An exact method for quantifying the reliability of end-of-epidemic declarations in real time

We derive and validate a novel and analytic method for estimating the probability that an epidemic has been eliminated (i.e. that no future local cases will emerge) in real time. When this probability crosses 0.95 an outbreak can be declared over with 95% confidence. Our method is easy to compute, only requires knowledge of the incidence curve and the serial interval distribution, and evaluates the statistical lifetime of the outbreak of interest. Using this approach, we show how the time-varying under-reporting of infected cases will artificially inflate the inferred probability of elimination, leading to premature (false-positive) end-of-epidemic declarations. Contrastingly, we prove that incorrectly identifying imported cases as local will deceptively decrease this probability, resulting in delayed (false-negative) declarations. Failing to sustain intensive surveillance during the later phases of an epidemic can therefore substantially mislead policymakers on when it is safe to remove travel bans or relax quarantine and social distancing advisories. World Health Organisation guidelines recommend fixed (though disease-specific) waiting times for end-of-epidemic declarations that cannot accommodate these variations. Consequently, there is an unequivocal need for more active and specialised metrics for reliably identifying the conclusion of an epidemic.Author summary: Deciding on when to declare an infectious disease epidemic over is an important and non-trivial problem. Early declarations can mean that interventions such as lockdowns, social distancing advisories and travel bans are relaxed prematurely, elevating the risk of additional waves of the disease. Late declarations can unnecessarily delay the re-opening of key economic sectors, for example trade, tourism and agriculture, potentially resulting in significant financial and livelihood losses. Here we develop and test a novel and exact data-driven method for optimising the timing of end-of-epidemic declarations. Our approach converts observations of infected cases up to any given time into a prediction of the likelihood that the epidemic is over at that time. Using this method, we quantify the reliability of end-of-epidemic declarations in real time, under ideal case surveillance, showing that it can depend strongly on past infection numbers. We then prove that failing to compensate for practical issues such as the time-varying under-reporting and importing of cases necessarily results in premature and delayed declarations, respectively. These variations and biases cannot be accommodated by current worldwide declaration guidelines. Sustained and intensive surveillance coupled with more adaptive declaration metrics are vital if informed end-of-epidemic declarations are to be made.