Speed and strength of an epidemic intervention

Jonathan Dushoff; Sang Woo Park

Here, we show that r can also serve as a threshold, and also provide a useful metric for difficulty of elimination. We first generalize the idea that R measures the difficulty of elimination by showing we can measure an intervention's "strength" on the same scale as the reproductive number. We then show that we can likewise measure an intervention's "speed", and that there is a duality between the threshold R = 1 and a corresponding minimal intervention strength required for elimination, and the threshold r = 0 and a corresponding minimal intervention speed. We argue that the historical primacy of R over r is partly artificial, and discuss cases where strength provides the better framing for practical disease questions and cases where speed does.