When I posted about Australia’s slow vaccination progress we were ranked dead last among OECD countries in the full vaccination “race“. We have now nosed past South Korea into second last place. Sydney’s COVID outbreak and lockdown is certainly a factor, but whatever the reason, the increased rate of vaccination we’re seeing is good news.

The Sydney outbreak is also leading to growing numbers of COVID victims being admitted to intensive care units (ICUs) and, sadly, to a number of deaths. So far, while a small number of the patients in ICU have had one vaccination shot, none have been fully vaccinated. But based on international experience, it’s only a matter of time before that will change. We should also expect to see some deaths of fully vaccinated people. I am sure that the minute that happens there will be enormous media attention, but will it actually say anything about the effectiveness of the vaccine?

In fact, it won’t. It will simply be a statistical consequence of an increasingly vaccinated population. It’s sobering to recall that in the race to develop vaccines last year, 50% efficacy in trials was set as the hurdle for regulatory approval. As it turned out, the vaccines all did far better with trial efficacies around 80-90%. These are extremely good vaccines, but they are still not 100% effective at preventing disease, hospitalisation or even death. As more and more people are vaccinated, we should therefore expect to see a higher proportion of fully vaccinated patients in ICU or dying (see chart below). Of course, many people will still see this outcome as an indictment of the vaccines. Friend of the Mule, Dan, gave me this ironic analogy for this confusion: “Now that nearly everyone in Australia wears seatbelts, it turns out that nearly 100% of people who die in road accidents were wearing their seatbelts. Proving that seatbelts are not effective anyway in preventing road fatalities!”.

Focusing on the proportion of people in ICU or dying who are vaccinated misses the important point here: as vaccination rates increase, the total number of people in hospital or dying will be dropping. John Burn-Murdoch of the Financial Times illustrates this point nicely with a clever infographic.

How much of a reduction on ICU admissions should we expect to see as a result of increased rates of vaccination? It will depend on how effective the vaccines are at preventing severe disease. While current estimates of the effectiveness of the vaccines are around 80% (with some variation across the vaccines), there is some evidence that the effectiveness of preventing severe disease is over 90%. The impact of vaccines on hospitalisation will also depend on how much COVID is circulating in the community: when the risk of contracting COVID is low, even unvaccinated people are unlikely to end up in hospital.

The chart below shows the expected effect of vaccination on rates of admission to ICU for four different assumed effectiveness rates of the vaccine and for three different scenarios for the prevalence of COVID in the community. These scenarios are taken from the Australian Technical Advisory Group on Immunisation (ATAGI) paper “Weighing up the potential benefits against risk of harm from COVID-19 Vaccine AstraZeneca“. The “low” risk scenario corresponds to an infection rate similar to the first COVID wave in Australia (29 infections per 100,000 over 16 weeks), “medium” to an infection rate similar to the Victorian second wave (275 per 100,000 over 16 weeks) and “high” is similar to Europe in January 2021 (3,544 per 100,000 over 16 weeks).

When the risk of contracting COVID is high, higher vaccination rates will dramatically reduce hospitalisation. This is particularly evident in the UK experience, where COVID peaked well above the “high” scenario in this chart in January 2021 and then again in July. In the intervening six months Britain has had one of the more successful vaccine roll-outs and, as a result, hospitalisation and death rates in July were a fraction of the January experience.

I hope Sydney’s lockdown will be successful in containing the current outbreak, but if it’s not, the faster we roll out the vaccine, the fewer people will end up in ICU and the fewer people will die.

To date Australia has fared relatively well by international standards in terms of its COVID-19 infection rates. Now, however, its vaccination progress does not compare so favourably to other countries. Charts showing Australia languishing at the bottom of a vaccination league table have been circulating widely online. The specimen below, which appeared in last weekend’s Saturday Paper, is a typical example.

The challenge when producing charts like this is that there are far too many countries to squeeze onto a bar chart, requiring a somewhat arbitrary choice of the countries to include. This chart suggests that Australia’s full vaccination rate is the worst and Chile’s is the best. Australia does not in fact have the lowest rate in the world, although it is the lowest among OECD countries. Chile, at the other end, is certainly doing very well, but is not the best in the world – that honour sits with Gibraltar (or Malta if we restrict to sovereign nations). Even considering only OECD countries, the chart omits Iceland and Israel which are both a little ahead of Chile.

