一类具有常数输入率的结核病模型稳定性分析

摘要

研究了一类具有接种仓室和潜伏仓室的结核病模型,得到了结核病灭绝与否的阈值——基本再生数R0,并运用Liapunov函数,中心流行理论、LaSalle不变集原理证明了当R0≤1时,此模型存在唯一的无病平衡点E0,且无病平衡点全局渐近稳定;当R0>1且无限接近于1时,地方病平衡点E﹡局部渐近稳定;当R0>1时,地方病平衡点E﹡全局渐近稳定.且用数值模拟进一步证明了无病平衡点和地方病平衡点稳定性.%A tuberculosis model with vaccination and latent chamber is studied, and the threshold of tuberculosis extinction was obtained.The existence and global stabilities of the disease-free equilibrium and the endemic equilibrium were proved by used the Liapunov function,the center manifold theory and LaSalle invariance principle.The stability of the dis-ease-free equilibrium and the endemic equilibrium point were further proved by numerical simulation.