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The dangers of allowing exponential growth

BMJ 2021; 374 doi: (Published 15 July 2021) Cite this as: BMJ 2021;374:n1770
  1. Kit Yates, senior lecturer
  1. Department for Mathematical Sciences, University of Bath, UK
  1. c.yates{at}
    Follow Kit Yates on Twitter @Kit_yates_maths

Why exponential growth is relevant to epidemics

Although the concept of exponential growth is not new to the public consciousness, a lot of misconceptions surround the idea. Exponential is often incorrectly used as a byword for rapid or large. It doesn’t have to be either of those. In fact, this is what’s so deceptive about exponential growth—when it first starts it doesn’t look fast at all.

When the delta variant of covid-19 first arrived in the UK, its week-on-week rise was small. On 20 March 2021, just two cases were sequenced by the covid-19 genomic consortium (COG-UK).1 A week later it was 18—still small numbers, seemingly nothing to worry about. The next week it had jumped to 60 and the week after to 186, and then to 369. By 1 May COG-UK sequenced 735 cases of the delta variant, accounting for 12% of all sequenced cases. Although these were a fraction of the cases spreading in the community, the trend was clear. Sequenced cases were doubling every week. By that point it was too late to stop its spread. The delta variant now comprises 99% of all …

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