The probability that an emerging infectious disease will burn out
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Overview
Overview
abstract
If a new pathogen causes a large epidemic, 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. In a poster at EEID 2014 \cite{Earn+14}, we argued, primarily based on simulations, that persistence after a major epidemic is puzzling for most infectious diseases. Using a conceptually simple approach, we have now derived \cite{Pars+24} an accurate and easily computable formula for the burnout probability for the stochastic SIR epidemic model with vital dynamics (host births and deaths), and for the stochastic SIRS model (which includes decay of immunity). Our analysis shows that the burnout probability is always smaller for diseases with longer infectious periods or shorter durations of immunity, but is bimodal with respect to transmissibility ($\Rn$) unless infectious periods are atypically long. Our SIRS results imply that failing to prevent SARS-CoV-2 from taking off initially made it almost certain that it would persist. Persistence of other common, human infectious diseases cannot be explained by susceptible recruitment alone.
