新疆布鲁氏菌病传播动力学模型研究

In this project we will establish and study the Brucellosis infection models considering the special geographic and climatic characteristics of Xinjiang region. Based on the spread mode of animal Brucellosis and the special animal breeding method of Xinjiang, we will give out the epidemic model which considers the role of four seasonal migration of animals, livestock marketing and livestock transportation in Brucellosis infection in Xinjiang region. Then we will consider the periodic model in which the seasonality, the survival time of the bacteria in the different environment are the basic elements. Furthermore, considering the special eating habits of the minorities in Xinjiang region, we will give out the Human-Animal co-infection model, in which people are derived to several groups according to their profession, their age, their eating habits. We will also consider the direct and indirect transmission. At the end using the methods of differential dynamical systems, Theory of Difference equations and Stocastic differential equations, we will study the mathematical characteristics such as existence and stability of equilibrium points, the basic reproduction number, existence and stability of the periodic solutions, exictence of the optimal control solutions, the persistence and extinction of the models.

本课题主要结合新疆地理环境，气候以及养殖模式，建立并研究新疆布鲁氏菌病传染模型。以新疆畜牧布鲁氏菌病所具有的特点和新疆特殊的养殖模式为切入点，着手建立能够体现出畜牧的季节性四次大转场，活蓄交易及活蓄调运等动态的畜牧间布鲁氏菌病具有反应扩散，多板块，网络传染病模型。再此基础上考虑季节因素，布鲁氏菌在环境中生存周期因素等的周期传染病模型以及考虑到暴风雪等自然灾害因素的随机扰动模型。最后根据新疆少数民族的特殊饮食习俗，将建立人与动物共同感染模型，不仅将易感人群根据职业，饮食习惯，年龄分分类，还要考虑直接感染和间接感染对疾病传播的影响。进一步运用微分方程动力系统理论，差分方程理论，随机微分方程理论，最优控制理论将研究上述模型衡点的存在性与稳定性，传染病阈值，周期解的存在性与稳定性，最优控制解的存在性，疾病的持久性与灭绝性等动力学性质。

本课题结合新疆地理环境，气候以及养殖模式，建立并研究新疆布鲁氏菌病传染模型。主要研究内容有考虑外部输入，阶段结构，疫苗接种等因素的确定性布病模型，考虑潜伏期时滞和布鲁氏菌病在环境中存活时间等因素的多时滞布病模型，考虑白噪声扰动，Levy跳等对疾病传播影响的随机布鲁氏菌病模型以及一些确定性，随机传染病模型和竞争-合作，捕食被捕食种群动力学模型等。利用微分动力系统理论，随机微分方程理论等对这些模型的动力学行为进行了研究。得到的主要结果包括对确定性布病模型给出了平衡点的存在性，局部稳定性和全局稳定性，判定疾病灭绝与持久的阈值条件，时滞对模型稳定性的影响等，对随机布病模型得到了系统全局正解的存在性，灭绝性以及遍历平稳分布存在性的充分条件，对于传染病模型和种群动力学模型主要建立了系统的平衡点的存在性与全局稳定性，系统的持久性，灭绝性，正周期解的存在性，全局吸引性等的一系列比较容易验证的条件。所得结论有一定的理论价值和应用价值。

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