一类考虑接种的结核病模型的稳定性分析

Dynamics of a TB Model with Vaccination

摘要:  本文研究一类考虑接种的结核病模型解的稳定性，定义了模型的基本再生数。通过构造Lyapunov函数，证明了当时无病平衡点是全局稳定的；利用一致持续理论，证明了当时疾病将一直存在下去；也证明了在一定条件下唯一的地方平衡点是全局渐近稳定的。最后通过数值模拟比较了不同的接种情况对结核传播的影响。

Abstract:  We establish and study a TB model with vaccination. The basic reproduction number  is defined. It is proved that the disease-free equilibrium is globally asymptotically stable when  by Lyapunov function. The disease is uniformly persistent when  by using uniformly persistent theory. We also prove that the unique endemic equilibrium is globally asymptotically stable under certain conditions. Finally, we compare the influence of vaccination on the spread of tuberculosis by numerical simulations.