ﻻ يوجد ملخص باللغة العربية
We derive the full kinetic equations describing the evolution of the probability density distribution for a structured population such as cells distributed according to their ages and sizes. The kinetic equations for such a sizer-timer model incorporates both demographic and individual cell growth rate stochasticities. Averages taken over the densities obeying the kinetic equations can be used to generate a second order PDE that incorporates the growth rate stochasticity. On the other hand, marginalizing over the densities yields a modified birth-death process that shows how age and size influence demographic stochasticity. Our kinetic framework is thus a more complete model that subsumes both the deterministic PDE and birth-death master equation representations for structured populations.
In a well-stirred system undergoing chemical reactions, fluctuations in the reaction propensities are approximately captured by the corresponding chemical Langevin equation. Within this context, we discuss in this work how the Kramers escape theory c
We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an age-structured multi
Cooperative interactions pervade the dynamics of a broad rage of many-body systems, such as ecological communities, the organization of social structures, and economic webs. In this work, we investigate the dynamics of a simple population model that
We investigate a model of cell division in which the length of telomeres within the cell regulate their proliferative potential. At each cell division the ends of linear chromosomes change and a cell becomes senescent when one or more of its telomere
We consider non-demographic noise in the form of uncertainty in the reaction step size, and reveal a dramatic effect this noise may have on the stability of self-regulating populations. Employing the reaction scheme mA->kA, but allowing, e.g., the pr