  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.
