climateetc--2020-05-16--Culturally-determined response to climate change: Part III

Climate change affirmative responses to all survey questions are culturally determined , and across National Publics related to religiousity .
Cultural attitudes inappropriately push climate policy .
Post one of this series demonstrated a strong correlation across nations between religiosity , and their responses to unconstrained questions aligned to Catastrophic Climate Change Culture ( CCCC ) , from a YouGov climate-change attitudes survey .
The bold-blue series in Chart 1 below shows this , with the muted-pink for a less strong alignment .
This expression of belief in CCCC I term Allied Belief ( ABel ) ; it ’ s @ @ @ @ @ @ @ of CCCC with ( all ) the main religious Faiths , which disables Innate Skepticism ( ISk ) of CCCC .
The second post showed that very different results are obtained for climate-change affirmative responses to reality-constrained questions ( muted-orange and muted-red series ) , which across nations anti-correlate with their religiosity .
The bold-orange series shows the ( estimated ) Core Belief ( CBel ) in CCCC , i.e .
from individuals who still grant it top-priority in the presence of ‘ ultimate ’ constraint .
The muted-red trend and red crosses @ @ @ @ @ @ @ .
Reality clashes re-enable ISk about CCCC for religious people .
The second post fully explains all Chart 1 features .
This ‘ big picture ’ chart is needed to better understand the following sections .
All of the questions that produce linear responses with religiosity per above , I term as ‘ Strongly-Framed ’ questions .
But we met some questions in Post 1 , such as ‘ Do you think that you personally could be doing more to tackle climate change ?
’ , for which ( as was confirmed ) @ @ @ @ @ @ @ ’ wasn ’ t expected .
However , this doesn ’ t mean such ‘ Weakly-Framed ’ questions necessarily have no relationship with religiosity ; it turns out that they do , but it ’ s not linear .
For clarity , Table 1 towards the end of this post lists which questions are Strongly/Weakly-Framed .
• The Envelope of responses to Weakly-Framed questions On the above chart , bold-orange to muted-red to muted-orange trends , represent responses to reality-constrained questions of decreasing constraint strength .
Imagine a trend a little weaker still @ @ @ @ @ @ @ so a bit higher up on the Y scale .
Bold-blue to muted-pink trends represent responses to unconstrained questions with decreasing emotive / existential alignment to CCCC .
Imagine a trend with somewhat weaker alignment still , so less gradient than pink .
It seems that responses to Weakly-Framed questions are ( in the main ) anywhere between these two imagined trendlines , smeared as it were between pink and orange ‘ modes ’ .
For example , Chart 2 below show national responses for the ‘ could be doing more ’ option @ @ @ @ @ @ @ above .
Note : The superimposed envelope of expected responses ( assuming the cultural modality explanation is true ) is notional , drawn by using Chart 1 as a guideline for where the imagined trends described above would approximately sit , plus some margin for variability around the trends .
In practice , I don ’ t know their precise positions and even less the legitimate variability of data-points relative to same [ albeit the orange variability about trend is a lot larger than pink ; I didn ’ t bother to depict @ @ @ @ @ @ @ most data , so is at least indicative of potential cause .
National publics aren ’ t climate literate , so it seems unlikely that even where strong reality or strong CCCC alignment isn ’ t invoked , rationality could get purchase .
It appears responses simply drift between the two main culturally-determined modes .
Given I don ’ t know where the edges of the envelope actually are , it seemed reasonable to speculate that Indonesia and Thailand might be legitimately covered , albeit an implication of noisy data .
However , @ @ @ @ @ @ @ all this couldn ’ t possibly be the case for Italy or Spain , which ought to have much lower climate concern scores , consistent with being closer to the low point between the two cones .
These two nations were noted in the last post to have a higher ‘ Children ’ s Strike Weekly ’ ranking than initially seemed likely for their religiosity level .
For Spain at least , this is probably due to an unusually high religiosity gap between children and adults .
Both nations also have very high @ @ @ @ @ @ @ for cultural causes claiming high moral ground , to which youths are more vulnerable .
So , when Weakly-Framed questions don ’ t invoke more potent effects , might irreligious and disaffected youth wield sufficient influence to shift national attitudes ?
I don ’ t know .
I figured looking at another Weakly-Framed question may help .
