不完全免疫的多阶段绵羊布鲁氏菌病模型的稳定性分析与最优控制  

Stability Analysis and Optimal Control of a Multistage Brucellosis Model in Sheep with Incomplete Immunity

作　　者：郑云 夏米西努尔·阿布都热合曼[1] ZHENG Yun;XAMXINUR Abdurahman(School of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《应用数学》2023年第3期800-807,共8页Mathematica Applicata

基　　金：国家自然科学基金资助项目(11861063)。

摘　　要：本文研究一个多阶段的不完全免疫的布鲁氏菌病模型,得到模型平衡点的存在唯一性以及基本再生数R_(0).通过构造合适的Lyapunov函数,证明了无病平衡点与地方病平衡点的全局渐近稳定性.在考虑控制成本的情况下,利用最优控制理论得到了布鲁氏菌病最优控制策略.最后用数值模拟验证了理论结果.In this paper,a multi-stage brucellosis model with incomplete immunity is investigated.The existence and uniqeness of the equilibrium point is given,and the basic reproduction number R_0 is calculated.The global asymptotic stability of the disease-free equilibrium and the endemic equilibrium is proved by constructing suitable Lyapunov functions.The optimal control strategy for brucellosis is determined by using optimal control theory with consideration of control cost.Finally,the theoretical results are verified by numerical simulations.

关 键 词：布鲁氏菌病 基本再生数 渐近稳定性 最优控制 

分 类 号：O193[理学—数学]