Laboratoire de Mathématiques de Bretagne Atlantique
A growth-fragmentation model for populations heterogeneous in growth rate: long-time behavior and Malthus parameter
In various experiments, biologists have been observing variability among cells of a same population in the way they were growing. This presentation addresses the question of the effects of such inter-cell variability in growth rate on the dynamics of the whole population. Do populations grow faster as variability increases? Does it depend on the individual growth rates and on the way they are inherited over divisions?
To investigate these questions, we will study the long-time behavior of a growth-fragmentation equation, structured in size and growth rate. We will first show that a solution of the equation, once renormalized by a time exponential, converges in time to a steady state -including in the case of individual exponential growth, known to exhibit oscillations in the absence of variability.
Theoretically and numerically, we will then investigate the dependence of the Malthus parameter -the constant in the exponential renormalizing factor, which directly characterizes the population growth- in the parameters of the problem.