I this talk I will try to give an overview of recent progress in
spatial stochastic modeling within the reaction-diffusion
framework. While much of the initial motivation for this work came
from problems in cell biology, I will also highlight some examples
from epidemics and neuroscience.
As a motivating introduction, some newly discovered properties of
optimal controls in stochastic enzymatic reaction networks will be
presented. I will next detail how diffusive and subdiffusive reactive
processes in realistic geometries at the cellular scale may be modeled
mesoscopically. Along the way, some different means by which these
models may be analyzed with respect to consistency and convergence
will also be discussed. These analytical techniques hint at how
effective (i.e. parallel) numerical implementations can be
designed. Large-scale simulations will serve as illustrations.
- Mathematical Biology and Ecology Seminar