A mathematical view on head lice infestations

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 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.