西北师范大学学报（自然科学版）2025，Vol.61Issue(3)：97-110,14.DOI:10.16783/j.cnki.nwnuz.2025.03.011
一类具有Logistic源及饱和发生率的反应扩散模型
A reaction-diffusion model with Logistic source and saturated incidence rate
摘要
Abstract
This article establishes a SIS reaction-diffusion model with Logistic sources and saturation incidence rates.Firstly,the uniform boundedness of the model solution is proved.Secondly,the threshold dynamics of the model based on the basic reproduction number is discussed.Finally,the asymptotic behavior of the equilibrium is further analyzed when the diffusion rate approaches zero or infinity.The results indicate that the logistic growth and population mobility of susceptible population play an important role in the spread of diseases,the faster the susceptibles reach saturation,the faster the disease is eliminated.关键词
反应扩散模型/饱和发生率/基本再生数/阈值动力学/渐近性态Key words
reaction-diffusion model/saturated incidence rate/basic reproduction number/threshold dynamics/asymptotic profile分类
数学引用本文复制引用
耿韶怡,蔺小林,庞丹凤,李国庆..一类具有Logistic源及饱和发生率的反应扩散模型[J].西北师范大学学报（自然科学版）,2025,61(3):97-110,14.基金项目
国家自然科学基金资助项目(12301634) （12301634）
