Keeping R0 below 1 can rid us of the virus. Eventually.

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While most of the world is seeing a slow and gradual decline in coronavirus cases, two countries in particular seem to be getting close to defeating it altogether. Iceland has reported no deaths from the disease in over a week and a half, with three days in the past week where no new cases were confirmed at all. Meanwhile, New Zealand has recorded only two such deaths in the past week, as the number of daily confirmed cases stays, for the most part, in the low single-figures.

It all comes down to that important number we’ve been hearing about a lot in recent weeks: R0. It’s the measure of how many people, on average, get infected as the result of a single infected person. An R0 of 1 means that the number of active infections goes neither up nor down. Above one, and the virus spreads out of control. Below one, and the virus slows down and eventually dies.

Of course, where “eventually” lives is a function of exactly where R0 is. In the UK, it is believed that R0 is currently somewhere between 0.6 and 0.9, as a result of the restrictions put in place nearly six weeks ago, and is most likely to be near the middle of that range.

Based on the antibody testing done in New York last week, and some calculations done on the back of an envelope, there were possibly around 75,000 new infections per day in the UK around three weeks ago. It’s worth stressing, though, that this is an educated guess, and we don’t know the true figure, but let’s use that as a starting point for our analysis. We also know that the generation interval for the virus is around five days.

If the R0 has been at a consistent 0.75, which is the midpoint of the estimated range, it would suggest that the rate of infections has reduced by nearly two thirds over the last three weeks, to around 25,000 infections a day. But while 0.6–0.9 may not look like a large range, the cumulative effect can become very large indeed: an R0 of 0.6 would have seen the rate of infections drop by nearly 87% over three weeks to just under 10,000 a day, while an R0 of 0.9 would have seen the rate of infections drop by only around a third over that same period, to 50,000 a day.

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If this R0 value stays constant for the remaining lifespan of this pandemic, how long would it take to be rid of the virus entirely (by this, my threshold is fewer than one case in two weeks)? If the R0 is in the middle of the range at 0.75, the virus would be wiped out from the UK just in time for Christmas. If it stays at the bottom of the range at 0.6, then it would be wiped out around the end of the summer. If it stays at the top of the range at 0.9, then it won’t be wiped out until January 2022. Of course, the R0 will never be constant, and it’s hard to say whether it can remain at or near that level in the latter stages of the pandemic, especially given that a large number of cases show mild or no symptoms.

That all being said, it’s going to be difficult to imagine the UK population willing to stay in lockdown for that long, even on the shorter end of that range. While the vaccine will be critical to sharply bringing R0 down, that is not going to be plausible for at least several months. Contact tracing, which is expected to begin later this month, should be able to bring R0 down, allowing certain restrictions on our usual liberties to be lifted. But if R0 is allowed to even get close to 1, small changes in our way of life could result in the epidemic lasting for months longer than it would otherwise.

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I am Joe. I am a techy at heart, a self-taught psephologist (political number cruncher), a pleasure cyclist, and someone who just calls things as he sees them.

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