## The Coronavirus Vaccine Effect

Posted in Covid-19, mathematics with tags , , , , , , on December 12, 2021 by telescoper

When I was updating my Covid-19 page today I thought I would try something a bit different. Here are the cases and deaths (in the form of 7-day rolling averages) as I usually plot them:

You can see a slight recent downturn – the latest 7-day average of new cases is 4214.3; it has been falling for a few days. A log plot like this shows up the changing ratio between deaths and cases quite well, as in l if you multiply a quantity by a factor that manifests itself as a constant shift upwards or downwards. There is clearly a bigger shift between the orange and blue curves after 500 days than there is, say, between, 300 and 400.

(I don’t think you can read much into the gap between the curves at the beginning (up to around 100 days in) as testing coverage was very poor then so cases were significantly underestimated.

Anyway, to look at this a bit more clearly I plotted the ratio of daily reported deaths to daily confirmed cases over the course of the pandemic. This is the result:

The sharp downward glitches occur whenever the number of reported deaths is zero, as log of zero is minus infinity. The broader downward feature after about 300 days represents the period in January 2021 when cases were climbing but deaths had not caught up. To deal with that I tried plotting the deaths recorded at a particular time divided by the cases two weeks earlier. This is that result:

The spike is still there, but is much decreased in size, suggesting that a two week lag between cases and deaths is a more useful ratio to look at. Note the ratio of deaths to cases is significantly lower from 500 days onwards than it was between 200 and 400 (say), by a factor a bit less than ten.

This obviously doesn’t translate into a direct measure of the efficacy of vaccines (not least because many of the recent cases and deaths are among the minority of unvaccinated people in Ireland) but it does demonstrate that there is a vaccine effect. Without them we would be having death rates up to ten times the current level for the same number of daily cases or, more likely, we would be in a strict lockdown.

On the other hand if cases do surge over the Christmas period there will still be a huge problem – 10 % of a large number is not zero.

## The vaccine effect

Posted in Covid-19 with tags , , , on July 28, 2021 by telescoper

I saw this nifty graphic from the Financial Times floating around on social media and thought I would share it here. It’s a nice demonstration of the way the use of vaccines has impacted mortality rates from Covid-19. Basically the vaccines reduce the probability of a death by a factor greater than 10 (i.e. are more than 90% effective in doing this). On the logarithmic plot this appears as a downward shift in the “risk of death” that is more or less independent of age.

This behaviour is generally consistent with the observation that while infections in the UK are quite high the mortality rate is still rather low. Low is not zero, however, and there will still be some deaths if infection levels are high: a small fraction of a large number can still be significant.

Incidentally, about 70% of the adult population of Ireland has now been vaccinated with about 80% having received partial vaccination. The fraction of the total population fully vaccinated is about 54%. On this measure Spain has just overtaken the UK in vaccinations; Ireland is well above average for the EU. The USA and Israel have both flattened out considerably.

When I got back from my break I tried my best to update the statistics relating to Ireland here. Doing so reminded me that when I first decided to plot the data on a log y-axis I got a slew of comments on Twitter complaining that I was “manipulating the data”! The backlash against anything even simple mathematics is quite extraordinary sometimes.

Anyway, the latest logarithmic plot looks like this:

The death figures are unreliable because of the lingering effects on the ransomware attack on the Health Service Executive IT system but do seem to be much lower relative to infections than they were at earlier stages of the pandemic, even allowing for the fact that the first peak in the case curve should be higher as testing was not so extensive at this early stage. The 7-day average of new cases is currently around 1200-1300 per day.

It still fascinates me how the case numbers managed to stay roughly constant for such a long time at such a high level earlier this year…

## Vaccination in Ireland

Posted in Covid-19 with tags , , , , , , , on December 5, 2020 by telescoper

A very interesting twitter thread from Dr Ronan Glynn (Ireland’s Deputy Chief Medical Officer) inspired me to write something in response to the very positive recent developments with regard to a SARS-CoV2 (Covid-19 vaccine). In Switzerland the regulator does not feel that there is enough data yet for approval to be granted yet, so I have some reservations about the fast-tracking of the process in the United Kingdom. Nevertheless there has to be a tradeoff between the risk of potential reactions or side-effects of a vaccination and the immediate danger to public health arising from Covid-19. As someone recently said to me on Twitter: “if you’re not going to fast-track during a global pandemic, when would you?”.

