Estimation in Multitype Epidemics

Abstract

Summary 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 size n it is shown that, for all three data sets, the susceptibility estimators are always efficient, i.e. consistent with a √n rate 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), not consistent and unidentifiable. The estimators are applied to simulated data.