So, how can we get a better picture covering all countries around the world? One approach is to use a map instead of a bar chart. The map below shows countries grouped into quintiles (five of them, of course), ranging from the 20% of countries with the lowest rates of vaccination through to the 20% of countries with the highest rates. On this basis, with a full vaccination rate of 7%, Australia just scrapes into the middle quintile along with countries with full vaccination rates ranging from 6-18%. So Australia may not be last in this “race”, but the countries with lower rates are all far poorer than Australia.

The striking band of top quintile blue between Russia and China is Mongolia, which has an interesting story behind its vaccination success (thanks to Dan for alerting me to that article).

Some notes on the data:

1. The data here is all sourced from Our World in Data (OWID), which in turn sources data from national authorities. A significant number of countries do not appear in the dataset and these are likely to be countries with very low rates of vaccination. If this data were available it would push up Australia’s ranking.
2. “Countries” includes dependencies (such as Gibraltar) and disputed territories not just widely recognised sovereign nations.
3. OWID reports a vaccination rate for Gibraltar of over 100%. This appears to be because vaccination figures include guest workers and, given Gibraltar’s small population, this has a big impact on the rate. Since there continue to be some cases of COVID-19 among unvaccinated people in Gibraltar, the true rate must be below 100% but as I have seen some estimates that the figure is more like 90%, Gibraltar is probably still in the lead.

The New South Wales Department of Health has now released a breakdown of COVID-19 data by suburb. The website – and much of the media reporting of this data – displays this in the form of colour-coded maps, highlighting the hotspots. But the data is also available in more detail as part of the government’s open data initiative. This provides the opportunity to explore the data in different ways.

As an example, the chart below shows the evolution of confirmed COVID-19 cases over time for all postcodes with more than 20 total cases. This shows clearly the impact of the social distancing measures from early April. Many areas have seen no new cases since mid April. The large spot that pushed Caddens near the top of the list is result of the cases in the Anglicare Newmarch aged care nursing home.

Note that most of the postcodes in New South Wales include multiple suburbs. Here I have picked a single representative suburb to label the chart.

Reportedly, Sweden has not gone into a COVID-19 lockdown, unlike its neighbours. While I am sure this is a deliberate policy choice, it will also serve as an interesting epidemiological experiment to test the effectiveness of different social response measures.

It is still early in the course of this international experiment, but a look at the growth in cases intially suggests that Sweden’s strategy is not leading to a significantly higher infection rate.

However, confirmed cases are difficult to compare across countries as they can be heavily influenced by the testing regimes each country implements How many tests are performed? Do they target particular groups (international travellers, those in contact with confirmed cases or are they driven by symptoms? It is very hard to account for these factors. Instead it is easier to compare the number of deaths. While there can still be differences (Under what circumstances are post-mortem deaths tested for COVID-19? How are co-morbidities accounted for? Are there more older citizens?), I think it is reasonable to expect less significant variation across neighbouring countries.

Looking at deaths, Sweden looks far worse than its neighbours. Sweden has approximately the same number of confirmed cases as Norway, but more than five times the number of deaths.

Interestingly, Sweden’s case count is very close to Australia’s, but Australia has to date seen 23 deaths, compared to 239 in Sweden – almost 10 times as many.

This suggests either that Sweden’s confirmed case count is significantly understated – it would be understated everywhere but likely more so in Sweden than elsewhere – or Sweden is suffering a far higher mortality rate.

The experiment is not yet over, but so far Sweden’s no lockdown strategy does not seem to be working.

There is no shortage of commentary on COVID-19 online and off. There is also an abundance of data available, which is as good a reason as any for the first Mule post of 2020.

One of the best data resources online is the Johns Hopkins dashboard created by the Center for Systems Science and Engineering (CSSE). For those interested in performing their own analysis, the CSSE has also made the underlying data available in a Github repository.

It has become commonplace to refer to the “exponential growth” of the disease. For many, this is just short-hand for “really” fast. Others may recognise an exponential curve in the charts below, with the exception of South Korea.

However, displaying the case data in this way does not give a very clear picture of what is actually going on. A better way to display the data (New York Times) is to use a logarithmic scale. In these charts, the values on the vertical axis increase exponentially (the labels here are successive powers of 10) and pure exponential growth would appear as a straight line. Of course, the real world is never pure, so the COVID-19 data do not appear straight lines, but for a number of countries – including Australia – there are periods where it comes very close.

When plotted on a logarithmic scale, the slope of the line corresponds to rate of growth. In late February, the slope of the curve for South Korea turns sharply up, as the number of cases exploded, only to flatten again as drastic measures began to slow the growth rate. In contrast, the slope of the curve for the USA is becoming steeper – disturbingly the rate on growth in confirmed cases is increasing.

