On an age structured population model with density-dependent dispersals between two patches

Chang Yuan Cheng, Shyan Shiou Chen, Xingfu Zou*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Motivated by an age-structured population model over two patches that assumes constant dispersal rates, we derive a modified model that allows density-dependent dispersal, which contains both nonlinear dispersal terms and delayed non-local birth terms resulted from the mobility of the immature individuals between the patches. A biologically meaningful assumption that the dispersal rate during the immature period depends only on the mature population enables us investigate the model theoretically. Well-posedness is confirmed, criteria for existence of a positive equilibrium are obtained, threshold for extinction/persistence is established. Also addressed are a positive invariant set and global convergence of solutions under certain conditions. Although the levels of the density-dependent dispersals play no role in determining extinction/persistence, our numerical results show that they can affect, when the population is persistent, the long term dynamics including the temporal-spatial patterns and the final population sizes.

Original languageEnglish
Pages (from-to)4976-4998
Number of pages23
JournalMathematical Biosciences and Engineering
Issue number5
Publication statusPublished - 2019


  • Age structure
  • Delay differential equation
  • Density-dependent dispersal
  • Global convergence
  • Patch
  • Uniform persistence

ASJC Scopus subject areas

  • Modelling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics


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