基于Holling II型功能反应的疟原虫感染动力学建模与稳定性分析

Dynamic Modeling and Stability Analysis of Plasmodium Infection Based on Holling Type II Functional Response

摘要: 疟疾是由按蚊传播的典型媒介传染病，一直以来是全球公共卫生领域的重大挑战。本文基于生物数学建模理论，构建了带有Holling第II型功能反应函数模型，描述红细胞–染虫红细胞–免疫效应(NETs)三者的动力学行为。我们定性分析了当$R_0\le 1$ 时，无病平衡点$E_0$ 全局渐近稳定；当$\text{1}<R_0<1+\frac{\eta }{\sigma }\left(\alpha +\frac{\beta }{d}\right)$ 时，边界平衡点$E_1$ 局部渐近稳定；当$R_{\text{0}}>1+\frac{\eta }{\sigma }\left(\alpha +\frac{\beta }{d}\right)$ 时，正平衡点$E^{\ast }$ 局部渐近稳定。本文研究在一定程度上为疟疾防控提供理论支持和实践指导。

Abstract: Malaria, a vector-borne disease transmitted by Anopheles mosquitoes, remains a major global public health concern. Based on the theory of biomathematical modeling, in this study, we develop a dynamic model incorporating Holling type II functional response to characterize interactions among erythrocytes, malaria-infected erythrocytes, and neutrophil extracellular traps (NETs) as immune effectors. We qualitatively analyzed that when $R_0\le 1$ , the disease-free equilibrium point $E_0$ is globally asymptotically stable; when $\text{1}<R_0<1+\frac{\eta }{\sigma }\left(\alpha +\frac{\beta }{d}\right)$ , the boundary equilibrium point $E_1$ is locally asymptotically stable; when $R_{\text{0}}>1+\frac{\eta }{\sigma }\left(\alpha +\frac{\beta }{d}\right)$ , the positive equilibrium point $E^{\ast }$ is locally asymptotically stable. This study aims to provide theoretical support and practical guidance for malaria control.