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Updated: Jul 10, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
Mathematical analysis of a metapopulation model with space-limited recruitment
1Department of Mathematical Sciences, University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo 153-8914, Japan. kkamioka@khaki.plala.or.jp
Abstract:
We investigate a mathematical aspect of a multi-species' sessile metapopulation model with space-limited recruitment proposed by Iwasa et al. in 1986. We define some basic reproduction numbers to show the threshold condition for the stability of trivial steady state and the existence of coexistent steady state. We show the existence of steady state where all species exist when some reproduction numbers are greater than one by the fixed point theorem. And we construct the Lyapunov function to show the global stability of trivial steady state when some basic reproduction numbers are not greater than one.
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