We present a stochastic model for the spread of small-pox after a small number of index cases are introduced intoa susceptible population. The model describes a branchingprocess for the spread of the infection and the effects ofintervention measures. We discuss scenarios in which ringvaccination of direct contacts of infected persons is suffi-cient to contain an epidemic. Ring vaccination can be suc-cessful if infectious cases are rapidly diagnosed. However,because of the inherent stochastic nature of epidemic out-breaks, both the size and duration of contained outbreaksare highly variable. Intervention requirements depend onthe basic reproduction number (R0), for which different esti-mates exist. When faced with the decision of whether to relyon ring vaccination, the public health community should beaware that an epidemic might take time to subside even foran eventually successful intervention strategy
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