In this paper, we investigate the influence of the effector-regulatory (Teff-Treg) T cell interaction on the T-cell-mediated autoimmune disease dynamics. The simple 3-dimensional Teff-Treg model is derived from the two-step model reduction of an established 5-dimensional model. The reduced 4- and 3-dimensional models preserve the dynamical behaviors in the original 5-dimensional model, which represents the chronic and relapse-remitting autoimmune symptoms. Moreover, we find three co-existing limit cycles in the reduced 3-dimensional model, in which two stable periodic solutions enclose an unstable one. The existence of multiple limit cycles provides a new mechanism to explain varying oscillating amplitudes of lesion grade in multiple sclerosis. The complex multiphase symptom could be caused by a noise-driven Teff population traveling between two coexisting stable periodic solutions. The simulated phase portrait and time history of coexisting limit cycles are given correspondingly.

在本文中，我们研究了效应调节（Teff-Treg）T细胞相互作用对T细胞介导的自身免疫疾病动力学的影响。简单的3维Teff-Treg模型是从建立的5维模型的两步模型简化中得出的。简化的4维和3维模型保留了原始5维模型中的动力学行为，这代表了慢性和复发性缓解自身免疫症状。此外，我们在简化的3维模型中发现了三个共存的极限环，其中两个稳定的周期解包含了一个不稳定的周期。多个极限循环的存在提供了一种新的机制来解释多发性硬化症中病变等级的不同振荡幅度。复杂的多相症状可能是由噪声驱动的Teff种群在两个并存的稳定周期解之间传播引起的。相应地给出了模拟的相像和共存极限周期的时间历程。