{"title":"Asymptotic profile of steady states for a partially degenerate Aedes aegypti population model","authors":"Jie Xing, Hua Nie","doi":"10.1016/j.aml.2025.109554","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"167 ","pages":"Article 109554"},"PeriodicalIF":2.9000,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965925001041","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍:
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.