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Coronavirus: the importance of stopping the upwards curve

Last week I wanted to check my 13-year-old daughter understood the concept of exponential growth, where numbers increase at an ever-faster rate. I asked her to continue the sequence 1, 2, 4, 8…  She gave me a huge eye roll and rattled it off, just as she would have done at half her age. But when I stopped her at 128 and explained what this means for coronavirus, that was new.  For every one person who catches the virus today, around 128 additional people will become infected on a day 2-3 weeks from now as a result. 

2, 4, 8, 16, 32 and 64 additional people are also infected along this chain, plus the original one. In total, this means 255 new cases.  2-3 of them will die.  But this is not inevitable: all could have been prevented by stopping that first infection.  Here is the process in action in the UK producing that familiar upwards curve.

Fig 1

This is why social distancing matters – to break the expanding chain of transmission. Breaking it today is twice as effective as breaking it in 2-3 days’ time and 8x as effective as breaking it next week. As of today (18th March, 2020) your own risk of becoming infected on a night out, or a day in the office, is still quite low. But if 500-1000 people go out, one or two of them will become that first person in a new chain of infections. Don’t be that person! As a society, we can only stop the exponential growth of coronavirus by staying in, keeping a 2-metre distance from others and washing hands and surfaces frequently.

It is not just new cases that rise exponentially. So do the number of patients requiring intensive care and those who die. This is why social distancing is so urgent. Unfortunately, overwhelm of the NHS already appears unavoidable, but for every 2-3 days we wait before stricter distancing, the level of overwhelm doubles again. Wait another week and the NHS becomes overwhelmed 8x over. No healthcare system in the world can cope with that.

The risk of becoming infected also keeps doubling. Government estimates of UK cases is currently around 1/1000. By this time next week that will be 1/125. A week later it approaches 1/15 (or probably slightly lower as the virus starts to encounter more people who had it before). This is no longer ‘someone else’s problem’. We are all at risk of infection, and if we want any other healthcare available for ourselves or relatives, we have to keep our distance right now.

Fig 2

To finish, here is some better news. Lockdown in Italy appears to have stalled the exponential growth of new cases there. For four days there has been very little change. An upwards blip remains possible but most likely these numbers will soon start falling, and 1-2 weeks later so will death rates, just as they did in China and South Korea. This may not be the end of the story entirely, but it does mean a return to some kind of normality is on the horizon while a vaccine is developed or another solution found. Without it, there is no return to normality until after at least a year and many, many more deaths.

The Coleman lab urges all readers of this blog to contribute to the worldwide effort to stop the exponential rise of COVID-19. Distance yourself today and spread the word, not the virus!

Fig 3

Please send your friends, family and colleagues the link to this article and please leave questions or comments.

Michael Coleman
Michael Coleman says:
Mar 19, 2020 07:42 AM

Update 19th March. New cases in Italy are up today but the recent rate of growth there is still far below exponential. This may be one of the ‘blips’ referred to above. Better news from China, however with zero new cases from within the country. A phenomenal achievement. This still leaves the question of how to prevent new outbreaks but buys some time to work that out and coordinate with other countries.

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