What’s a logarithmic graph and how does it help explain the spread of COVID-19?

coronavirus CDC

(Credit: Unsplash)

This article is brought to you thanks to the collaboration of The European Sting with the World Economic Forum.

Author: Sean Fleming, Senior Writer, Formative Content


  • Exponential lines showing increases in COVID-19 cases might not always show the full story.
  • While the raw numbers don’t change, the way they are represented can affect perceptions.
  • Logarithmic scale charts can help show the bigger picture.

The coronavirus pandemic is undoubtedly the greatest challenge the world has faced in over a generation. But is the presentation of data about the outbreak leading us to overlook any cause for optimism?

 

There is an alternative to the commonly seen linear graph that could help give a more detailed picture. It’s called a logarithmic graph.

Interpreting information

The most common form of a line-graph has a linear scale. Along the Y axis, the numbers progress in a steady, linear form – 1, 2, 3, 4, or 10, 20, 30 and so on.

What is the World Economic Forum doing about the coronavirus outbreak?

A new strain of Coronavirus, COVID 19, is spreading around the world, causing deaths and major disruption to the global economy.

Responding to this crisis requires global cooperation among governments, international organizations and the business community, which is at the centre of the World Economic Forum’s mission as the International Organization for Public-Private Cooperation.

The Forum has created the COVID Action Platform, a global platform to convene the business community for collective action, protect people’s livelihoods and facilitate business continuity, and mobilize support for the COVID-19 response. The platform is created with the support of the World Health Organization and is open to all businesses and industry groups, as well as other stakeholders, aiming to integrate and inform joint action.

As an organization, the Forum has a track record of supporting efforts to contain epidemics. In 2017, at our Annual Meeting, the Coalition for Epidemic Preparedness Innovations (CEPI) was launched – bringing together experts from government, business, health, academia and civil society to accelerate the development of vaccines. CEPI is currently supporting the race to develop a vaccine against this strand of the coronavirus.

But infectious diseases don’t spread in an even, linear fashion. On a linear scale graph, the rate of growth keeps going up and up – the line can become almost vertical and appear to go on forever. That can create the impression measures like social distancing aren’t working.

On a logarithmic scale, numbers on the Y-axis don’t move up in equal increments but instead each interval increases by a set factor – it’s often 10 but could be a factor of 3 or 350 or 3,500, anything at all. It all depends on what is deemed to be the most effective way of interpreting the data in question. The Richter scale is logarithmic – an earthquake that measures 6 is 10- times more destructive than one that measures 5.

The logarithmic scale is ideal for measuring rates of change, particularly rates of growth, explains mathematician, teacher, and author of The Life-Changing Magic of Numbers, Bobby Seagull.

It “flattens out the rate of growth so it becomes easier to see,”, he says. “On a logarithmic graph of COVID-19 infections, even though the overall numbers are still increasing, you can see the point at which the rate of growth starts to level off when that exponential growth has stopped.”

At that point, the logarithmic scale makes it possible to see when public health measures are starting to have the desired effect.

This is what the COVID-19 situation in China looks like when plotted on a linear graph.

Coronavirus china virus health healthcare who world health organization disease deaths pandemic epidemic worries concerns Health virus contagious contagion viruses diseases disease lab laboratory doctor health dr nurse medical medicine drugs vaccines vaccinations inoculations technology testing test medicinal biotechnology biotech biology chemistry physics microscope research influenza flu cold common cold bug risk symptomes respiratory china iran italy europe asia america south america north washing hands wash hands coughs sneezes spread spreading precaution precautions health warning covid 19 cov SARS 2019ncov wuhan sarscow wuhanpneumonia  pneumonia outbreak patients unhealthy fatality mortality elderly old elder age serious death deathly deadly
The number of cases presented on a linear scale.
Image: Worldometers

And this is how it appears when plotted on the logarithmic scale.

Coronavirus china virus health healthcare who world health organization disease deaths pandemic epidemic worries concerns Health virus contagious contagion viruses diseases disease lab laboratory doctor health dr nurse medical medicine drugs vaccines vaccinations inoculations technology testing test medicinal biotechnology biotech biology chemistry physics microscope research influenza flu cold common cold bug risk symptomes respiratory china iran italy europe asia america south america north washing hands wash hands coughs sneezes spread spreading precaution precautions health warning covid 19 cov SARS 2019ncov wuhan sarscow wuhanpneumonia  pneumonia outbreak patients unhealthy fatality mortality elderly old elder age serious death deathly deadly
The number of cases presented on a logarithmic scale.
Image: Worldometers

Same data, different perspectives

Both charts tell the same story – that China’s coronavirus cases have started to flatline. But the logarithmic graph shows a flattening of the line much earlier because of the way the scale has been compressed. It also makes it possible to fit a large or widespread set of results onto a graph that might otherwise not fit in a linear way.

A logarithmic graph can also help make it clear if the apparent evening-out of the curve started to change. While a linear curve would keep on pushing ever higher regardless, the logarithmic graph would highlight any substantial changes to the trend – whether upward or downward.

It’s an approach that is often preferred when there are huge numbers involved and a linear scale would just produce a dramatic-looking exponential curve.

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