Here in Ireland it is likely that a vaccination programme will commence early in the New Year. To answer a question I posed a few weeks ago, priority will be given to front-line health care workers, especially those working in care homes, and the elderly. If all goes to plan there will be something like full vaccination of the population by September 2021.

I am not in a priority group so will have to wait a while for my jabs, but I will certainly take the vaccine as soon as it is available to me.

No doubt there are some people out there who for various reasons will refuse to be vaccinated. I doubt anything I say here will persuade them but it is I think valuable to look at the history of vaccination programmes in Ireland for various illnesses, which is what Dr Glynn’s thread does.

To give a few examples:

• Smallpox. In 1863 vaccination against smallpox was made compulsory for all children born in Ireland. Deaths fell from 7,550 for the decade to 1880 to the last reported death from smallpox here in 1907. Smallpox was declared eradicated in 1979 – this one vaccine saved 100s of millions of lives globally.
• Diptheria. Diphtheria was a very common cause of death among children until the 1940s – there were 318 deaths from it reported in Ireland  1938. With the introduction of a vaccine, the number of deaths fell year on year with 5 deaths in 1950; the last death notified from diphtheria was in 1967.
• Poliomyelitis. In Ireland, polio infection (mainly affecting young children causing long term paralysis) became more common after 1920 with major epidemics during the 1940s & 1950s. A vaccine was introduced in 1957. The last reported case of polio here in Ireland 1984.
• Measles. The number of cases of measles declined dramatically after introduction of measles vaccine in 1985, from 10,000 cases in 1985 to 201 cases in 1987.
• Meningococcal Meningitis. In 1999, there were 536 cases of meningococcal meningitis in Ireland The meningitis C vaccine was introduced in 2000, with the meningitis B vaccine introduced in 2016. Cases of meningococcal meningitis have dropped more than 80% since these vaccines were introduced.

These are of course wonderful advances in public health, but none of them provided total relief immediately. It will be the same with Covid-19. The availability of a vaccine will not end the pandemic overnight, but at least it will enable us to plan for a phased return to normal.

While there is great cause for long-term optimism, there are still reasons to be anxious in the short term. There will be many months before a full vaccination programme is in place and in that time cases (and, sadly, deaths) could rise substantially. There is a real danger will think that it’s all over, that they can let down their guard and ignore social distancing.

Ireland is currently relaxing its Covid-19 restrictions for the Christmas period, but it is doing so from a level of over 260 new cases per day. The Coronavirus is currently circulating in the community at a far higher rate than it was in the summer and if it increases at a similar rate to August then we could be in for a huge surge. I fear that by the New Year we might be in real trouble again. It would be tragic if people lost their lives owing to complacency with safety so nearly in sight.

## Dare we hope?

Posted in Covid-19, Poetry, Politics with tags , , , , , on November 9, 2020 by telescoper

A short passage from Seamus Heaney’s verse play The Cure at Troy: A Version of Sophocles’ Philoctetes has been much quoted recently. It even ended the RTÉ News last night:

The passage begins

History says, Don’t hope
On this side of the grave.

Well, there’s an additional reason for hope this morning, in the announcement of good progress in the search for a vaccine against Covid-19. The two pharmaceutical companies involved are Pfizer (USA) and BioNTech SE (Germany). The reported efficacy of the vaccine tested so far is over 90%, which is far higher than experts have predicted. Now these are preliminary results, not yet properly reviewed, based on a sample of only 94 subjects, and I’m not sure what motivated the press release so early in the process. I’m given to understand that the type of vaccine concerned here would also be challenging to manufacture and distribute, but we’re due for some good news on the Coronavirus front so let’s be (cautiously) optimistic.

On top of that it seems that Ireland at least is turning the tide against the second wave, with new cases falling every day for over a week:

Dare we hope?