Abstract In this paper, we developed a novel deterministic coupled model tying together the effects of within-host and population level dynamics on malaria transmission dynamics. We develop within-host and within-vector dynamic models, population level between-hosts models, and a nested coupled model combining these levels. The unique feature of this work is the way the coupling and feedback for the model use the various life stages of the malaria parasite both in the human host and the mosquito vector. Analysis of the coupled and the within-human host models indicate the existence of locally asymptotically stable infection- and parasite-free equilibria when the associated reproduction numbers are less than one. The population-level model, on the other hand, exhibits backward bifurcation, where the stable disease-free equilibrium co-exists with a stable endemic equilibrium. A global sensitivity analysis was carried out to measure the effects of the sensitivity and uncertainty in the various model parameters estimates. The results indicate that the most important parameters driving the pathogen level within an infected human are the production rate of the red blood cells from the bone marrow, the infection rate, the immunogenicity of the infected red blood cells, merozoites and gametocytes, and the immunosensitivity of the merozoites and gametocytes. The key parameters identified at the population level are the human recovery rate, the death rate of the mosquitoes, the recruitment rate of susceptible humans into the population, the mosquito biting rate, the transmission probabilities per contact in mosquitoes and in humans, and the parasite production and clearance rates in the mosquitoes. Defining the feedback functions as a linear function of the mosquito biting rate, numerical exploration of the coupled model reveals oscillations in the parasite populations within a human host in the presence of the host immune response. These oscillations dampen as the mosquito biting rate increases. We also observed that the oscillation and damping effect seen in the within-human host dynamics fed back into the population level dynamics; this in turn amplifies the oscillations in the parasite population within the mosquito-host.

中文翻译：

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宿主内和宿主间疟疾模型的传播动力学

摘要 在本文中，我们开发了一种新的确定性耦合模型，将宿主内和种群水平动态对疟疾传播动态的影响联系在一起。我们开发了宿主内和向量内的动态模型、宿主间的种群水平模型以及结合这些水平的嵌套耦合模型。这项工作的独特之处在于模型的耦合和反馈使用疟疾寄生虫在人类宿主和蚊子载体中的各个生命阶段的方式。对耦合和人体内宿主模型的分析表明，当相关的繁殖数小于 1 时，存在局部渐近稳定的无感染和无寄生虫平衡。另一方面，人口级别的模型表现出向后分叉，其中稳定的无病平衡与稳定的地方病平衡共存。进行了全局敏感性分析以测量各种模型参数估计中的敏感性和不确定性的影响。结果表明，驱动受感染人体内病原体水平的最重要参数是骨髓中红细胞的产生率、感染率、受感染红细胞、裂殖子和配子细胞的免疫原性以及免疫敏感性裂殖子和配子体。在人口层面确定的关键参数是人类康复率、蚊子的死亡率、易感人群进入人群的招募率、蚊虫叮咬率、蚊子和人类每次接触的传播概率，以及蚊子中寄生虫的产生和清除率。将反馈函数定义为蚊子叮咬率的线性函数，耦合模型的数值探索揭示了在存在宿主免疫反应的情况下人类宿主体内寄生虫种群的振荡。随着蚊虫叮咬率的增加，这些振荡会减弱。我们还观察到，在人类宿主动态中看到的振荡和阻尼效应反馈到种群水平动态中；这反过来又放大了蚊子宿主体内寄生虫种群的波动。耦合模型的数值探索揭示了在存在宿主免疫反应的情况下人类宿主内寄生虫种群的振荡。随着蚊虫叮咬率的增加，这些振荡会减弱。我们还观察到，在人类宿主动态中看到的振荡和阻尼效应反馈到种群水平动态中；这反过来又放大了蚊子宿主体内寄生虫种群的波动。耦合模型的数值探索揭示了在存在宿主免疫反应的情况下人类宿主内寄生虫种群的振荡。随着蚊虫叮咬率的增加，这些振荡会减弱。我们还观察到，在人类宿主动态中看到的振荡和阻尼效应反馈到种群水平动态中；这反过来又放大了蚊子宿主体内寄生虫种群的波动。