To get a better sense of these growth rates, the charts below show the daily growth rate in confirmed cases. The data is noisy, so smoothed curves are added to give a sense of the trend. In mid-February, the number of confirmed cases was growing extremely rapidly. As containment measures were introduced, the growth rate was quickly reduced, but not before cases had reached the thousands. After that, the gains became harder fought and, while the growth rate is still falling, but only slowly and is currently around 12-13% daily. In contrast, South Korea has managed to bring its growth rate down to only 1%.

Although the case count in Australia is still only in the hundreds, it is growing at a similar rate to that seen in Italy in mid-March. Confirmed cases inevitably lag actual cases, as detection takes time, and as a result there will be a lag in the impact of any containment measures. So, it is too early to tell how much impact the recently imposed travel and social distancing restrictions will have.

Everyone will be hoping these measures will help, but if they do not and the current growth rate persists in Australia, the confirmed case count in New South Wales will be over 7,000 in two weeks, around 30,000 in three weeks and heading towards 200,000 in a month. The prospects in the USA look scarier still: there are already over 5,000 cases and the daily growth rate is around 30%. If that rate doesn’t slow, in a month there will be around 50 million confirmed cases.

Here is hoping those log scale curves start to flatten.

It has been almost two years since there has been a new post here at the Mule, so you would be forgiven for thinking that the blog was defunct. But, I have now been prodded into action by the need to change my hosting provider.

For over 10 years a friend has very generously hosted the Mule on his servers but he is now shutting down the operation. So a big thank you to Brendan for those years of hosting.

Now that I have successfully moved the site to its new home, I will have to prod myself into action and start posting again more regularly.

For the first time in a while, John Carmody returns to the Stubborn Mule with the first of two guest posts. He argues that the government’s proposed medical “co-payments” do not add up.

The government continues to flounder about many details of its budget and part of the reason is a lack of stated clarity about its intentions (although the electors are drawing their own conclusions about those intentions and whether they are fair and honest). The proposed $7 “co-payment” for GP visits is an example of this lack of frankness.

On the one hand, the Government – purporting to be concerned about an excessive patronage of GPs – seems to want us to visit our doctors less frequently than the 6 visits which every man, woman and child currently makes each year (i.e. about once in two months for all of us, an internationally comparable figure, incidentally) . On the other hand, it has, so to speak, attempted to sugar-coat this unpleasant pill by promising that, while a little of that fee will go to the practitioners, most of it will go into a special fund (to be built up to $20 billion over the next 6 years) to boost medical research (and thereby do us all a great deal of good). Neither claim survives scrutiny.

The $2 proposed share to GPs will not compensate them for the extra administrative costs which they will have to carry on behalf of the Government; nor will that nugatory sum compensate for the progressive tightening of the reimbursement of doctors from “Medicare”; so the Government’s share will, to be realistic, need to be significantly less than $5. After dealing with its own extra administrative costs, therefore, the Government will probably only be able to put $3-4 per GP consultation into the proposed research fund. To build that fund up to the $20 billion proposed will require every Australian to visit the GP about 50 times each year – once each week. How this is going to reduce our alleged “overuse” of medical services has not been explained. Nor has how, in practice, it can be achieved. The Government is living in Fairyland.

Somehow September has passed by without a single post. During that time, the Mule has travelled to the other side of the world and back (primarily for a one day workshop in Switzerland). Also, James Glover (regular contributor to the blog) and I have been exploring the statistical significance of global temperatures. That will, eventually, crystallise into a future post but in the meantime James has been driven to reflect on cats rather than climate.

There are, apparently, two kinds of people. Those who like cats and those who don’t have personalities. I am of the former and am onto my 5th and 6th cats (a mother/daughter pair of rescue cats). I’ve been reading (another) book on cat behaviour which traces the domestication of the cat from solitary hunters to domestic pets (John Bradshaw’s Cat Sense: The Feline Enigma Revealed). Most domesticated animals are herd beasts whose natural behaviours lend them to domestication. A really great read on this is Jared Diamond’s Guns, Germs and Steel. Cats, however, are naturally solitary creatures whose real benefit to humans became obvious when agrarian societies stored grains which attracted rodents, the cat’s natural food source. It’s hard to imagine now, when we get our daily bread from Woolies, but think back to the day when farmers were (literally) plagued by mice and rats, and cats served to control them.

