布鲁氏菌病人-畜动力学建模及稳定性分析

Dynamics of Animal-human Epidemic Model of Brucellosis and Analysis of Its Stability

根据布鲁氏菌病传播的特点,建立了具有病菌传染项的人畜动力学模型。在该模型中,动物种群分为易感项、潜伏期项和感染项,人类则被分为高危人群和低危人群;感染个体主要是由染病的动物或者环境中的病菌传染。从理论上求出了系统的基本再生数,分析了各平衡点局部稳定性并且通过极限系统和构造适当的Lyapunov函数,证明了无病平衡点和惟一的正平衡点是全局渐近稳定的。

According to the characteristics of Brucellosis,a dynamic model with Brucella in environment was established. In this model,the animal population was divided into susceptible,latent,infected. Human was divided into high-risk group and low-risk group;Susceptible individuals can contract the disease in two ways： infected animals and Brucella in environment. The basic reproductive number was calculated theoretically, the local stability of each equilibrium point was analyzed, then through the limit system and constructing appropriate Lyapunov functions to prove that the disease-free equilibrium and the unique positive equilibrium was globally asymptotically stable.