LAUSR

Significance If a new pathogen causes a large epidemic, then it might “burn out” before causing a second epidemic. The burnout probability can be estimated from large numbers of computationally intensive simulations, but an easily computable formula for the burnout probability has never been found. Using a conceptually simple approach, we derive such a formula for the standard SIR epidemic model with vital dynamics (host births and deaths). With this formula, we show that the burnout probability is always smaller for diseases with longer infectious periods, but is bimodal with respect to transmissibility (the basic reproduction number). Our analysis shows that the persistence of typical human infectious diseases cannot be explained by births of new susceptibles, clarifying an important epidemiological puzzle.