Extinction and uniform strong persistence of a size-structured population model

Keng Deng; Yixiang Wu

doi:10.3934/dcdsb.2017041

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2017, Volume 22, Issue 3: 831-840. Doi: 10.3934/dcdsb.2017041

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Extinction and uniform strong persistence of a size-structured population model

Keng Deng and
Yixiang Wu^,

Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA

* Corresponding author
* Corresponding author

Dedicated to Steve Cantrell in honor of his 60th birthday

Received: July 31, 2015

Revised: December 31, 2015

Published: September 2017

Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA.

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Abstract

In this paper, we study the long-time behavior of a size-structured population model. We define a basic reproduction number $\mathcal{R}$ and show that the population dies out in the long run if $\mathcal{R}<1$. If $\mathcal{R}>1$, the model has a unique positive equilibrium, and the total population is uniformly strongly persistent. Most importantly, we show that there exists a subsequence of the total population converging to the positive equilibrium.

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Mathematics Subject Classification: 92D25, 35B40, 35L04.

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