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How likely are you to die from measles?

A graph a day: 30th April 2025

The US is at a tipping point for the return of measles and possibly other vaccine-preventable diseases. Other countries might follow if the vaccination levels drop below the herd immunity threshold.

Measles and vaccination are such broad subjects, and well covered in the new book, How vaccines work, as well as in many other publications, like one of my favourites, Vaccine Nation published over a decade ago.

The measles vaccination campaign is indeed one of the success stories of modern medicine and public health. The population health had been improving since the end of the 19th Century, leading to the decline in the rate of death due to measles. By the 1940s, with the advent of novel treatments and eventually antibiotics, the probability of death due to measles became about 0.01%.

However, the number of cases was steady throughout this time until the government, concerned about the health of the nation, started a massive vaccination campaign in the early 1960s.

Given that the population was already close to herd immunity, due to the immunity caused by past infections, the campaign brought a spectacularly fast decline in the number of cases, followed by a drop in the number of deaths.

A similar picture emerged in the UK (my graph based on the UK government data). The number of deaths went down remarkably, even before the vaccination was introduced in 1967. The number of cases declined very quickly in 1970s, but it was the introduction of the second dose recommendation that brought it almost to zero by 1990.

The UK measles mortality rate (deaths per case) was going down in the 1940s and 1950s, but it stabilised in the late 1950s at about 0.02% – showing the limits to what doctors can do to save a difficult measles case and complications following the infection. Note the logarithmic scale on the graph above.

Why has the death rate gone up in the late 1990s? Firstly, we need to be very careful with the interpretation of the results, as the number of deaths is very low (1-5 per year). Most of the deaths since 2000 are either for adults (late effects of measles) or immuno-compromised children.

It is these deaths in the vulnerable population that are particularly concerning once the measles vaccination levels go below the herd immunity threshold. The resulting wave will particularly hit those whose immunity is compromised.

How does risk compare for vaccination and for measles disease?

The graph from How effective and safe are measles vaccines? at OurWorldinData.org, and retrieved from: [Online Resource], is based on the “gold-standard” in literature reviews.

It is not to diminish the side effects of the vaccine. Perhaps surprisingly, I support RFK Jr’s call for more research on the autism-vaccination link, provided it is done correctly – although see here for the rebutal.

As I mentioned before, I am a sceptical supporter of vaccination. As with other medical advances – sulfamids, antibiotics, prosthetics – they are absolute life-savers.

Since the 1970s, infant mortality has dropped from 10% to below 3% globally. It is difficult to deduce how much of it is due to vaccination and how much to other improvements. There has been fantastic progress in the general public health support, despite the advances of civilisation-related diseases like obesity or diabetes.

It is likely that 2% of this 7% drop is due to vaccination. It might sound small, but I do not think any parent would like their child to be among these 2%.

UK elections July 2024

A graph a day… 5th July 2024

People in the UK have chosen new Members of Parliament (MPs), and although not unexpected, the results are still very interesting. Due to the voting system – First-Past-the-Post – which means that only one person is chosen in a given district, regardless of how close other parties were – there could be a discrepancy between the overall percentage of votes and the number of MPs.

The Labour Party has won by a huge margin in terms of the number of MPs, but its undoubted success is perhaps less due to the number of votes than to the collapse of the Conservative and Unionist Party—which has been in power for the last 14 years.

It is perhaps easier to identify losers: Conservatives, Scottish National Party (SNP), and Democratic Unionist Party (DUP), but there are also clear winners besides Labour: Liberal Democrats, Reform, Greens, and Sinn Fèin.

Some interesting graphs I picked up this morning:

These are voting intentions, so comparable to the vote share. I was particularly struck by the age profile. The shift from Labour to Conservative vote as the voters age has been expected, but I also expected a higher Reform share in the younger populations. Yet, their share in 18-24 is the lowest at 8%, rising to 16% for over 55s. Instead, the younger population decided to vote Green!

The vote share for both main parties is roughly equal across the income. A slightly higher proportion is voting Conservatives among the highest income (AB), which is surprising given that this party presided over the Brexit catastrophe. But, perhaps this class is more shielded than others and more likely to (still) believe that Conservatives will reduce taxes. AB also has the highest share of LibDems which traditionally is the party of higher end of the middle class.

Reform in turn does best in C2, D and E – most deprived classes – as they have been mostly affected by the economic crisis – and the associated loss of trust in the established politics.

Two graphs here show how FPTP works in the UK. Labour’s lead over Conservatives is only 10% in terms of the vote share, but more than 300% in terms of seats. Even worse, Reform 14% translates into only 1% of the vote while LibDems 12% vote share becomes 11% seat share.

Secondly, it shows that 30% of the vote share is now taken by parties different from the “big ones”, a much higher proportion than in the previous years. Perhaps it is time for a Proportional Representation?

This is also reflected in how tight the vote becomes. I love the graph above, showing how big a majority was for all seats contested in recent years. There are just more and more seats that are marginal. Under the FPTP a candidate is thus selected over another one, on the basis of an almost equal vote. It also means that the results over years will be characterised by large swings.

More graphs coming soon…

A graph a day… March 19, 2024

It has been a while since I have posted here—a combination of work and personal commitments and stresses. But I miss writing, and I hope you, my readers, miss my posts.

COVID-19 is slowly being normalised, and hence, there are fewer occasions to write about epidemiology and statistics. But this blog has never been only about Covid-19, so it is a good time to return to its main purpose—writing about mathematics and statistics.

As I hope to get back into regular blogging, I want to start a new series, A Graph a Day, where I regularly show an interesting graph with a short comment. It is probably too ambitious and unrealistic to expect a graph daily, but I will do my best to do it regularly.

I am still planning to write longer posts on using mathematics and statistics in epidemiology, but they will appear on Substack – particularly as it now allows mathematical formulas.

So, welcome to the first release of A graph a day…


I found this picture fascinating. It shows that international trade is like water—if you block one channel, it will find another. Unfortunately, this also shows that unless the trade restrictions are very strict (i.e. a physical blockade, or a very broad international consensus), they are not likely to work. The price of the goods will surely go up, but the trade will continue.

I also find the oscillations in the yearly trade to Russia, both from the UK and from Germany, fascinating. I am sure that there are good reasons for it – particularly as we are not talking large numbers (£30m probably means 1,000 cars per year) – but wondering what an AR process fitted to the data would look like…