Castelletti Noemi, Barbarossa Maria Vittoria
Institute of Radiation Medicine, Helmholtz Zentrum München, Ingolstädter Landstraße 1, D-85764, Neuherberg, Germany.
Institute of Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany.
Infect Dis Model. 2020 Jun 9;5:386-404. doi: 10.1016/j.idm.2020.05.002. eCollection 2020.
are human ectoparasites which cause infestations, mostly in children, worldwide. Understanding the life cycle of head lice is an important step in knowing how to treat lice infestations, as the parasite behavior depends considerably on its age and gender. In this work we propose a mathematical model for head lice population dynamics in hosts who could be or not quarantined and treated. Considering a lice population structured by age and gender we formulate the model as a system of hyperbolic PDEs, which can be reduced to compartmental systems of delay or ordinary differential equations. Besides studying fundamental properties of the model, such as existence, uniqueness and nonnegativity of solutions, we show the existence of (in certain cases multiple) equilibria at which the infestation persists on the host's head. Aiming to assess the performance of treatments against head lice infestations, by mean of computer experiments and numerical simulations we investigate four possible treatment strategies. Our main results can be summarized as follows: (i) early detection is crucial for quick and efficient eradication of lice infestations; (ii) dimeticone-based products applied every 4 days effectively remove lice in at most three applications even in case of severe infestations and (iii) minimization of the reinfection risk, e.g. by mean of synchronized treatments in families/classrooms is recommended.
头虱是一种人类体表寄生虫，在全球范围内导致感染，主要发生在儿童身上。了解头虱的生命周期是掌握如何治疗头虱感染的重要一步，因为寄生虫的行为在很大程度上取决于其年龄和性别。在这项工作中，我们提出了一个数学模型，用于研究宿主（可能被隔离或治疗，也可能未被隔离或治疗）头上头虱种群的动态变化。考虑到按年龄和性别结构化的头虱种群，我们将该模型表述为一个双曲型偏微分方程组，该方程组可以简化为延迟或常微分方程的 compartmental 系统。除了研究模型的基本性质，如解的存在性、唯一性和非负性外，我们还展示了（在某些情况下存在多个）平衡点的存在，在这些平衡点处，感染会在宿主头上持续存在。为了评估治疗头虱感染的效果，我们通过计算机实验和数值模拟研究了四种可能的治疗策略。我们的主要结果可以总结如下：（i）早期检测对于快速有效地根除头虱感染至关重要；（ii）即使在严重感染的情况下，每 4 天使用一次基于二甲硅油的产品，最多三次应用就能有效去除头虱；（iii）建议将再感染风险降至最低，例如通过在家庭/教室中同步治疗的方式。
