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Updated: Jul 13, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
Mathematical analysis of an integral equation arising from population dynamics
1Department of Mathematics, Mantell Building, University of Sussex, Falmer, Brighton, UK. d.a.kay@sussex.ac.uk
Abstract:
In this paper, we establish the existence of travelling wave solution to an intrinsically non-linear differential-integral equation formed as a result of mathematical modelling of the evolution of an asexual population in a changing environment. This equation is first converted to a non-linear integral equation. The discretization and manipulation of the corresponding eigenvalue problem allows us to use the theory of positive matrices to get some very useful estimates and then to confirm the existence of solution. We also exhibit numerical simulation results and explain the biological meaning of the results.
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