A mathematical view on head lice infestations
Noemi Castelletti, Maria Vittoria Barbarossa

TL;DR
This paper develops a mathematical model of head lice population dynamics to evaluate treatment strategies, emphasizing early detection, effective product application, and minimizing reinfection for better eradication.
Contribution
It introduces a novel age- and gender-structured PDE model for head lice, analyzing its properties and applying it to assess treatment effectiveness through simulations.
Findings
Early detection is crucial for eradication.
Dimeticone-based treatments are highly effective with regular application.
Synchronized treatments reduce reinfection risk.
Abstract
Commonly known as head lice, Pediculus humanus capitis are human ectoparasites which cause infestations 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…
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Taxonomy
TopicsDermatological diseases and infestations · Allergic Rhinitis and Sensitization · Zoonotic diseases and public health
