To herd or not to herd

I was drafting a new post on herd immunity and the way to approach the second wave, but have just found the text of the John Snow Memorandum which does it much better than what I could do.

The Memorandum, currently signed by nearly 400 people, addresses the temptation to try to achieve “herd immunity” among young people, while protecting the “vulnerable”. This idea is not something very outlandish as shown by the Great Barrington Declaration as well as by signals from different governments:

“We heard strong reinforcement of the Trump Administration’s strategy of aggressively protecting the vulnerable while opening schools and the workplace,”

The John Snow Memorandum responds:

Any pandemic management strategy relying upon immunity from natural infections for COVID-19 is flawed. Uncontrolled transmission in younger people risks significant morbidity and mortality across the whole population. In addition to the human cost, this would impact the workforce as a whole and overwhelm the ability of healthcare systems to provide acute and routine care.

Moreover, the Memorandum gives a solution:

Once again, we face rapidly accelerating increase in COVID-19 cases across much of Europe, the USA, and many other countries across the world. It is critical to act decisively and urgently. Effective measures that suppress and control transmission need to be implemented widely, and they must be supported by financial and social programmes that encourage community responses and address the inequities that have been amplified by the pandemic.

Continuing restrictions will probably be required in the short term, to reduce transmission and fix ineffective pandemic response systems, in order to prevent future lockdowns. The purpose of these restrictions is to effectively suppress SARS-CoV-2 infections to low levels that allow rapid detection of localised outbreaks and rapid response through efficient and comprehensive find, test, trace, isolate, and support systems so life can return to near-normal without the need for generalised restrictions.

Protecting our economies is inextricably tied to controlling COVID-19. We must protect our workforce and avoid long-term uncertainty.

I could not agree more.

PS. A great thread on Twitter with a lot of number-crunching:

More on 1-1/R formula and herd immunity

The concept of “herd immunity” is still being widely discussed, both from the policy point of view (should we just simply be “flattening the curve” and letting the nature take its course?) and medical and modelling (has Manaus in Brazil reached the “herd immunity” level with 44-66% infected?).

The result that the formula 1-1/R is referring to has been known for a long time, at least since the 1970s. It is quite a powerful result, as it is quite independent of the modelling assumptions. However, it needs to be properly interpreted. As I said in my earlier posts, the term “herd immunity” and the associated 1-1/R formula can be used in different ways.

Firstly, in a generic sense, “herd immunity” simply means the proportion of immune individuals in the population.

Secondly, for an ongoing epidemic, it means a threshold proportion of immune individuals at the point when the incidence starts declining because of the diminishing supply of susceptibles (as opposed to the reduction in the transmission due to lockdown). When the proportion of immune individuals reaches the level of 1-1/R, the number of newly infected individuals stops growing. But, this does not mean the disease will immediately stop. Assuming no loss of immunity (and ignoring that new-born babies will probably be susceptible), we can predict that the disease will then start very slowly decaying.

As can be seen in the graph below, the actual final number of people who will go through disease will be massively higher. For coronavirus, the “herd immunity” level is believed to be around 40-70%, and the corresponding final number of infected individuals will be about 80-99%.

Dependence of the herd immunity level and the final epidemic size on the reproductive number, R. Cited with permission from The Conversation article (TBC).

Thirdly, it is the level of immunity after the outbreak that prevents the emergence or re-emergence of the disease. In this context, 1-1/R determines the vaccination threshold that needs to be reached for protection over the future outbreaks. For example, for measles, this is about 90%, so if the proportion of children vaccinated against measles drops below this level (as it has done in several European countries and the USA), an introduction of measles from outside the country will result in an outbreak.

We also need to understand what R in this formula corresponds to. Normally, we will think of it as the basic reproductive number, i.e. the number of secondary cases resulting from one case, in the absence of any other control measure, like social distancing or masks. In other words, we usually think of it as a potential for the disease to spread under the “business as usual pre-pandemic” scenario. This is where the 40-70% range comes from; a wide range as we are not that sure how fast the virus would have been spreading if we removed all social-distancing measures.

How can we predict/measure “herd immunity”? There are two problems. Firstly, we do not know very well what R is and therefore what 1-1/R is.

Secondly, the formula 1-1/R, while applicable to a wide range of models, is by no means universal. We know, for example, that people and populations differ by how much they are susceptible and how much they contact each other. If the society is highly stratified, with some people living very close to each other and some widely apart, the “herd immunity” level might be smaller (some say 10-20% under some conditions).

There are some speculations that Manaus in Brazil has reached the herd immunity levels at about 44-66% infected, but apparently, they now do see new infections (possibly a result of waning immunity).

