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

1 Department of Applied Mathematics, National Pingtung University, Pingtung, ROC 90003, Taiwan
2 Department of Mathematics, National Taiwan Normal University, Taipei, ROC11677, Taiwan
3 Department of Applied Mathematics, University of Western Ontario, London, ON, N6A 5B7, Canada

Special Issues: Recent Advances in Mathematical Population Dynamics

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.
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Keywords age structure; patch; density-dependent dispersal; delay differential equation; uniform persistence; global convergence

Citation: Chang-Yuan Cheng, Shyan-Shiou Chen, Xingfu Zou. On an age structured population model with density-dependent dispersals between two patches. Mathematical Biosciences and Engineering, 2019, 16(5): 4976-4998. doi: 10.3934/mbe.2019251

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