A nonlinear model of age and size-structured populations with applications to cell cycles

Abstract

The Sharpe-Lotka-McKendrick (or von Foerster) equations for an age-structured population, with a nonlinear term to represent overcrowding or competition for resources, are considered. The model is extended to include a growth term, allowing the population to be structured by size or weight rather than age, and a general solution is presented. Various examples are then considered, including the case of cell growth where cells divide at a given size. Copyright © Australian Mathematical Society 2007.