Journal of Mathematical Biology

, Volume 56, Issue 6, pp 743–763

A stochastic model for head lice infections

  • Patricia Stone
  • Hilde Wilkinson-Herbots
  • Valerie Isham
Article

Abstract

We investigate the dynamics of head lice infections in schools, by consideringa model for endemic infection based on a stochastic SIS (susceptible-infected-susceptible) epidemic model, with the addition of an external source of infection. We deduce a range of properties of our model, including the length of 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, and employ maximum likelihood methods to obtain estimates of the model parameters. A complication is that, for each school, only a sample of the pupils was checked for infection. Our likelihood function takes account of the missing data by incorporating a hypergeometric sampling element. We arrive at estimates of the ratios of the “within school” and “external source” transmission rates to the recovery rate and use these to obtain estimates for various quantities of interest.

Keywords

Head lice Epidemic Stochastic SIS model Transmission dynamics 

Mathematics Subject Classification (2000)

62M05 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Patricia Stone
    • 1
  • Hilde Wilkinson-Herbots
    • 1
  • Valerie Isham
    • 1
  1. 1.Department of Statistical ScienceUniversity College LondonLondonUK

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