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Updated: Oct 14, 2025

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
One Dimensional Reduction of a Renewal Equation for a Measure-Valued Function of Time Describing Population Dynamics
Eugenia Franco1, Mats Gyllenberg1, Odo Diekmann2
1Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland.
Abstract:
Despite their relevance in mathematical biology, there are, as yet, few general results about the asymptotic behaviour of measure valued solutions of renewal equations on the basis of assumptions concerning the kernel. We characterise, via their kernels, a class of renewal equations whose measure-valued solution can be expressed in terms of the solution of a scalar renewal equation. The asymptotic behaviour of the solution of the scalar renewal equation, is studied via Feller's classical renewal theorem and, from it, the large time behaviour of the solution of the original renewal equation is derived.
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