Affirmative answers to : ‘ The climate is changing and human activity is mainly responsible ’ ( the very first question mentioned in this series ) , are plotted below .
The superimposed pink / orange @ @ @ @ @ @ @ on Chart 2 above .
The first thing to note is that this question is slightly more CCCC-aligned than I guessed .
There appears to be more grouping around the pink line than the orange , albeit this isn ’ t quite enough to have broken the smeared / dual-mode pattern .
This could mean the true pink line ought to be a little steeper , which in turn means Thailand is possibly within the envelope .
However , not only are Spain and Italy clearly outside again ( and in similar positions @ @ @ @ @ @ @ by Indonesia and India .
Interestingly , Indonesia has recently seen a wave of mass youth protests against perceived threats to democracy and liberal values , in a country where conservatism and Islamist elites are gaining more power .
Countering with accusations of blasphemy can only help open a religiosity gulf between secular youth and religious elites ( very relevant here ) .
The linked article notes regional support and even direct links to youth climate protest , with Thailand , Malaysia and the Philippines all named .
India has a massive youth @ @ @ @ @ @ @ population below the age of 25 , and has also featured mass youth protests over recent years .
These have now coalesced against the new citizenship laws , but this wave started back in 2016 and is ultimately generic opposition to conservative religious power ( this time Hindu ) , again seen as a perceived threat to liberal values and democracy .
All the nations mentioned in the above paragraph have national religiosity 50 % or higher ( however much less this is for youth ) , and are at the upper-edge of @ @ @ @ @ @ @ 2 or Chart 3 , or both .
It seems something systemic is happening that can ’ t just be noise and is pretty likely linked to youth protest , but quite what ?
If I assume a youth influence , however this works it may be a pointer to the future of the relevant nations , albeit interpreting that future isn ’ t so easy .
It hinges upon what type of youth belief is the driver .
Although some would represent an increase of core believers in CCCC , albeit occurring @ @ @ @ @ @ @ total belief is high , meaning much is likely Allied Belief .
However , not this time through an alliance with religious faiths , but political culture , like the strong alliance between CCCC and Lib/Dem culture within the US .
So , at the very least the relevant nations would shift leftwards on Chart 1 , but could potentially fall out of the plot altogether if like the US ( or Vietnam ) a more complex local cultural jigsaw emerges , which needs a targeted analysis .
Interestingly , about half the @ @ @ @ @ @ @ 2 and 3 .
This plus the bounded area is enough for a fairish correlation between the two responses ( SI Chart F5yx , r=0.68 ) .
If we needed another hint that it is not rationality driving affirmative responses to ‘ The climate is changing and human activity is mainly responsible ’ , this is it .
As the first post notes , publics can ’ t possibly give rational responses to the correlating Chart 2 question .
The apparent lack of rationality in the above responses prompted me to hunt for @ @ @ @ @ @ @ ‘ envelope ’ charts as above , mapping responses to one of the most objective questions from the main YouGov climate-change attitudes survey .
This Weakly-Framed question asks which countries have had the most negative impact on climate-change and , as demonstrated in the first post of the series , responses aren ’ t linear with religiosity .
Answers are available from relatively common and culturally unconflicted knowledge .
However , even in this case rationality plays a very modest role , very much second fiddle to cultural influence that occurs via the @ @ @ @ @ @ @ to word-count limitation , I shunted this analysis to SI Footnote 2 .
Similarly to children , another sub-demographic within irreligious nations at the LHS of Chart 1 where core belief in CCCC prospers more than in the general population , is the elite .
Even within democracies , small elites can heavily sway policy to a direction not supported by the populace .
For instance , the UK , Germany and Scandinavia , all have very strong emissions policies despite per the bold-blue series in Chart 1 , having a very high @ @ @ @ @ @ @ plus , all nations have very small Core Belief in climate catastrophism ) .
This wouldn ’ t be a problem if the policies were aligned to mainstream science conclusions .
But ultimately , being initiated by an emotive belief in CCCC , they are latterly and inevitably trending towards CCCC goals ; i.e .
the emergency avoidance of imminent global catastrophe .
The easy acceptance of Greta/CSW by secular elites is not a coincidence .
In highly religious countries , much of the influence of elites and the functioning of society is @ @ @ @ @ @ @ Notwithstanding the relatively new ( and superficially high , i.e .
from ABel ) climate concerns , those elites and indeed society generally haven ’ t to date abandoned this model .
