Monthly Archives: July 2021

Careful with that thing – you could kill someone

It’s been a while, but guest author Mark Lauer is returning to the Mule. While in COVID-induced lockdown, the mind naturally turns to armchair epidemiology, but here Mark goes beyond mere amateur probability to add a sprinkling of ethics.

So, you’re in lockdown during a COVID-19 outbreak in your city. And you’re wondering, now that most of the elderly are vaccinated, if all the fuss is really justified. After all, only a tiny proportion of the city has caught COVID so far, and even if you get it, statistically speaking it is unlikely to harm you. The number of people dying is a small fraction of the population, especially now that effective vaccines are being rolled out. So just how dangerous would it be if you popped down to see that friend you’ve been missing?

It turns out, if you happen to have COVID, it could be rather dangerous indeed.  It may not be too risky for you, or your friend, but let’s do some simple mathematics to see what the consequences might be for others if you do pass on the virus.

In what follows, I’ll focus on the current outbreak here in Sydney, which began on June 16. It’s unusual at this stage of the global pandemic, since the population has lived largely unrestricted for over a year and perhaps some have become complacent about dealing with the virus, despite the carnage and sacrifices of freedom seen overseas. But the general gist applies anywhere that has significant case counts which aren’t falling dramatically.

Please note though, I am not an epidemiologist. There are many more qualified people, building far more sophisticated models. Listen to them and follow their advice.

One obvious factor to consider is how likely it is that you’re infected.  This will vary depending on the number of cases in the outbreak, how many cases are near you, and how often you go shopping or meet others.  But remember it takes several days for testing to reveal where cases are, during which time the outbreak can spread far across the city.  Also many people with COVID are asymptomatic, or at least asymptomatic for a period while they are infectious. None of the people who’ve passed on the virus so far have thought they had it at the time.  And it seems the Delta strain may take as little as a few seconds of contact to transmit.  But let’s set that question aside, and look at what happens if you do transmit it.

So suppose you unknowingly have the virus, and choose between two courses of action, one that passes it on to another person, and the other that avoids doing so.  From an ethical stand point, just how bad is it if you opt for the former?

To start, let’s consider the average risk of death for the person you infect. Case fatality rates for COVID-19 are in the range of 1-3% in most countries, but of course these will vary depending on many factors: the standard and capacity of health facilities, who in the population is getting the disease, how many of those are vaccinated, and the virulence of the prevalent strain.

In the Sydney outbreak we’ve had relatively few deaths. As at July 26, there have been 10 in this outbreak, whereas total case counts are now above 2000. However, that neglects the delay between cases being identified and consequent deaths. A study in the Journal of Public Health published in March finds the average lag is 8 days (even longer if a lower proportion of those infected are over 60 years old).

So a more comparable estimate of cases might be the number of locally acquired cases reported up to July 18, which is 1364. That yields a case fatality rate in this outbreak of 0.73%, which is indeed low by global standards of COVID. But while it might seem like a small number, that’s 7300 micromorts, which is equivalent to spending over 7 months as a British soldier serving in Afghanistan.

Now perhaps you and your friend are vaccinated, in which case the mortality risk to you is substantially lower. But while vaccination helps prevent your death, it is far less effective against transmitting the virus. And ethically speaking we need to consider what happens if your friend then passes the virus on further. The probability of this will vary according to the situation. If your friend is actually someone you’re  keeping locked in your cellar as a slave, then there’s no way for them to pass it on, and you can feel relieved of any moral qualms about deaths due to passing on the virus further (we can set aside other moral considerations in this scenario, since we’re talking about manslaughter here, so why worry about a minor case of enslavement).

Since normally we have little control over how others behave, even friends, let’s assume the friend is exactly like the average other Sydneysider in this outbreak. We can roughly guess the effective reproduction rate of the virus in the conditions of this outbreak by looking at case counts over time. Here is a chart of the number of new locally acquired cases by date during the outbreak so far.

Bar chart of new locally acquired cases in NSW 16.6-26.7.2021

Source: NSW Government

In the 24 days through to the imposition of city-wide stay-at-home restrictions on July 10, new cases grew exponentially to reach 103. For the purpose of this argument, I’ll assume a fixed cycle of infection lasting 3 days (this is not essential, since values below are still valid albeit with slightly different timeframes if the cycle is longer or shorter). A quick calculation yields a reproduction rate, r = 1.8.  That is, each infected person infects an average of 1.8 other people every three days.

At this level of transmission, 100 people will infect 180 people in three days, who will infect another 324 people after six days, and so on. If this continues for 15 days, the total number of resulting infections will be 4126, or 41.26 people per original infected person. If each of the 41 people infected via our friend has a 0.73% chance of dying from the virus, there is over 25% chance that at least one person will die. And that’s only counting infections in the next 15 days.  Giving the virus to one person is significantly worse than Russian roulette under these conditions.

Of course, as Sydneysiders are uncomfortably aware, the government here has been instituting successively more stringent restrictions across the city. And in the two weeks or so since July 11, the growth in case counts has happily slowed somewhat. Unfortunately, lockdown efforts so far appear to be insufficient to bring case counts down dramatically, with over 170 new cases reported on July 25.

But let’s be wildly optimistic and say that the reproduction rate is now down to 0.9. In that case, 100 people infect 90 people who infect 81 people, so that after 15 days the expected total number of resulting cases is 469. Your single transmission to your friend then leads to around 3.4% chance of at least one death as a result of infection in the next 15 days.

While that’s much better than before the citywide restrictions, it is nothing to shrug off. It’s similar to the chance of dying:

Most would agree that all these events have a “reasonable chance of killing someone”. And so too does passing on the virus under the current Sydney outbreak conditions.

So please, please be careful. Your choices can save lives.

Vaccination of the Nation

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.

(Click image to expand for full view)

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).

World Map of Vaccination Rate Quintiles
(Click image to expand for full view)

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.