 09 July 1979 DOI:
Cite this article as: Hethcote, H.W. & Tudor, D.W. J. Math. Biology (1980) 9: 37. doi:10.1007/BF00276034 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.
Key words Epidemiology Endemic infectious diseases Deterministic models Thresholds Distributed delays Stability
This work was partially supported by NIH Grant AI 13233.
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