# Be sufficiently worried

Though Smartodds loves Statistics is in hibernation while we work out what direction it should take in the future, the current Coronavirus epidemic raises important questions – many of which are statistical in nature – so I thought I would write some occasional posts specific to this topic.

First off, Richard.Greene@smartodds.co.uk pointed me at this topical video showing how the growth in the number of cases of Coronavirus can be modelled by exponential and logistic curves.

Take a look:

As the video explains – admittedly with numbers that are now a little out of date – while an epidemic is in its exponential growth phase, the daily increase in the number of cases is given by:

$E \times p \times N$

where:

• E is the expected number of people an infected person is exposed to;
• p is the probability an infected person will infect a person to which they are exposed;
• N is the number of people currently infected.

What this means is that the number of new infections is proportional to the number of current infections. So the rate of infections grows just as the number of infections grow, and this is what leads to the familiar exponential growth curve.

But crucially, although the growth curve will always be exponential in shape, the precise trajectory is massively affected by the values of E and p, each of which we have some individual control over during the epidemic. In particular:

• E can be reduced by reducing the number of daily contacts we make;
• p can be reduced by improving our personal hygiene habits.

So, although this is just a mathematical idealisation of the virus spread, it tells us in material terms what we can do in our day-to-day lives to minimise the growth. And slowing the trajectory of the growth is essential in allowing health systems time to manage the epidemic; in allowing time for possible seasonal effects to kick in – the hope that warmer weather will stunt virus transmissions; and allowing time for the identification and testing of potential vaccines and cures.

The other crucial fact is that in practice the exponential growth phase won’t continue indefinitely. The video discusses the consequences of having a finite population – as the number of infected people increases, an infected person is bound to meet fewer uninfected people – leading to the exponential-type curve flattening into a logistic shape and the eventual termination of the epidemic. But other factors too will halt the exponential growth. These include the development and  distribution of a vaccine, and the socio-demographic measures – progressively and aggressively altering E and p through strict social management – as seen in China, South Korea and more recently Italy.

So, although exponential growth is alarming – as the video shows, the current data suggest that the number of infections will multiply by 100 every month or so – there are also reasons to be optimistic about the demise of the epidemic. We can slow its progress through the reinforcement of sensible hygiene practices and modifications to our social behaviour, each of which will quicken the progress of the epidemic from the exponential growth phase to the  part of the logistic curve where the rate of growth diminishes and the epidemic peters out.

As the video concludes: be sufficiently worried. In other words, don’t panic, but don’t be complacent either. Good habits will offer you the best personal protection against the virus, while also helping stem the spread worldwide.

I’m no expert on epidemiology, but if you have any questions about the video above in particular, or about statistical aspects of the Coronavirus in general, I will try to answer them.

As the epidemic continues, I’ll also include further posts here from time to time, some linking to interesting articles, others, like this one, trying to explain the role of statistics in understanding the way the epidemic is likely to develop.