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Keywords:

  • Basic reproduction number;
  • Consistency;
  • Final size data;
  • Multitype epidemic;
  • Vaccination coverage;
  • Vaccine efficacy

A stochastic multitype model for the spread of an infectious disease in a community of heterogeneous individuals is analysed. In particular, estimates of R0 (the basic reproduction number) and the critical vaccination coverage are derived, where estimation is based on final size data of an outbreak in the community. It is shown that these key parameters cannot be estimated consistently from data; only upper and lower bounds can be estimated. Confidence regions for the upper bounds are derived, thus giving conservative estimates of R0 and the fractions necessary to vaccinate.