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Covid Immunity Calculus

Quiz Questions:

  • Which foreign country or territory is closest to New Zealand by jetplane?
  • Which foreign country or territory had the world's highest per capita incidence of Covid19 last week?

Before giving the answers, I would note that the worst-affected region of the world in September 2021 is the Caribbean, from where the West Indies cricket team comes. In the last week, these countries affiliated to the West Indies were in the Covid19 top 20 (for cases): Grenada (#3), Dominica (#5), St Vincent (#10), Barbados (#13), St Lucia (#16), Antigua (#18). Most of these countries have not previously featured in the Covid League Table. And then there was Bermuda (#2) (which has previously featured), where New Zealand won the Americas Cup in 2017. In the Covid19 top 20 (deaths) last week were: Grenada (#1), Saint Lucia (#4), Bermuda (#5), Antigua (#8), Dominica (#9), Anguilla (#17). How many of us in New Zealand have a clue about the tragedy the West Indies – our sporting brethren – are facing right now? (There are also, in both top-20 lists, a number of other Caribbean countries which do not play cricket.)

Number 20 in the deaths' list last week was French Polynesia, homeland of New Zealand's first colonisers, homeland of Tupaia. French Polynesia was number 1 at the beginning of this month. Their caseload in August became so high that they stopped counting cases in September.

Back to the Quiz Questions, both have the same answer: New Caledonia. New Zealand's nearest neighbour (excluding Norfolk Island) is the worst afflicted territory in the world, yet hardly anybody in New Zealand knows how affected they are. We in Aotearoa are so self-absorbed. For Covid19 deaths per capita last week, New Caledonia was ranked second (to Grenada). Up until this month, New Caledonia was the one French territory that had seemed immune from Covid19. (And France itself is doing surprisingly well this year, at least in terms of covid-attributable deaths.)

The vulnerability of regions such as the South Pacific and the Caribbean should come as no surprise to us in New Zealand. After all, the worst afflicted territory in the world from the 1918 to 1919 influenza pandemic was New Zealand 'protected' Samoa, then recently 'liberated' from Germany.

More quiz questions. Which polities in the 'white' British Commonwealth were most afflicted by Covid19 last week? In cases, the United Kingdom as a whole is worst, plus the Isle of Man. But deaths are much less than in previous British outbreaks. So, which 'white' Commonwealth polities are in covid crisis at present? The worst is the Canadian province of Saskatchewan, closely followed by the more populous Alberta. British Columbia – think Vancouver – is not looking too good, either. Manitoba is not so bad this time for Covid19, but my contact in Winnipeg tells me that there is a different severe respiratory illness happening there. This is particularly worrying, because September in Canada is like March in New Zealand. It's late summer, and probably the month least likely to be affected by regular winter infections.

(I note that Victoria, Australia, with record case numbers reported today, has now reached a daily incidence half of that of Alberta last week.)

In the United States, the northern Rocky Mountain states are now particularly badly afflicted: Montana, Idaho, Wyoming. Also the northern prairie states that border Canada. All of these areas in Canada and USA are noteworthy because, hitherto, they were the least inflicted parts of those two countries. Yes, these are among the least vaccinated provinces of both countries, and these regions have been taunted as being hotbeds of anti-vaxxer stupidity. More pertinently, these are places that are very similar to New Zealand, and are familiar to many New Zealanders. The main reason that they have comparatively low vaccination rates is the same as for Aotearoa New Zealand; they had a sense of exceptionalism, that Covid19 was mainly a problem somewhere else, and that they could take a comparatively sedate approach to protecting themselves by boosting their immunity levels. As in New Zealand, vaccination hesitancy in those places tends to melt away when the public health crisis takes hold.

Canada is a particularly useful country for doing comparative regional analysis of Covid19's spread, and the different vulnerabilities of the different regional population spaces. The other particularly useful set of population spaces is the European Union. I have hardly ever seen any reporting of New Zealand's public health experts doing useful statistical comparative analysis of either Canada's provinces or European Union countries.

Immunity Calculus

So, what makes some populations more vulnerable to Covid19 (and to those other diseases most comparable to Covid19)? A calculus approach can work – not formal calculus as in differentiation and integration – but an approach which assigns good-guess numbers to relevant concepts; numbers that are fully contestable, and which some people (but not all people) might believe to be zero.