As a kid growing up in suburban Townsville we had an un-neutered tom cat called Whiskey. We weren’t allowed to play with Whiskey, and I have vague memories of him bringing home litters which lived briefly under the house and my mother throwing him the occasional piece of liver on the back steps. He wasn’t what you would call a friendly cat. As an 8 year old we moved and I recall driving with my father to take Whiskey to a “cat home”. I still have an image of dozens of cats climbing up the side of a large wire cage. I am guessing Whiskey didn’t last there for long, and, of course was happily re-homed with another loving family. Yes, that’s what happened.

Almost every website on cats says not to feed them cow’s milk because adult mammals don’t produce lactase, the enzyme required to break down lactose in milk, into sugar. Mammals stop producing lactase once they are weaned because their mothers no longer provide them with milk and they instead produce enzymes which turn proteins, in animal and vegetable matter, into sugars. Producing lactase would be pointless and require resources better devoted to other enzymes and hence has been adapted against. The idea is that if cats can’t digest lactose, it stays in their gut and bacteria feeding on it leads to an upset stomach and diarrhoea. But I see several problems with this view.

1. Humans can produce lactase as adults*, due to a variety of different genetic mutations which stop the shutdown of lactase production in adults. So the genetic mutation doesn’t have to suddenly find a way to produce lactase, just a way to stop stopping it. Basically this is because of the nutritional benefits of cow’s milk to dairy farmers which started about 10,000 years ago. Comparisons of 10,000 year old human DNA to modern descendants of dairy farmers show this is a widespread adaptation due to its obvious nutritional benefits. Indigenous Australians and Inuit don’t have this mutation because they have no dairy farmer ancestors. This is still an open question however as curdled milk and cheese doesn’t have much lactose so do not require lactase to digest them. Personally I suspect that hunters which killed a lactating cow were able to drink the milk immediately and benefited. Other theories say cow’s milk, as an alternative to water, may have saved them from diseases. Not all humans can do this. My own father, for example, can’t drink milk.
2. Cats are quickly put off foods that make them feel sick and my cats love milk. It’s possible there is something in milk which they love (like cat nip) even if it makes them sick, but they are quick learners and I doubt it.
3. There is a lack of eye witness evidence from vets and catteries back in the day when cats were fed milk that they suffered diarrhoea when they drink milk. But none of the evidence against cats drinking cow’s milk seems to be based on this. I’ve not found a single account of someone whose cats were fed cow’s milk and suffered.
4. Cats have adapted to human living rapidly in the last 2-3 thousand years. This is equivalent to 4-5 times the length of time for humans due to their shorter lifespans, about the same time humans have adapted to drinking milk as adults.
5. It makes sense that cats which were given milk by humans, and could process it, would have a better chance of reproducing. It would have a nutritional advantage over cats which couldn’t, the same evolutionary pressure on humans should operate on cats and they should (most of them anyway) have adapted to being able to drink milk as adults.
6. I can’t find a single study which shows cats can’t produce lactase as adults, it just seems to be assumed because they are non-human mammals.

My guess is that cats descended from European cats can (most of them anyway) drink cow’s milk safely. If they drink it and come back for more it probably doesn’t upset them. My own cats, when they drink milk, run around like kids on sugary drinks, displaying very kittenish behaviour. That makes me think they are turning lactose into sugar, which means they are still producing lactase as adults.

I still find it quite amazing how memes like “cats shouldn’t drink milk” propagate across the internet without any back up evidence–like an actual study which shows it. Like climate skeptics, cat people latch onto “evidence” which supports their point of view. In any event if anyone has firm evidence that adult cats don’t produce lactase I would be happy to hear about it.

Two cats both called Minoo because cats don’t actually know their names

* Editor’s note: a recent episode of Science Friday touched on this and other evolutionary changes in the human diet. The theme of the podcast is that humans are still evolving, faster than ever. So, perhaps cats are too, as James suggests.

Those of you who have subscribed to email updates from the Stubborn Mule will have noticed some strange behaviour lately, as old blog posts have appeared in your inboxes. Why this is happening remains a mystery to me. The email subscriptions are powered by Google’s Feedburner service and, with the recent announcement that Google is shutting down Google Reader, I am starting to wonder whether Google is deliberately sabotaging Feedburner as a precursor to shutting it down too.

The sabotage theory is a bit too extreme, but certainly others are speculating that Feedburner’s days may be numbered. In any event, the time has come for me to look for an alternative in an attempt to stop the random emails.