Can any country or region achieve herd immunity before the vaccine becomes widely available? As explained above, this depends on what exactly we mean by “herd immunity”. It is not inconceivable that some places in the world where the disease is particularly widely spread – as in Brazil or possibly in Indian slums – but achieving this more widely is going to be difficult and also it is not clear how long it will last.

And then there is a non-lasting immunity. This will make it very difficult to achieve the second objective listed above (eradication) and we will need to be re-vaccinated (or re-infected) multiple times.

Plant Health Week – day 5

Humble spuds have a very interesting history. Originating in South America, the earliest finds date from about 2500 BCE. It subsequently became a staple food for indigenous people in Andes region, the main energy source for those living in the Inca Empire. It arrived in Europe as early as mid-16th century but the acceptance as the food was initially low. It took the efforts of the French and German governments and landowners in the second half of the 18th century for the potato to become a staple crop in northern Europe. Perhaps the famines of 1770s helped as well. The crop was resistant to spoilage, easy for cultivation even on small fields and gardens, and a good source of calories and some vitamins and minerals. It appears to have arrived in the US via Ireland. Today, potatoes are grown across the globe, but with the highest concentration in Europe, India, China and the US.

Frederick the Great encouraging potato planting. By Robert Müller –, Public Domain,

King of Prussia, Frederick the Great, is sometimes called der Kartoffelkönig – potato king – as he was instrumental in introducing the crop into Prussia and Eastern Europe. By 1840s, potatoes accounted for 11% of Prussian and 14% of Belgian arable land, but it was Ireland that adopted the plant as the main source of food (32% of arable land). A whole Irish (or British, or German, or Polish) family could survive by growing potatoes on a single acre of land. It could also be grown in city gardens, supplementing the diet of Industrial Revolution workers.

Symptom of late blight on the underside of a potato leaf
Phytophthora infestans symptoms. By Howard F. Schwartz, Colorado State University, United States –, CC BY 3.0,

The rapid growth of potato cultivation was not, however, associated with good biosecurity practices. The American and European crops were dominated by a single variety (called Lumper; it was not resistant to blight but with a high yield), so it was a disaster in waiting. Indeed, in the early 1800s, potato blight (Phytophthora infestans) started spreading in Central and North America and it arrived in Europe in 1840s.

The map of approximate potato blight spread in 1845.Source unknown.

Starting in northern France and Belgium in June 1845, it rapidly spread throughout Europe, reaching Ireland in September-October. A catastrophic failure in the crop that supported the Irish combined with the failure to help the starving population led to a million deaths and possibly two million leaving the country.

Population of Ireland. Source unknown.

Scotland, and particularly Scottish Highlands, were affected as well leading to migration. US and Canadian people celebrate their Irish and Scottish ancestry, perhaps not realising that their origins are due to a plant pathogen.

However, it was not only the populations of Ireland and Scotland who were affected, as the famine spread throughout Europe resulting in losses as high as 80% in Belgium and 50% in Denmark and parts of German Empire. As other crops (wheat, rye, oats) also failed in 1845 and 1846, there was a general shortage of food. Food prices were rising and the demand for goods produced in newly industrialising nations fell. Unemployment led to general dissatisfaction with the governments. The Spring of Nations, the Revolutions of 1848 followed suit.

Philippoteaux - Lamartine in front of the Town Hall of Paris rejects the red flag.jpg
By Henri Félix Emmanuel Philippoteaux, Public Domain,

While it is perhaps a stretch of the imagination to say that the 1848 revolutions were the result of the potato famine, the loss of food security – caused by Phytophthora infestans – certainly contributed to people’s dissatisfaction with the governments.

The potato blight is still a huge problem, even though we now have ways to treat it. Some pesticides are based on copper. Because of the shortages of the metal during World War 1 (used to produce shells and wires), a major outbreak devastated potato crop in Germany, leading to mass starvation. Using resistant varieties is one way to battle it, as is using good quality seed potatoes (Scottish ones are best in the world!).

Visit The Grave Of Frederick The Great - Berlin Experiences
Frederick the Great’s grave.

And, people still remember the Prussian King, Frederick the Great and his contribution to potato cultivation by placing tubers on his grave (thanks to Agnieszka for this link!).

[The previous version associated the 1848 Revolution with Les Miserables, but of course the events in Victor Hugo’s book are the 1832 uprising, not the 1848 revolution; apologies for the mix-up! In fact, the 1832 uprising was also associated with harvest failures and cholera outbreaks – epidemics are everywhere!]