Asymptotic profile of steady states for a partially degenerate Aedes aegypti population model

Abstract

This paper explores the asymptotic profile of steady states in a partially degenerate Aedes aegypti population model within advective environments. By reducing the model to a scalar equation, we establish the existence and uniqueness of positive steady-state solutions using the method of upper and lower solutions. We analyze the interaction between diffusion and advection, focusing on their effects on the species’ spatial distribution. Specifically, we examine how variations in diffusion and advection rates impact the asymptotic profiles. Our results show that high advection rates and low diffusion rates lead to species concentration downstream. These findings provide important insights into Aedes aegypti population dynamics in bounded domains, highlighting the critical roles of advection and diffusion in shaping spatial patterns of the species.