Estimation in multitype epidemics
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1998 · Volume 60 · Issue 4
Abstract
A multitype epidemic model is analysed assuming proportionate mixing between types. Estimation procedures for the susceptibilities and infectivities are derived for three sets of data: complete data, meaning that the whole epidemic process is observed continuously; the removal processes are observed continuously; only the final state is observed. Under the assumption of a major outbreak in a population of sizenit is shown that, for all three data sets, the susceptibility estimators are always efficient, i.e. consistent with a √nrate of convergence. The infectivity estimators are ‘in most cases’ respectively efficient, efficient and unidentifiable. However, if some susceptibilities are equal then the corresponding infectivity estimators are respectively barely consistent (√log(n) rate of convergence),notconsistent and unidentifiable. The estimators are applied to simulated data.
Keywords
Consistent estimator, Counting processes, Estimating equations, Martingales, Multitype epidemics, Susceptibility and infectivity
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