摘要
文中建立了一类具有非局部扩散的霍乱传染病模型,证明了模型正解的全局存在性和全局吸引子的存在性.通过定义基本再生数,得到系统平衡态的全局性质,即当基本再生数小于1时,系统的无病平衡态是全局吸引的;当基本再生数大于1时,系统是一致持久的.此外,在一定条件下,系统存在全局吸引的地方病平衡态.表明基本再生数是控制疾病生存和消亡的重要阈值.
This paper established a cholera epidemic model with nonlocal diffusion and obtains the global existence of positive solutions and the global attractor.By defining the basic reproduction number,the global properties of the steady state of the system are obtained,that is,when the basic reproduction number is less than 1,the disease-free steady state is globally attractive;When the basic reproduction number is greater than 1,the system is uniformly persistent.In addition,under certain conditions,the system has a globally attractive endemic disease steady state.This indicates that the basic reproduction number is an important threshold for controlling the disease.
作者
曲思聪
张冉
刘利利
QU Si-cong;ZHANG Ran;LIU Li-li(School of Mathematical Science,Heilongjiang University,Harbin 150080,China;Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems,Heilongjiang University,Harbin 150080,China;Complex Systems Research Center,Shanxi University,Taiyuan O30006,China;Shanxi Key Laboratoryfor Mathematical Technology in Complex Systems,Shanxi University,Taiyuan 030006,China)
出处
《高校应用数学学报(A辑)》
北大核心
2025年第4期445-455,共11页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金(12101309,12126349,12401638)
山西省自然科学基金(202303021211003)
黑龙江省自然科学基金优秀青年项目(YQ2024A011)
黑龙江省省属高等学校基本科研业务费(2022-KYYWF-1113)
黑龙江大学杰出青年科学基金(JCL202203)。
关键词
霍乱
传染病动力学模型
非局部扩散
全局稳定性
cholera
infectious diseases dynamical model
nonlocal diffusion
global stability
