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Stochastic models for head lice infections

Stone, P.M.; (2010) Stochastic models for head lice infections. Doctoral thesis, UCL (University College London).

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Abstract

Outbreaks of head lice are a persistent problem in schools in the UK and elsewhere, and it is widely reported that the prevalence of head lice infections is increasing, especially since the 1990s. Research has largely focused on clinical trials of insecticidal treatments. Our research aims to construct stochastic models for the infection process that allow the investigation of typical properties of outbreaks of infection, and that might assist in examining the effectiveness of alternative strategies in controlling the spread of infection. We investigate the dynamics of head lice infections in schools, by considering models for endemic infection based on a stochastic SIS (susceptible-infected-susceptible) epidemic model. Firstly we consider the SIS model with the addition of an external source of infection, and deduce a range of properties of the model relating to a single outbreak of infection. We use the stationary distribution of the number of infected individuals, in conjunction with data from a recent study carried out in Welsh schools on the prevalence of head lice infections, to obtain estimates of the model parameters and thus to arrive at numerical estimates for various quantities of interest, such as the mean length of an outbreak. Secondly, we consider the structured nature of the school population, namely its division into classes, and examine the effect of this population structure on the various properties of an outbreak of head lice infection. Estimation of the parameters in a structured model presents certain challenges, due to the complexity of the model and the potentially enormous number of states in the Markov chain. We examine the feasibility of finding reasonable estimates for the parameters in the full structured model (for example, that of a population of seven classes within a school), by considering simpler versions which utilise only subsets or pooled versions of the data.

Type:Thesis (Doctoral)
Title:Stochastic models for head lice infections
Language:English
Additional information:Authorisation for digitisation not received
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science

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