Persistence and extinction of diffusing populations with two sexes and short reproductive season

Wen Jin, Horst Thieme

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

A model is considered for a spatially distributed population of male and female individuals that mate and reproduce only once in their life during a very short reproductive season. Between birth and mating, females and males move by diffusion on a bounded domain Ω. Mating and reproduction is described by a (positively) homogeneous function (of degree one). We identify a basic reproduction number R0 that acts as a threshold between extinction and persistence. If R0 < 1, the population dies out while it persists (uniformly weakly) if R0 > 1. R0 is the cone spectral radius of a bounded homogeneous map.

Original languageEnglish (US)
Pages (from-to)3209-3218
Number of pages10
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume19
Issue number10
DOIs
StatePublished - Dec 1 2014

Keywords

  • Basic reproduction number
  • Cone spectral radius
  • Difference equation
  • Discrete dynamical system
  • Discrete semi-flow
  • Eigenvector
  • Homogeneous map
  • Impulsive reaction diffusion system
  • Ordered Banach space
  • Stability.
  • Two-sex population

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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