开放异质环境下考虑外源输入及频率依赖发生率的反应-扩散-对流SIS模型  

Analysis on a SIS Epidemic Reaction-Diffusion-Advection Model with External Source and Frequency-Dependent Incidence Rate in an Open Spatial Heterogeneous Environment

作　　者：饶旭 张国洪[1] RAO Xu;ZHANG Guohong(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China;Chengdou NO.36 Middle School,Chengdu 610083,China)

机构地区：[1]西南大学数学与统计学院,重庆400715 [2]成都市第三十六中学校,成都610083

出　　处：《西南师范大学学报（自然科学版）》2023年第3期52-60,共9页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11871403)。

摘　　要：研究了开放异质环境下带有线性外源项及频率依赖发生率的反应-扩散-对流SIS模型.首先证明了解的一致有界性,然后引入了基本再生数R_(0),获得了模型关于R_(0)的阈值动力学行为:当R_(0)<1时,唯一的无病平衡点局部渐近稳定;当R_(0)>1时,系统一致持续且存在流行病平衡点.最后研究了R_(0)对感染者的扩散速度dI和对流率q的依赖性,发现在开放对流环境下,对流率的增加有利于传染病的控制.A SIS epidemic reaction-diffusion-advection model with linear source and frequency-dependent incidence rate in an open heterogeneous environment has been investigated.Firstly,the uniform boundedness of the solution is obtained.Secondly,the basic reproduction number R_(0)is introduced and the threshold dynamics behavior of the model about R_(0)is obtained.The unique disease-free equilibrium is linearly stable if R_(0)<1 and the system is uniformly persistent if R_(0)>1,which implies the existence of endemic equilibrium.And finally,the dependence of R_(0)on advection rate q and diffusion rate dIis studied.It is known that the increase of q is helpful in controlling infectious disease in an open spatial heterogeneous environment.

关 键 词：开放对流环境 线性外源项 SIS传染病模型 频率依赖发生率 基本再生数 

分 类 号：O175[理学—数学]