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Stability analysis of pathogen-immune interaction dynamics

机译：病原体-免疫相互作用动力学的稳定性分析

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The paper considers models of dynamics of infectious disease in vivo from the standpoint of the mathematical analysis of stability. The models describe the interaction of the target cells, the pathogens, and the humoral immune response. The paper mainly focuses on the interior equilibrium, whose components are all positive. If the model ignores the absorption of the pathogens due to infection, the interior equilibrium is always asymptotically stable. On the other hand, if the model does consider it, the interior equilibrium can be unstable and a simple Hopf bifurcation can occur. A sufficient condition that the interior equilibrium is asymptotically stable is obtained. The condition explains that the interior equilibrium is asymptotically stable when experimental parameter values are used for the model. Moreover, the paper considers the models in which uninfected cells are involved in the immune response to pathogens, and are removed by the immune complexes. The effect of the involvement strongly affects the stability of the interior equilibria. The results are shown with the aid of symbolic calculation software.
机译：本文从稳定性的数学分析角度考虑了体内传染病动力学模型。这些模型描述了靶细胞，病原体和体液免疫反应的相互作用。本文主要关注内部平衡，内部平衡都是正的。如果模型忽略了由于感染引起的病原体吸收，则内部平衡总是渐近稳定的。另一方面，如果模型考虑了这一点，则内部平衡可能不稳定，并且可能发生简单的Hopf分叉。获得内部平衡渐近稳定的充分条件。该条件说明，当将实验参数值用于模型时，内部平衡是渐近稳定的。此外，本文考虑了未感染细胞参与对病原体的免疫反应并被免疫复合物去除的模型。参与的影响强烈影响内部平衡的稳定性。结果借助符号计算软件显示。

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