Asymptotic speed of propagation of wave fronts in a lattice delay differential equation with global interaction

In this paper, we derive a lattice model for a single speciesin a one-dimensional patchy environment with infinite numberof patches connected locally by diffusion. Under the assumptionthat the death and diffusion rates of the mature populationare age independent, we show that the dynamics of the maturepopulation is governed by a lattice delay differential equationwith global interactions. We study the well-posedness of theinitial-value problem and obtain the existence of monotone travellingwaves for wave speeds c > c_*. We show that the minimal wavespeed c_* is also the asymptotic speed of propagation, whichdepends on the maturation period and the diffusion rate of maturepopulation monotonically.