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Assessing the Impact of Intervention Delays on Stochastic Epidemics

Author

Listed:
  • Simon Edward Frank Spencer

    (University of Nottingham)

  • Philip D. O’Neill

    (University of Nottingham)

Abstract

A stochastic model of disease transmission among a population partitioned into groups is defined. The model is of SEIR (Susceptible-Exposed-Infective-Removed) type and features intervention in response to the progress of the disease, and moreover includes a random delay before the intervention occurs. A threshold parameter for the model, which can be used to assess the efficacy of the intervention, is defined. The threshold parameter can be calculated either in closed form or via recursion, for a number of different choices of exposed, infectious and delay period distributions, both for the epidemic model itself and also a large-group approximation. In particular both constant and Erlang-distributed delay periods are considered. Sufficient conditions under which a constant delay gives the least effective intervention are presented. For a given mean delay, it is shown that the two-point delay distribution provides the optimal intervention.

Suggested Citation

  • Simon Edward Frank Spencer & Philip D. O’Neill, 2013. "Assessing the Impact of Intervention Delays on Stochastic Epidemics," Methodology and Computing in Applied Probability, Springer, vol. 15(4), pages 803-820, December.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:4:d:10.1007_s11009-012-9278-7
    DOI: 10.1007/s11009-012-9278-7
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    References listed on IDEAS

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    1. Michael J. Tildesley & Nicholas J. Savill & Darren J. Shaw & Rob Deardon & Stephen P. Brooks & Mark E. J. Woolhouse & Bryan T. Grenfell & Matt J. Keeling, 2006. "Optimal reactive vaccination strategies for a foot-and-mouth outbreak in the UK," Nature, Nature, vol. 440(7080), pages 83-86, March.
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