Data from: Waiting time to infectious disease emergence

Emerging diseases must make a transition from stuttering chains of
transmission to sustained chains of transmission, but this critical
transition need not coincide with the system becoming supercritical. That
is, the introduction of infection to a supercritical system results in a
significant fraction of the population becoming infected only with a
certain probability. Understanding the waiting time to the first major
outbreak of an emerging disease is then more complicated than determining
when the system becomes supercritical. We treat emergence as a dynamic
bifurcation, and use the concept of bifurcation delay to understand the
time to emergence after a system becomes supercritical. Specifically, we
consider an SIR model with a time-varying transmission term and random
infections originating from outside the population. We derive an analytic
density function for the delay times and find it to be, in general, in
agreement with stochastic simulations. We find the key parameters to be
the rate of introduction of infection and the rate of change of the basic
reproductive ratio. These findings aid our understanding of real emergence
events, and can be incorporated into early-warning systems aimed at
forecasting disease risk.