基于博弈的布鲁氏菌病传播动力学建模及其应用

Brucellosis is a zoonotic infectious disease caused by Brucella. In China, the spread of brucellosis is related to the scale of livestock farming, while the scale of farming is affected by livestock market price. Conversely, the spread and control of brucellosis can also cause economic losses to farmers, increase farming cost and further affect the scale of farming. Therefore, for government and farmers, the spread and control of brucellosis are essentially a game process. In this project, aiming at the characteristics and mechanisms of brucellosis, considering the livestock market price and vaccination price factors, and combining control cost and economic loss game strategy, three kinds of transmission dynamic brucellosis model with game theory are established, respectively. Theoretically, we compute the basic reproduction number and Nash equilibrium, and study the model dynamical behaviors including the existence and stability of equilibria and periodic solutions. In the application, combining with real data of some provinces in Northern China, the statistics is used to estimate and optimize the model parameters, and to predict epidemic trend in these provinces. The economic game theory is used to calculate the cost-effectiveness of prevention and control measures under the relevant game strategy, and to give the optimal control program. The results of this project can provide theoretical guidance for the prevention and control of brucellosis, and also improve the monitoring and control system of brucellosis, which have great significance.

布鲁氏菌病是由布鲁氏菌引起的一种人畜共患传染病。在中国，其传播与家畜养殖规模相关，而养殖规模受到市场价格的影响；反过来，布鲁氏菌病的传播和控制又给养殖户带来经济损失，加大养殖成本，从而影响养殖规模。因此，对于政府和养殖户，布鲁氏菌病的传播和控制本质上都是一个博弈过程。本项目针对布鲁氏菌病的发病特点和传播规律，考虑家畜市场价格和接种价格因素，结合控制成本和经济损失博弈策略，分别建立三类具有博弈的布鲁氏菌病传播动力学模型。理论上，计算模型的基本再生数和纳什均衡点，研究模型平衡点和周期解的存在性和稳定性等动力学行为。应用上，结合中国北方某些省份布鲁氏菌病人畜间数据，利用统计学方法对模型参数进行估计与优化，预测流行趋势；利用经济学博弈论方法计算相关博弈策略下的防控措施成本效益，给出最优控制方案。该项目研究结果可为布鲁氏菌病的预防与控制提供理论指导，也可完善布鲁氏菌病监测、防控体系，具有重要意义。

布鲁氏菌病在人间和畜间广泛传播，严重影响了我国人民的身体健康和畜牧业的发展，带来了巨大的经济损失。本项目结合动物市场价格和动物免疫价格等经济学博弈因素，将人类权衡利弊行为加入到模型中，建立基于博弈的布鲁氏菌病传播动力学模型，研究我国布病传播风险，为布病防控提供理论依据。..在项目执行期间(2019.01-2021.12)，围绕申请书提出的研究计划与内容，完成了关于布鲁氏菌病从博弈对象的寻找、动态博弈模型的建立、动力学分析和最优控制策略的选择等方面研究，实现了预期目标。主要包括：1、根据潜在的博弈对象和布鲁氏菌病的传播机理，结合布鲁氏菌病在畜间感染以及人畜间感染等，建立了一套涉及动物产品价格、平衡利益得失的动态博弈传染病模型的基本方法；2、通过对模型的动力学性态分析，评估了布病流行趋势，得出了影响该病流行的主要因素；3、结合实际布鲁氏菌病发病数据以及经济学分析，给出了一套评价博弈优劣策略的评估方案，为布鲁氏菌病的预防与控制提供理论指导。本项目的完成将扩展传染病动力学建模方法及理论研究。..在研究成果、人才培养和学术交流等方面，均实现了预期目标。本项目在Journal of Theoretical Biology, Computational and Structural Biotechnology Journal, Mathematical Biosciences and Engineering, Infectious Disease Modelling, International Journal of Biomathematics,《系统科学与数学》，《工程数学学报》和《应用数学和力学》等国内外期刊发表学术论文17篇, 其中SCI收录10篇。在人才培养方面，项目负责人2019年入选山西省“三晋英才”支持计划青年优秀人才，培养硕士研究生2名，继续招收研究生5名。