垂直传染与环境因素对野牛布鲁氏菌传播的影响研究  

Study on the Effects of Vertical Infection and Environmental Factors on the Transmission of Bison Brucella

作　　者：康瑶瑶 夏米西努尔·阿布都热合曼[1] KANG Yao-yao;Xamxinur Abdurahman(College of Mathematics and Systems Science,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：《数学的实践与认识》2020年第18期139-146,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11861063)。

摘　　要：研究了布鲁氏菌通过水平和垂直传染在野牛种群中传播的非线性动态模型.在SIR模型中引入了环境中的布鲁氏菌对野牛的影响,并提出了一种SIRB模型.分别算出了该模型的无病平衡点P0和地方病平衡点P*,利用再生矩阵得到模型的阈值R0,证明了模型平衡点的稳定性由阈值的大小所决定,即R0<1时,通过构造合适的Lyapunov函数,证得无病平衡点全局渐近稳定.当R0>1时,利用几何方法,证得地方病平衡点全局渐近稳定.This paper studies the nonlinear dynamic model of Brucella infection in bison populations by horizontal and vertical transmission.Based on the SIR model,we considered the factors of brucellosis in the environment and proposed a new SIRB model.This paper calculates the disease-free equilibrium P0 and the endemic equilibrium P*of the model.Using the next generation matrix,we get the threshold R0 of the model.We proved that the stability of the equilibrium points is determined by the size of the reproduction number.When R0<1,by constructing a suitable Lyapunov function,we proved the globally asymptotic stability of the disease-free equilibrium.When R0>1,using the geometric method,we proved the globally asymptotic stability of the endemic equilibrium under certain condition.

关 键 词：垂直传染 布鲁氏病 李雅普诺夫函数 几何方法 

分 类 号：O175[理学—数学] S858.9[理学—基础数学]