In this paper, we explore the dynamics of tuberculosis (TB) epidemic model that includes the recruitment rate in both susceptible and infected population. Stability and sensitivity analysis of the classical TB model is carried out. Caputo-Fabrizio (CF) operator is then used to explain the dynamics of the TB model. The concept of fixed point theory is employed to obtain the existence and uniqueness of the solution of the TB model in the light of CF operator. Numerical simulations based on Homotopy Analysis Transform Method (HATM) and padé approximations are performed to obtain qualitative information on the model. Numerical solutions depict that the order of the fractional derivative has great dynamics of the TB model.

中文翻译：

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具有指数衰减律算子的结核病模型分析

在本文中，我们探索了结核病 (TB) 流行模型的动态，其中包括易感人群和感染人群的招募率。进行了经典 TB 模型的稳定性和敏感性分析。然后使用 Caputo-Fabrizio (CF) 算子来解释 TB 模型的动力学。根据CF算子，利用不动点理论的概念，得到TB模型解的存在唯一性。执行基于同伦分析变换方法 (HATM) 和 padé 近似的数值模拟，以获得模型的定性信息。数值解描述了分数阶导数的阶数对 TB 模型具有很大的动态性。