The calculus I am setting-up attributes modern first-world populations with an average pre-2020 immunity score of 95, and postulates a covid-target score of 100 that would be the minimum required to live normally in a covid-endemic world. This means that immunisation processes – vaccinations and natural exposure – are needed to raise a population's score to above 100. And it means that processes which diminish the immunity score need to be avoided or offset. (For the technically minded, I am also postulating a population standard deviation of 5 immunity points. And I suggest that covid immunity has a negative skew, with various comorbidity and age factors combining to create a tail of under-immunity.)

(I am also suggesting that modern third-world populations have an average score of 90 with a standard deviation of 10, and that small island and other remote but still connected populations had an average pre-covid immunity score of 85, with a standard deviation of 7½. Thus these populations have larger proportions of more vulnerable people.)

First, what does an average score of 95 mean. It represents acquired immunity to a whole range of infectious diseases; acquired through exposure and imprinting since (and indeed before) the dawn of humanity, and also through being otherwise healthy. If a population had an average score of 95 (and the standard deviation is 5), then about 16% of its members will have had a pre-covid score of over 100. If everybody in such a population has an equal chance of catching Covid19, then 84% of those catching the virus would test positive, and about 50% of victims would have symptoms of different degrees of severity. (For more transmissible covid variants, such as Delta, the 'equal chance' of catching Covid19 is greater than for less transmissible variants.)

If, as a consequence of Covid19 and the defensive measures taken, a population can get its mean immunity score up to 105, then only around 2½ percent of that population will be vulnerable to a symptomatic expression of the disease. (That's two standard deviations, for the statistically-literate.)

On the matter of 'defensive measures', there are broadly two kinds, all of which have some associated costs. There are barrier measures, which come with some costs. Then there are two kinds of immunisation measures; natural infection, and vaccination. Natural infection has considerably more potential costs than vaccination. The cost of barrier defensive measures is a reduction in a person's immunisation score. If such measures – quarantines, lockdowns, facemasks, physical distancing – are mandated at the population level, then that population's average immunity score will decrease; the extent of this fall in population immunity will be related to both the comprehensiveness and the duration of the 'defensive mandate' imposed by government.

Population immunity scores are raised by, say 1 point per each 10% of the population double-vaccinated. However, because RNA virus infection immunity is generally temporary, by six months after the second vaccination shot, a person's immunity may have halved, and halved again over the next six months. To avoid this waning immunity, booster vaccinations are required. Vaccinations potentially have some costs – side effects – but these are very small for most modern vaccinations.

Population immunity scores are also raised by epidemic and endemic natural infection. (I was gratified to finally hear two New Zealand epidemiologists finally acknowledge the population vulnerability associated with low levels of natural immunity. Shaun Hendy did so last week, and Rod Jackson yesterday morning.)

Natural infection is of course, very costly. The costs are in deaths, illness, ongoing symptoms, and possibly reduced life expectancy through organ inflammation and the like. Nevertheless, if it happens, it is necessary to account for the immunity gains as well as the mortality and morbidity losses. And, for a novel virus, there can be no vaccination during its first epidemic waves. For a population's first unmitigated exposure to Covid19, I would estimate an increment of 4 immunity points, with 3 immunity points from the next wave, then 2 and then 1. (Mitigations reduce these numbers.) As with vaccinations, natural immunity also wanes; immunity is supported, eventually, by endemic infection.

Defensive barrier measures give substantial gains during the early phase of a new epidemic disease. The biggest potential gain is the possibility of elimination – as indeed appears to have occurred with SARS in 2003. This was a serious event with similar origins to Covid19 that did escape the bounds of Asia; Toronto, Canada, had a significant outbreak which it eliminated. Nevertheless, such defensive measures have a cost, in both lost general immunity and lost specific immunity. So, the ideal barrier measures are short-lived; further, they should never be implemented if there is statistical certainty (about 95% certainty) that the virus of concern is not circulating in the population of concern.

Barrier defence undertaken when there is (with statistical certainty) no threat involves costs without offsetting benefits. I am estimating a loss of 2½ immunity points for every six months of substantial barrier defence.


