A stage-structured delayed advection reaction-diffusion model for single species

Abstract

In this paper, we derived a delay advection reaction-diffusion equation with linear advection term from a stage-structured model, then the derived equation is used under the homogeneous Dirichlet boundary conditions u_m (0,t)=0, u_m (L,t)=0, and the initial condition u_m (x,0)=u_m^0 (x)>0,x∈[-τ,0] with u_m^0 (0)>0 in order to find the minimum value of domain L that prevents extinction of the species under the effect of advection reaction diffusion equation. Finally, for the measurement the time lengths from birth to the development of the species population, time delays are integrated.