Carrying capacity, viral media, and the logarithmic scale

Dear Student, Let’s think about your comment. “For example, in preliminary calculations, it is thought that the 2 months of pollution reduction in China has probably saved the lives of 4,000 children under 5 and 73,000 adults over 70 (Bowler, 2020). That’s pretty significant.”

I read that as 77,000 more people who are alive thereby contributing to overpopulation and also thereby enhancing the risk of coronavirus. 

In the end, air pollution and coronavirus are the same thing. They are human population controls that derive from human overpopulation itself. 

Assignment: Interpret this series of graphs. You tell me what you see here. 

Carrying capacity- An ecological concept

Here is the classic carrying capacity graph that we look at in the ecology unit. The y-axis is human population. The x-axis is time. The black line is the population over time. The red dashed line is the critical human population the Earth can support. There are no numbers here because this is a theoretical interpretation. Scientists spent some time in the 1990s trying to model and estimate what the actual number of humans the Earth can support but we are way beyond their estimates already.

Most scientists agree that we are in the first overshoot. Pollution, contamination, famine, water scarcity, and disease are all environmental factors that limit the population. The carrying capacity graph is telling us about an ecological relationship. The relationship described by the graph can be applied to any species in any specific ecosystem.


“Flatten the curve” as viral media (in more ways than one…)

I am trying to find primary evidence for the flatten the curve graph. This is the graph that went viral in the media giving rise to isolation orders across the globe. It makes sense, but is it supported by scientific evidence? Epidemiology is essentially a math problem about rates. In this graph, we are looking the number of cases of coronavirus (y) as a function of time (x). You could also think of it as a population graph for the coronavirus. If we don’t reduce the number of cases (ie the coronavirus population), more people will die because the health care system will be overburdened by the number of people who need medical intervention.

In this graph, the carrying capacity line is the healthcare system. The healthcare system is the ecosystem the coronavirus-infected population will inhabit. It can only support so many individuals before the functionality of the system is depleted (see carrying capacity graph above).

Logarithmic scales and graphing

Next, here is a New York Times article. This is a great math-focused answer to understanding how you can perceive of rate changes with a logarithmic scale. The numbers of cases are increasing exponentially, but are they increasing faster or more slowly as a result of self isolation?

If we just look at number of cases, all we see is the exponential curve. That is the raw data. It looks like the number of cases is increasing because they are. Notice the y-axis. On the left, it’s y = number of cases (x).

On the logarithmic graph (right), the y-axis is orders of magnitude of cases. y=log10(x). A logarithmic scale depicts large ranges of numbers as a function of a base exponent, usually 10. Each unit on the axis is not equidistant. Each unit on the axis is a base number raised to an exponent. 10^1 = 10, 10^2 = 100, 10^3 = 1,000

Chang, 2020

To understand these graphs, keep reading here:

Chang, K. 3/20/2020. A Different Way to Chart the Spread of Coronavirus. The New York Times.


  1. Is the rate of coronavirus infection increasing or decreasing in Italy?
  2. Is the rate of coronavirus infection increasing or decreasing in the United States?

Primary data in graphical form

Here is a Science article that shows the dynamics of contraction in China, ground zero for coronavirus.

Chinazzi, M. et al. 3-6-2020. The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak. Science. DOI: 10.1126/science.aba9757

Fig. 1 Effect of the Wuhan travel ban on the COVID-19 epidemic (Chinazzi, et al, 2020). 

Fig. 1 (A) Trajectory of the 2019-nCoV epidemic in Chinese locations (excluding Wuhan) under the travel ban to and from Wuhan in effect as of 23 January 2020. The lines represent the median cumulative number of cases while the shaded areas represent the 90% reference range. The figure includes also the scenarios with relative transmissibility reduction r, and international travel restrictions.

Fig. 1 (B) Correlation plot between the number of cases reported in each province by the WHO situation report and model projections on 1 February 2020. The size of the circles are proportional to the population size in each province. We note that no provinces were reporting zero cases by that date.

Fig. 1 (C) Projections of the average, detected number of daily international case importations for different modeling scenarios. Shaded areas represent the 99% reference range. We report the observed data of international case importations with a travel history from China by arrival date. We also report scenarios with relative transmissibility reduction r. Data points after 23 January 2020 are used as out of sample validation and not used in the model calibration.

A note about peer-review and scientific publication

Look- this is an early release publication. In other words, the information is so important, this was not significantly slowed by the peer-reviewed process. Probably the editor-in-chief reviewed the article and then it went to publication. Usually a jury of reviewers offers comments and unless they all recommend “accept without revision,” it takes some time to publish a paper. I have been working on publishing a single paper for several months, for example. Hopefully, this is not a statement on the quality of my research but rather on the tenacity of peer-reviewers. 🙂

Be a keen observer of science

Just looking at these three graphs to interpret them could take us all day. I have already been working on this blog post for two hours! Here are some things to look at, to become a discerning observer of science:

1. Read the captions for the first figure and gaze at that figure for a few minutes. Then move on to the next. It is impossible to keep it all straight if you look at all three graphs and then read all three captions.

Ask yourself:

2. What’s on each axis in each graph? Is it a logarithmic scale?

3. What does each line or shading or dot mean? What is it’s color, shape, and size supposed to communicate?

4. Finally, what trends do you see? What are the conclusions?

5. Now go through the captions again and see if they make more sense. You have the whole article here in the reference but that is only more complex. This is the basic process I suggest for reviewing science articles in any context. Look at the figures and captions first. They should summarize the numeric scientific inquiry. 

Summarizing Question:

Is their primary scientific evidence that self-isolation slows the coronavirus infection rate?

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