一类具有双重免疫清除策略的疟原虫红细胞内期模型动力学分析

Dynamics Analysis of a Class of Models for the Erythrocytic Stage of Plasmodium with Dual Immune Clearance Strategies

摘要: 为探究疟原虫红细胞内期健康红细胞、感染红细胞与免疫效应因子NETs之间的相互作用机制，本文基于免疫清除的双重策略，建立了一类常微分方程动力学模型。模型的核心创新在于耦合了两种截然不同的免疫清除途径：其一，针对感染红细胞，引入Holling II型功能反应函数以刻画免疫效应因子的饱和清除作用；其二，针对健康红细胞，采用线性项以刻画NETs非特异性免疫损伤导致的病理消耗。首先证明了解的非负性和有界性；其次得到了基本再生数，无病平衡点稳定的条件，以及边界平衡点和正平衡点存在且稳定的条件；最后，通过数值模拟验证了所得结论。

Abstract: To explore the interaction mechanisms among healthy red blood cells, infected red blood cells, and the immune effector NETs during the erythrocytic stage of Plasmodium, this paper establishes a class of ordinary differential equation models based on a dual immune clearance strategy. The core innovation of the model lies in the coupling of two distinct immune clearance pathways: on the one hand, a Holling type II functional response is introduced to characterize the saturable clearance of infected red blood cells by immune effectors; on the other hand, a linear term is employed to describe the pathological consumption of healthy red blood cells resulting from nonspecific immune damage induced by NETs. First, the non-negativity and boundedness of the solutions are proved. Second, the basic reproduction number is derived, and the stability conditions for the disease‑free equilibrium, as well as the existence and stability conditions for both the boundary equilibrium and the positive (endemic) equilibrium, are obtained. Finally, numerical simulations are performed to verify the theoretical results.