Health and Healthcare Systems

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

First responders evacuate sick crew members with flu-like symptoms from two cruise ships, the Costa Favolosa and Costa Magica at U.S. Coast Guard station at Port of Miami after the Florida Department of Health reported more than 2300 confirmed cases of coronavirus disease (COVID-19), in Miami, Florida U.S., March 26, 2020. REUTERS/Carlos Barria 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

Logarithmic scale charts can help show the bigger picture, allowing for a better understanding of the coronavirus pandemic. Image: REUTERS/Carlos Barria

Sean Fleming
Senior Writer, Forum Agenda
Share:
Our Impact
What's the World Economic Forum doing to accelerate action on Health and Healthcare Systems?
The Big Picture
Explore and monitor how Global Health is affecting economies, industries and global issues
A hand holding a looking glass by a lake
Crowdsource Innovation
Get involved with our crowdsourced digital platform to deliver impact at scale
Stay up to date:

Global Health

  • 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?

Have you read?

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.

Discover

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

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 confirmed 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 confirmed 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.

The raw numbers aren’t affected by the choice of chart. The reality is that (as of 4 April 2020) there are more than 1 million confirmed cases globally and 55,000 deaths. But more than 219,000 people have also recovered – and that’s a part of the coronavirus story that’s just as important to tell.

Don't miss any update on this topic

Create a free account and access your personalized content collection with our latest publications and analyses.

Sign up for free

License and Republishing

World Economic Forum articles may be republished in accordance with the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Public License, and in accordance with our Terms of Use.

The views expressed in this article are those of the author alone and not the World Economic Forum.

Share:
World Economic Forum logo
Global Agenda

The Agenda Weekly

A weekly update of the most important issues driving the global agenda

Subscribe today

You can unsubscribe at any time using the link in our emails. For more details, review our privacy policy.

Feeding the future: why Renovation and Reinvention are key to saving our food system

Juliana Weltman Glezer

June 13, 2024

About Us

Events

Media

Partners & Members

  • Join Us

Language Editions

Privacy Policy & Terms of Service

© 2024 World Economic Forum