考虑一般发生率的结核病模型的稳定性分析

Stability Analysis of a Tuberculosis Transmission Model with General Incidence

建立了一个考虑带有一般发生率、离散时滞和疾病复发的肺结核传播的动力学模型.证明了解的正性和有界性,得到了基本再生数R_0.通过构造合适的Lyapunov泛函,得到当R_0≤1时,无病平衡点是全局渐近稳定的;当R_0>1时,存在唯一的地方性平衡点,同时它也是全局渐近稳定的.

In this paper, a tuberculosis transmission model concerning the general incidences, discrete time delay and disease relapse is studied. We prove the positivity and boundedness of the solutions and obtain the basic reproduction number R0. Using the method of Lyapunov functions, we obtain that when R0≤1, the disease-free equilibrium is globally asymptotically stable; and when R0 〉 1, there exists a unique endemic equilibrium, which is globally asymptotically stable under certain conditions.