具有饱和发生率和环境传播的多时滞霍乱模型分析  

Analysis of Multi-Delay Cholera Model with Saturation Incidence and Environmental Transmission

作　　者：侯兴壹 郝新杰 聂麟飞[1] HOU Xing-yi;HAO Xin-jie;NIE Lin-fei(School of Mathematics and System Sciences,Xinjiang University,Urumqi 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017

出　　处：《数学的实践与认识》2024年第11期161-171,共11页Mathematics in Practice and Theory

基　　金：国家自然科学基金(12361103);新疆维吾尔自治区自然科学基金(2022TSYCCX0015,2021D01E12)。

摘　　要：考虑到霍乱弧菌传播途径的多样性和时滞效应的普遍存在性,建立一类具有多种传播途径和多时滞的霍乱传播模型.首先,给出基本再生数的精确表达式,分析平衡点的存在性与稳定性,讨论模型Hopf分支的存在性.进一步,运用分支理论讨论Hopf分支的方向和周期解的稳定性.最后,利用数值模拟解释主要的理论结果,并讨论时滞对疾病传播的影响.In this paper,considering a cholera transmission model with multiple transmission routes and delays due to the diverse routes and delay effects,calculating the precise expression of the basic reproduction number and analyzing the existence and stability of the equilibrium,while also discussing the potential Hopf bifurcation in the model.Furthermore,the directional properties of the Hopf bifurcation and the stability of periodic solution are discussed using bifurcation theory.Finally,using numerical simulation to explain the main theoretical results and discuss the influence of time delays on disease.

关 键 词：霍乱弧菌 饱和发生率 HOPF分支 基本再生数 全局吸引 

分 类 号：R181.3[医药卫生—流行病学] O175[医药卫生—公共卫生与预防医学]