多种群布鲁氏菌病模型的动力学分析及最优控制

Dynamic Analysis and Optimal Control of a Multi-Group Brucellosis Model

摘要: 布鲁氏菌病是世界动物卫生组织划定的重点烈性人畜共患病之一。我国牛羊养殖业体量庞大、养殖覆盖面广，使得布鲁氏菌病已成为国内突出的公共卫生问题。鉴于此，本文构建包含牛、羊、人三类宿主种群的多种群布鲁氏菌病传播动力学模型，重点刻画牛羊种群间的交叉混合感染机制，以此探究布鲁氏菌病在不同宿主种群间的传播演化规律。理论分析结果表明，当基本再生数$R_0\le 1$ 时，系统无病平衡点具有全局渐近稳定性；当基本再生数$R_0>1$ 时，系统存在唯一的地方病平衡点，且该平衡点同样满足全局渐近稳定条件。在此基础上，本文采用最小二乘法完成模型参数拟合与参数估计，通过敏感性分析筛选影响疾病传播的关键参数，并进一步构建布鲁氏菌病传播最优防控控制系统，结合数值模拟验证模型动力学特征与防控策略有效性。研究结果证实，规范牛羊养殖模式、杜绝混养混饲行为，能够有效阻断牛羊种群间的交叉混合传播路径，是降低布鲁氏菌病人群与畜禽感染率、遏制疾病扩散的核心防控举措。

Abstract: Brucellosis is classified as one of the most severe zoonotic diseases by the World Organization for Animal Health. Due to the large-scale cattle and sheep breeding industry in China, brucellosis has become a prominent public health problem nationwide. Accordingly, this paper establishes a multi-species brucellosis transmission dynamics model involving three host populations: cattle, sheep, and humans, with a particular focus on characterizing the cross-infection mechanism between cattle and sheep populations, to explore the transmission and evolution rules of brucellosis among different host populations. Theoretical analysis results demonstrate that when the basic reproduction number $R_0\le 1$ , the disease-free equilibrium of the system is globally asymptotically stable; when the basic reproduction number $R_0>1$ , the system admits a unique endemic equilibrium, which is also globally asymptotically stable. On this basis, the least squares method is adopted for model parameter fitting and estimation. Furthermore, sensitivity analysis is performed to identify the key parameters affecting disease transmission, an optimal control system for brucellosis transmission is constructed, and numerical simulations are carried out to verify the dynamic characteristics of the proposed model and the effectiveness of prevention and control strategies. The research findings confirm that standardizing breeding patterns and prohibiting mixed breeding of cattle and sheep can effectively block the cross-transmission pathways between cattle and sheep populations, which serves as a core prevention and control measure to reduce the infection rate of brucellosis in livestock and humans and curb the spread of the disease.