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The Analysis of Some Characteristic Equations Arising in Population and Epidemic Models

  • Fred Brauer
Article

Abstract

Epidemic models with a general infective period distribution are formulated as functional differential equations, as are population models with a general life span distribution. The analysis of the local stability properties of equilibria of such models leads to a characteristic equation involving the Laplace transform of the infective period (or life span) distribution. We obtain conditions under which all roots of the characteristic equation are in the left half plane, implying asymptotic stability of equilibrium, for every infective period distribution. We also consider the converse problem of describing when instability can occur for specific infective period distributions.

Characteristic equations epidemic models infective period distributions 

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Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • Fred Brauer
    • 1
  1. 1.Department of MathematicsUniversity of Brtish ColumbiaVancouverCanada

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