Date(s) - 21/04/2015
11 h 00 min - 12 h 00 min
Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a particular type of nonlinear integro-differential equation (system).
In the case where the redistribution kernels are highly concentrated, we show that the integro-differential equation can be approximated by a reaction–diffusion equation, in which the proliferation rate contributes to both the diffusion term and the reaction term. We completely solve the corresponding critical domain size problem and the minimal wave speed problem.
Birth-jump models can be applied in many areas in mathematical biology. We highlight an application of our results in the context of nonlocal forest fire spread through spotting. We also emphasize several open problems, both pure and applied, associated with the birth-jump models.