The distribution of time to extinction in subcritical branching processes: applications to outbreaks of infectious disease

Abstract

We consider the distribution of the number of generations to extinction in subcritical branching processes, with particular emphasis on applications to the spread of infectious diseases. We derive the generation distributions for processes with Bernoulli, geometric and Poisson offspring, and discuss some of their distributional and inferential properties. We present applications to the spread of infection in highly vaccinated populations, outbreaks of enteric fever, and person-to-person transmission of human monkeypox.