Traveling wave dispersal in partially sedentary age-structured biological populations

TL;DR

This paper investigates the existence of traveling wave solutions in a mathematical model of dispersal for partially sedentary, age-structured populations, extending previous theories to include age-dependent migration and sedentary behavior.

Contribution

It extends existing traveling wave theory to models with age-dependent migration and sedentary subpopulations in age-structured populations.

Findings

Existence of traveling waves in the model is established.

The model incorporates age-dependent migration and sedentary behavior.

Theoretical extension of Weinberger's population genetics model.

Abstract

In this paper we present a thorough study on the existence of traveling waves in a mathematical model of dispersal in a partially sedentary age-structured population. This type of model was first proposed by Veit and Lewis in [{\it Am. Nat.}, {\bf 148} (1996), 255-274]. We choose the fecundity function to be the Beverton-Holt type function. We extend the theory of traveling waves in the population genetics model of Weinberger in [{\it SIAM J. Math. Anal.}, {\bf 13} (1982), 353-396] to the case when migration depends on age groups and a fraction of the population does not migrate.