EXTINCTION AND UNIFORM STRONG PERSISTENCE OF A SIZE-STRUCTURED POPULATION MODEL

摘要

In this paper, we study the long-time behavior of a size-structured population model. We define a basic reproduction number R and show that the population dies out in the long run if R < 1. If 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.