A mathematical view on head lice infestations

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 headlice 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 hyper-bolic 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  non negativity  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.