2019/12/17 by Mostafa Fazly, Mark A. Lewis, Fazly, Mostafa +3 · 1 citation
Mathematics · Medicine · #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Biological sciences #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.1912.08711
openalex publication_date 2019/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a hybrid impulsive reaction-advection-diffusion model given by a reaction-advection-diffusion equation composed with a discrete-time map in space dimension n∈\mathbb N. The reaction-advection-diffusion equation takes the form u(m)t = div(A∇ u(m)-q u(m)) + f(u(m)) for (x,t)∈\mathbb Rn × (0,1] , for some function f, a drift q and a diffusion matrix A. When the discrete-time map is local in space we use Nm(x) to denote the density of population at a point x at the beginning of reproductive season in the mth year and when the map is nonlocal we use um(x). The local discrete-time map is \ u(m)(x,0) = g(Nm(x)) for x∈ \mathbb Rn ,
Nm+1(x):=u(m)(x,1) for x∈ \mathbb Rn ,. for some function g. The nonlocal discrete time map is \ u(m)(x,0) = um(x) for x∈ \mathbb Rn ,
um+1(x) := g(∫\mathbb Rn K(x-y)u(m)(y,1) dy) for x∈ \mathbb Rn,. when K is a nonnegative normalized kernel. SEE THE ARTICLE FOR COMPLETE ABSTRACT.