一类具有隔离和消毒剂影响的霍乱模型研究  

Study on a Cholera Model with the Incorporation of Isolation and Disinfectant Effects

作　　者：刘慧[1] 乔志琴[1] LIU Hui;QIAO Zhiqin(School of Mathematics,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学数学学院,山西太原030051

出　　处：《中北大学学报(自然科学版)》2025年第2期261-270,共10页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11401541);山西省回国留学人员科研资助项目(2024-110)。

摘　　要：本文建立了一个考虑隔离和消毒剂影响的霍乱传染病模型,探究了这些因素对霍乱传播动态的影响。运用微分方程理论描述了模型的传播动力学,使用下一代矩阵法对模型的基本再生数进行了计算。在此基础上,详细阐述了无病平衡点和地方病平衡点的存在性和局部渐近稳定性,并对各平衡点处的全局渐近稳定性进行了深入讨论。结果显示,当基本再生数R_(0)<1时,模型的无病平衡点具有全局渐近稳定性;而当基本再生数R_(0)>1时,得出了地方病平衡点全局渐近稳定的充分条件。此外,采用PRCC法进行了敏感性分析,模拟隔离率和消毒剂对感染者和霍乱弧菌密度的影响,使用数值模拟验证了理论结果的正确性。对具有隔离和消毒剂双重控制策略影响下的霍乱传染病模型的研究表明,多重控制策略能够更加有效地抑制霍乱的传播。This paper established an cholera epidemic model considering the influence of isolation and dis-infectants to investigate their impact on the dynamics of cholera transmission.The transmission dynamics of the model were described using the theory of differential equations,and the basic reproduction number of the model was computed using the next-generation matrix method.On this basis,our study thoroughly investigate the conditions for the existence of disease-free and endemic equilibrium points,along with their global asymptotic stability.Findings reveal that with a basic reproduction number of R_(0)<1,the disease-free equilibrium point gradually stabilizes globally,while for a basic reproduction number of R_(0)>1,the endemic equilibrium point’s gradual stabilization towards a stable value and attainment of global stability are delineated.Furthermore,sensitivity analysis is conducted using PRCC method,considering the impact of isolation rates and disinfectants on the density of infected individuals and cholera Vibrio.Theo-retical findings are validated through numerical simulations.Through investigating a cholera model with dual control strategies of isolation and disinfectants,it is concluded that multiple control strategies can more effectively suppress the transmission of cholera.

关 键 词：霍乱模型 基本再生数 稳定性 平衡点 

分 类 号：O175.1[理学—数学]