The Final Size of Multitype Chain-Binomial Epidemic Processes

Doctoral thesis, 1995

A multitype chain-binomial epidemic process is defined for a closed finite population by sampling a simple multidimensional counting process at certain points. The final size of the epidemic is then characterised, given the counting process, as the smallest root of a non-linear system of equations. Finally, by letting the population grow, this characterisation is used, in combination with a weak convergence result for the counting process, to derive the asymptotic distribution of the final size. This is first done for processes with an irreducible contact structure both when the initial infection increases at the same rate as the population size and when it stays fixed. Then the asymptotic description of the latter fixed size initiated epidemics are extended to epidemics with reducible contact structures and almost reducible structures, where certain infection intensities tend to zero at suitable rates. The asymptotic behaviour is derived by using properties of approximating branching processes and normal distributions. AMS 1991 subject classification: 60J99, 60K40, 60J80, 92D30