基于动态价格与行为意识因素下的宁夏布鲁氏菌病最优控制策略研究

Research on Optimal Control Strategies for Brucellosis in Ningxia Based on Dynamic Pricing and Awareness Factors

摘要: 布鲁氏菌病是一种典型的人畜共患传染病，对畜牧业生产和公共卫生安全均造成严重影响。本文引入羊肉市场动态价格与养殖户养殖意愿因素，构建了一个耦合经济行为与疾病传播机制的绵羊–布病动力学模型。理论证明了在引入五类控制措施下的控制模型，关于两类最优控制问题最优控制解的存在性，并给出关于农户收益最大化问题控制解的显示格式，以及布病控制时间最小化控制解只能是bang-bang控制。利用宁夏地区2012~2024年的统计数据对模型参数进行估计，并通过数值模拟分析不同控制策略的作用效果。研究结果表明：在无控制情形下布鲁氏菌病将持续传播；实施最优控制策略能够显著降低感染羊数量与人间病例增长速度，并在长期内提高养殖系统整体收益。在收益最大化情形下，扑杀感染羊群与政府经济干预措施在最优控制策略中发挥重要作用，而减少人畜接触措施未被采用。在有限资源条件下，减少人与感染羊群接触在缩短疾病控制时间方面表现出最显著效果，但资源受限将导致控制时间延长并增加累计感染人数。

Abstract: Brucellosis is a typical zoonotic disease that has a serious impact on both livestock production and public health. This paper incorporates the dynamic market price of mutton and farmers’ willing-ness to rear sheep to construct a sheep-brucellosis dynamic model that couples economic behaviour with disease transmission mechanisms. Theoretical analysis verifies the existence of optimal con-trol solutions for two types of optimal control problems under five categories of control measures, provides an explicit form for the control solution regarding the farmer’s profit maximisation prob-lem, and demonstrates that the control solution for minimising the duration of brucellosis control can only be a bang-bang control. Model parameters were estimated using statistical data from the Ningxia region for the period 2012~2024, and numerical simulations were conducted to analyse the effectiveness of different control strategies. The results indicate that, in the absence of control measures, brucellosis will continue to spread; implementing optimal control strategies can signifi-cantly reduce the number of infected sheep and the rate of increase in human cases, whilst improv-ing the overall profitability of the livestock system in the long term. Under the profit-maximisation scenario, the culling of infected flocks and government economic intervention measures play a cru-cial role in the optimal control strategy, whereas measures to reduce human-animal contact were not adopted. Under conditions of limited resources, reducing human contact with infected sheep flocks demonstrated the most significant effect in shortening the duration of disease control; how-ever, resource constraints would lead to prolonged control periods and an increase in the cumula-tive number of infections.