On the variations of the principal eigenvalue with respect to a parameter in growth-fragmentation models

TL;DR

This paper investigates how the principal eigenvalue in growth-fragmentation models changes with a parameter, using probabilistic methods and linking survival probability to eigenvalue variations.

Contribution

It introduces a probabilistic approach to analyze the eigenvalue variations in growth-fragmentation models, connecting survival probability with eigenvalue changes.

Findings

Eigenvalue variations are linked to survival probability changes.

Probabilistic interpretation provides new insights into model behavior.

Method can be applied to similar structured population models.

Abstract

We study the variations of the principal eigenvalue associated to a growth-fragmentation-death equation with respect to a parameter acting on growth and fragmentation. To this aim, we use the probabilistic individual-based interpretation of the model. We study the variations of the survival probability of the stochastic model, using a generation by generation approach. Then, making use of the link between the survival probability and the principal eigenvalue established in a previous work, we deduce the variations of the eigenvalue with respect to the parameter of the model.