An epidemic may exhibit a “boom then bust” on its initial outbreak. The number of infected individuals reaches a high first peak, and then falls to a low first trough as individuals recover and become immune. During this first trough the infection may fade out completely (“epidemic fade-out”), or rise again to an endemic level due to the gradual influx of new susceptible individuals.
We consider the probability of epidemic fade-out in the Markovian “SIR with demography” model. An exact calculation is computationally intensive, while previously published (“Fokker-Planck” and “WKB”) approximations are not always accurate. We propose an efficient computation method, using an approximation of the exact model. This gives only a small error, and is fast enough to be practical even for large population sizes.