On a size-structured two-phase population model with infinite states-at-birth

TL;DR

This paper introduces and analyzes a size-structured population model with two life-stages and infinite states-at-birth, demonstrating that solutions exhibit asynchronous exponential growth under certain conditions.

Contribution

It develops a new mathematical framework for a two-phase population model with infinite states-at-birth and analyzes its long-term behavior using spectral theory.

Findings

The model is governed by a positive quasicontractive semigroup.

Under plausible assumptions, solutions show asynchronous exponential growth.

The spectral analysis confirms the stability and growth properties of the population.

Abstract

In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an "active" phase when individuals grow, reproduce and die and a second "resting" phase when individuals only grow. Transition between these two phases depends on individuals' size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant state space. Then we investigate, in the framework of the spectral theory of linear operators, the asymptotic behavior of solutions of the model. We prove that the associated semigroup has, under biologically plausible assumptions, the property of asynchronous exponential growth.