Cell cycle length and long-time behaviour of an age-size model

TL;DR

This paper analyzes an age-size structured cell population model focusing on cell cycle length, establishing new criteria for asynchronous exponential growth, and exploring models with constant and target size division, including heterogeneity.

Contribution

It introduces new mathematical criteria for asynchronous exponential growth in age-size models and extends analysis to heterogeneous populations.

Findings

Established criteria for asynchronous exponential growth.

Analyzed models with constant and target size division.

Extended models to include population heterogeneity.

Abstract

We consider an age-size structured cell population model based on the cell cycle length. The model is described by a first order partial differential equation with initial-boundary conditions. Using the theory of semigroups of positive operators we establish new criteria for an asynchronous exponential growth of solutions to such equations. We discuss the question of exponential size growth of cells. We study in detail a constant size growth model and a model with target size division. We also present versions of the model when the population is heterogeneous.