I have looked at Feedblitz and have been bombarded with marketing materials as a result, so that one is not for me. Mailchimp is a possibility.

While I am weighing my options, I would welcome suggestions from other bloggers who have successfully made the move from Feedburner.

Just when I was reflecting that a post on the Mule was long overdue and I really should get on to writing something, guest poster James Glover has come to the rescue to share his reflections in a guest post on space jumping.

You may have seen media reports of “Fearless” Felix Baumgartner, an Austrian, who takes BASE jumping to a whole new level (literally). He ascended to a height of 40km over the US in a helium balloon and then free-jumped back to Earth, eventually landing safely and breaking several long held records in the process. What I found curious when I looked at the photos though was how far away from the Earth he looked. You might disagree, after all 40km is a long way up. Curiously it is just under the standard distance for a marathon (42km). Humans though have a curious mental process aberration –  vertical heights appear much more significant than horizontal ones. That’s why we get scared at the top of a 20m building but think nothing of that as a horizontal distance. If I said a man had just run 40km you’d think him a marathon runner and not having just completed a singular feat of human daring, unless you were actually at Marathon on Greece in 490BC when the first “marathon” supposedly took place.

In fact given the Earth has a radius of 6,400km, 40km represents less than 1% of that. If the Earth were a globe 30cm across (I hear that such things exist!) then his jump would be from a height of 1mm. From that height the Earth is still pretty up close and in your face. By comparison the International Space Station or ISS has an average height of 360km and that is considered to be only in “near Earth orbit”. That vision you see of astronauts floating around the ISS in zero-g isn’t because they are outside the Earth’s gravitational field. At 360km gravity is 90% what is in on the Earth’s surface. They float because the orbital velocity of the ISS, about 7.7kms^-1, needed to stop it falling, means they are in free fall – albeit on a trajectory that means they don’t head straight down.

I have been on a bit of an Earth geometry kick lately so I applied some trigonometry to this problem. Firstly I worked out that at 40km the angle the Earth subtends to a viewer is 167 degrees, compared to 180 degrees at the surface. By contrast at the moon (distance from Earth approximately 380,000km) the angular width of the earth is 2 degrees. In fact you can also show that the distance Fearless Felix could see on the Earth’s surface from (his) horizon to horizon is 1,400km or about the distance from Adelaide to Sydney. From the top of the Sydney Tower (height 260m) the horizon is about 58km away or approximately the distance to Penrith. This also explained why when in Tokyo you can see about 80% of Mt Fuji (height 3776m), from the ground, even though it is 104km away and hence well over the standard horizon. Actually I tried to see it from the top of Roppongi Tower (height 238m) and from there you can potentially see 96% of Mt Fuji. Unfortunately I got there at midday and to see it you have to get there before the smog thickens, by about 11am.

So what of the picture of the jump by Fearless Felix? Well using the same geometric principles and applying some advanced beer coasterology I think the picture is a fake. Fake in the sense that they have used a special lens to deliberately increase the apparent curvature of the Earth to make it look like he was jumping from deeeeep spaaaaace! It is the astronomical equivalent of photo shopping on a few curves to a model to improve her wow factor (though I understand, in practice, the opposite usually occurs).

To see why consider the image of FF himself. Assuming he was about 2m tall I would estimate that the apparent diameter of the Earth in the photo would be about 5ff (a new astronomical unit I invented). It is possible to show that for that to be a true image the picture must have been taken at a distance of 56cm from Felix. Judging by the craft next to him my guess is it was taken at least 4m away. (If in the picture Earth was only 3ff wide it would need to have been taken at a distance of 34cm)

For that to be a true image, from 4m away, geometry shows, he would have to be not 40km but 500km above the Earth. At that height the Earth would subtend an angle of about 135 degrees which also seems to fit the picture as the human field of vision is about 120 degrees. In fact if the impression they are trying to give with the photo is that he could just see the whole image of the Earth floating in space before him, in his normal field of vision, then he would need to be at least 1,000km above the Earth, not a ground hugging 40km.

My suspicions were confirmed when I saw some vision on the tv news that night shown as FF descended. Whenever the camera pointed to the horizon it was almost flat but when it pointed straight down suddenly the Earth appeared as a ball. It is the camera lens rather than some advanced photo shopping to blame. While this does not detract from the fearlessness of Felix’s jump it is a sad indictment that the organisers of the jump felt the need to up the wow factor so as to make it seem more impressive. I guess they never learned their lesson from when NASA faked the moon landings.