Tuberculosis infection is still a major threat to humans and it may progress slowly or rapidly to clearance, latent infection, or active disease. In this paper, considering T cells can perform acceleration effect on their own recruitment, an in-host model of Mycobacterium tuberculosis is studied. Focus type and elliptic type of nilpotent singularities of codimension 3 are analyzed in this four dimensional model. Complex dynamical behaviors such as homoclinic loop, saddle-node bifurcation of limit cycle and co-existence of two limit cycles are revealed by bifurcation analysis. Especially, the slow-fast periodic solution with large-amplitude or small-amplitude is observed in numerical simulations, which provides a perfect explanation for the reactivation of latent infection.

中文翻译：

---

宿主内结核分枝杆菌模型的分叉分析

结核感染仍然是对人类的主要威胁，它可能缓慢或迅速发展为清除，潜伏感染或活动性疾病。在本文中，考虑到T细胞可以在自身募集过程中发挥加速作用，研究了结核分枝杆菌的宿主模型。在此四维模型中分析了余维3的幂型奇点的焦点类型和椭圆类型。通过分叉分析揭示了复杂的动力学行为，例如同宿环，极限环的鞍节点分叉和两个极限环的共存。特别是，在数值模拟中观察到了大振幅或小振幅的慢速周期解，这为潜伏感染的重新激活提供了一个完美的解释。