Dengue hemorrhagic fever (DHF) can occur in primary dengue virus infection of infants $$<1$$ < 1 year of age. To understand the presumed role of maternal dengue-specific antibodies received until birth in the development of this primary DHF in infants, we investigated a mathematical model based on a system of nonlinear ordinary differential equations that mimics cells, virus and antibodies interactions. The neutralization and enhancement activities of maternal antibodies against the virus are represented by a function derived from experimental data and knowledge from the medical literature. The analytic study of the model shows the existence of two equilibriums, a disease-free equilibrium and an endemic one. We performed the asymptotic stability analysis for these two equilibriums. The local asymptotic stability of the endemic equilibrium (DHF equilibrium) corresponds to the occurrence of DHF. Numerical results are also presented in order to illustrate the mathematical analysis performed, highlighting the most important parameters that drive model dynamics. We defined the age at which DHF occurs as the time when the infection takes off that means at the inflection point of the curve of infected cell population. We showed that this age corresponds to the one at which maximum enhancing activity for dengue infection appears. This critical time for the occurrence of DHF is calculated from the model to be approximately 2 months after the time for maternal dengue neutralizing antibodies to degrade below a protective level, which corresponds to what is observed in the experimental data from the literature.

中文翻译：

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母体被动免疫与婴儿登革出血热

登革出血热 (DHF) 可发生于 1 岁以下婴儿的原发性登革热病毒感染。为了了解在婴儿出生前接受的母体登革热特异性抗体在婴儿原发性 DHF 发展中的假定作用，我们研究了基于非线性常微分方程系统的数学模型，该系统模拟细胞、病毒和抗体相互作用。母体抗病毒抗体的中和和增强活性由源自实验数据和医学文献知识的函数表示。该模型的分析研究表明存在两种平衡，即无病平衡和地方病平衡。我们对这两个平衡进行了渐近稳定性分析。地方病平衡（DHF 平衡）的局部渐近稳定性对应于 DHF 的发生。还提供了数值结果以说明所执行的数学分析，突出显示驱动模型动力学的最重要参数。我们将 DHF 发生的年龄定义为感染开始的时间，即感染细胞群曲线的拐点。我们表明，这个年龄对应于出现登革热感染最大增强活性的年龄。DHF 发生的关键时间从模型计算为母体登革热中和抗体降解至保护水平以下的时间后大约 2 个月，这与文献中的实验数据中观察到的情况相对应。