Sweden is an economically advanced country, and with a population with fewer comorbidities than most. I will give Sweden a standard pre-covid immunity score of 95 in January 2020. In the following 12 months, Sweden adds 5 points for natural immunity from two large outbreaks with little mitigation. Since then it scores 3 more natural immunity points (for Alpha and Delta outbreaks), and seven points for 70% vaccination. Sweden's four outbreaks have all been within six months of each other, so I take away no points, so far, for lost immunity. Sweden's present immunity score is 110. So just 0.5% of its population is at present risk from Covid19, and much less than that at serious risk.

Sweden's cost has been a somewhat high death and illness toll, mainly incurred during its first two outbreaks.


Poland has a slightly lower life expectancy than Sweden, so I'll give it a starting score of 94. As a result of barrier defences before its outbreak in late 2020, it will have had an estimated immunity score of 91 when the outbreak hit. Three outbreaks have taken its natural immunity to 100. And 50% vaccination takes it up to 105. After the first outbreak hit, barrier defences have been ineffective, so I will only deduct 1 immunity point for later barrier protection, giving Poland a present score of 104.

Excess deaths in Poland are 3.7 times as great as in Sweden. This is, it would appear, mainly because the principal effect of the initial barrier protection (which kept out the first European outbreak) was to increase the vulnerability of the Polish population to the second 2020 European outbreak of Covid19.

Alberta, Canada

The situation here would appear to be similar to Poland (albeit with a starting score of 95), except that I would give Alberta a natural immunity increment of just 2, a vaccination score of 6, a loss of immunity score of 8 (7 as a result of barrier defences, 1 as a result of waning vaccination immunity given than Canada was an early vaccinator). That gives Alberta a present score of 95, making it as vulnerable as Sweden was in January 2020. We are seeing the consequences of that vulnerability now, in Alberta, given that the barrier defences have breached.

The health costs in Alberta so far have been much less than in Poland, but will be significantly worse than in Sweden.

Victoria, Australia

Starting at 95, down to 89 as a result of its strong barrier defences (including the longest big city lockdown in the world), up 1 for natural immunity from its 2020 outbreak, and up to 95 as a result of vaccination. Thus Victoria is at a similar vulnerability level as Alberta was before its present outbreak. The latest figures for Victoria suggest that its present outbreak is currently at half the intensity of Alberta's; but it's looking like a 'slow train wreck', with signs that increased immunity is only just outpacing increased vulnerability. Further, once Victoria is fully vaccinated, if it persists with barrier defensive measures then its immunity score will decrease in 2022 unless it compensates with an adequate booster vaccination program.

Costs in terms of deaths and illnesses so far are less in Victoria than in Sweden. But the final tally is not in, and Victoria has suffered much more disruption to its people's day-to-day lives. Also, Victoria would appear to be very vulnerable to other diseases, as Manitoba Canada is experiencing.

Aotearoa New Zealand

Starting out at 95, New Zealand loses 5 immunity points for its barrier defences, and gains 5 points for its vaccinations to date. New Zealand has no natural immunity to Covid19, to speak of. Aotearoa New Zealand has the same inadequate immunity measure as Alberta and Victoria; 95, the same that Sweden had in January 2020.

Fortunately, barrier protection in New Zealand has yielded low rates of death and illness so far. But the disruptive effects from those measures have been high, and projections are that these costs will be higher in 2022 than in Victoria. As in Victoria, the risk for 2022 is that decreased immunity from barrier measures, and from waning vaccination immunity, will decrease New Zealand's covid immunity score in 2022.

The biggest problem in New Zealand has been the misuse of barrier defences, with the most glaring example being a substantial imposition of barrier protections onto parts of the country (eg the South Island) that clearly have not had any presence of the Covid19 virus for a very long time.

Aotearoa New Zealand will be, in 2022, at increased risk from Covid19, from other illnesses, and from substantial economic disruption.

Pacific Islands

I won't do the sums here. We can see from the French Pacific territories, and also from the experiences of Fiji and of the Caribbean Islands, that such islands are extremely vulnerable, in part because they are islands which are somewhat sheltered from the pathogens that circulate endemically through the world's most connected cities.

We think of Samoa's experience in 1919.

And we think of the impact that metropolitan France – with its high endemic incidence of Covid19, and high associated immunity levels – is having on its island territories. The most significant group of Covid19 victims to date are poorer less immune people, such as working people in these territories, who out of necessity provide services to richer more immune people.


Keith Rankin (keith at rankin dot nz), trained as an economic historian, is a retired lecturer in Economics and Statistics. He lives in Auckland, New Zealand.

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