A within-human-host malaria parasite model, integrating key variables that influence parasite evolution-progression-advancement, under innate and adaptive immune responses, is analyzed. The implicit role of immunity on the steady state parasite loads and parasitemia reproduction number ([Formula: see text]), a threshold parameter measuring the parasite’s annexing ability of healthy red blood cells (HRBCs), eventually rendering a human infectious to mosquitoes, is investigated. The impact of the type of recruitment function used to model HRBC growth is also investigated. The model steady states and [Formula: see text], both obtained as functions of immune system variables, are analyzed at snapshots of immune sizes. Model results indicate that the more the immune cells, innate and adaptive, the more efficient they are at inhibiting parasite development and progression; consequently, the less severe the malaria disease in a patient. Our analysis also illustrates the existence of a Hopf bifurcation leading to a limit cycle, observable only for the nonlinear recruitment functions, at reasonably large [Formula: see text].

中文翻译：

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先天和适应性免疫反应对人体内恶性疟原虫寄生虫水平的隐含作用的数学研究

分析了在先天和适应性免疫反应下，整合了影响寄生虫进化 - 进展 - 进展的关键变量的人类宿主内疟疾寄生虫模型。免疫对稳态寄生虫负荷和寄生虫血症繁殖数的隐含作用（[公式：见正文]）是衡量寄生虫对健康红细胞 (HRBC) 的附着能力的阈值参数，最终使人类感染蚊子，是进行了调查。还研究了用于模拟 HRBC 增长的招聘功能类型的影响。模型稳态和[公式：见正文]，都是作为免疫系统变量的函数获得的，在免疫大小的快照上进行分析。模型结果表明，免疫细胞越多，先天性和适应性，它们在抑制寄生虫发育和进展方面的效率越高；因此，患者的疟疾疾病越轻。我们的分析还说明了存在导致极限环的 Hopf 分岔，仅在非线性招募函数中可观察到，并且相当大 [公式：见正文]。