Department of Mathematics, University of Buea, P.O. Box 63, Buea, Cameroon.
African Institute for the Mathematical Sciences (AIMS) Cameroon, Limbe, Cameroon.
Bull Math Biol. 2019 Nov;81(11):4564-4619. doi: 10.1007/s11538-018-0436-0. Epub 2018 May 24.
A model is developed and used to study within-human malaria parasite dynamics. The model integrates actors involved in the development-progression of parasitemia, gametocytogenesis and mechanisms for immune response activation. Model analyses under immune suppression reveal different dynamical behaviours for different healthy red blood cell (HRBC) generation functions. Existence of a threshold parameter determines conditions for HRBCs depletion. Oscillatory dynamics reminiscent of malaria parasitemia are obtained. A dependence exists on the type of recruitment function used to generate HRBCs, with complexities observed for a more nonlinear function. An upper bound that delimits the size of feasible parasitized steady-state solution exists for a logistic function but not a constant function. The upper bound is completely characterized and is affected by parameters associated with HRBCs recruitment, parasitized red blood cells generation and the release and time-to-release of free merozoites. A stable density size for mature gametocytes, the bridge to invertebrate hosts, is derived.
建立并使用了一个模型来研究人体内疟原虫动力学。该模型整合了参与疟原虫发育-进展、配子体发生和免疫反应激活机制的因素。在免疫抑制下的模型分析揭示了不同健康红细胞（HRBC）生成功能的不同动力学行为。存在一个阈值参数决定了 HRBC 耗竭的条件。获得了类似于疟疾寄生虫血症的振荡动力学。对用于生成 HRBC 的招募功能的类型存在依赖性，对于更非线性的功能观察到了复杂性。对于逻辑函数存在上限，上限限定了可行的寄生稳定状态解的大小，但对于常数函数则不存在。上限完全被特征化，并且受到与 HRBC 招募、寄生性红细胞生成以及游离裂殖子的释放和释放时间相关的参数的影响。衍生出了成熟配子体的稳定密度大小，这是通向无脊椎动物宿主的桥梁。