Yet in countries where religion has long atrophied over generations , newer culture can more easily muscle into elite layers via the provision of high-moral-ground plus emotive persuasion .
Subconsciously , the latter features are extremely desirable as shortcuts for promoting / extending an elite profile ( see SI Footnote 3 ) , when exhausted religion no longer supplies this service @ @ @ @ @ @ @ irreligious nations ( per the last post ) are not expressions of what the local publics think , en-masse , but extreme frustration expressed by small minorities because for sure their local publics mostly don ’ t think like them .
In mistakenly assuming such actions reflect popular feeling , and thus compliantly onboarding extreme demands ( which also contradict mainstream science ) , already culturally compromised elites are marching dangerously further and further out of alignment with the mass of their own publics .
Tension from such dislocations is already causing some @ @ @ @ @ @ @ 4 ) .
Highly religious nations are protected from similar extreme policy choices , by the strongly continuing commitment of their elites to much older irrational fairy stories , aka religions .
The expectation is that policy push from elite attitudes would occur most within nations from the LHS of Chart 1 , much like XR and CSW presence .
This expectation can be checked by looking at the penetration of highly challenging policies ( socially or to infra-structure or both ) that also have a high virtue-signaling aspect .
Whether or not @ @ @ @ @ @ @ emissions reduction or the environment generally , is not particularly relevant .
A suitable such policy is the promotion of Electric Vehicles ( EVs ) .
Chart 4 , introduced in the last post , represents either of the orange series on Chart 1 ( depending on the scale ) , with many more nations thrown in .
The Y scale happens to match estimated CBel , i.e .
the original UN poll vote-share for action on climate-change , divided by 6 .
The blocks a ) to d ) and the color-coding @ @ @ @ @ @ @ about the main trend is largely due to GDP-per-Capita ( GDPpC ) within each religio-regional group .
So , we expect EV policy penetration to largely be dictated by cultural motivation , and hence be highest at the LHS .
BUT… this won ’ t be wholly independent of economic issues ; those countries that are motivated for this policy must also have a robust enough economy to create incentives plus charging infra-structure , plus a high enough GDPpC for the local market to afford EVs .
Adapted to economic necessity , the @ @ @ @ @ @ @ economies ( in an absolute sense ) plus at the top-leftmost , will have the greatest EV penetration .
The numbers trailing some of the nation labels derive from the Top 18 Electric Car Countries in 2020 , showing penetration per nation by market-share of new EV sales .
Eleven nations in Chart 4 also appear within that league table ; I compressed the ranking into a scale 1 to 11 , in order to skip the missing ones .
While strict ranking order from top-left isn ’ t observed , all but @ @ @ @ @ @ @ at the top-left corner , as expected .
The only exception in that peer-group without a ranking , is the Czech Republic , which has the lowest absolute GDP ( 45th in IMF list ) of the peer group .
Conversely , the only nation not in the top-leftmost bunching , is Japan .
This nation ( in a unique religio-regional group unrelated to the dark blue coding ) , possess the highest absolute GDP ( 3rd in IMF list ) on the chart .
This data reasonably confirms the above expectations from @ @ @ @ @ @ @ .
As noted in section 4 of the last post and even in normal times , a huge problem for those governments trying to push this and other challenging policies , is that once the public grasp the reality issues associated with implementation , their support is unlikely to get beyond the thick orange Core Belief line in Chart 1 , maybe at the most the muted-red Strongly-Constrained Belief line .
Unless for special circumstances , like the immense amounts of hydro-electricity in Norway .
And in current times , a huge new @ @ @ @ @ @ @ of COVID-19 , which for a year or two at least will squeeze even the CBel line still further downwards regarding the choice of a true top priority .
• What this series tells us Assuming findings are confirmed , and that my explanations are the best fit for same .
Affirmative attitudes to climate-change in the public sphere are cultural .
As such they ’ re also the product of net cultural interaction , mainly with wrt the long-established religious faiths .
The surface alliance of CCCC with religion creates an impression @ @ @ @ @ @ @ resistance for any reality- constrained circumstances .
Overall , where religiosity is low , climate activism is higher ( including child religiosity for child activism ) , likewise for main policy .
A secondary influence in reality-constrained scenarios is GDP-per-Capita .
This likely exacerbates a cultural factor , modulating the main religiosity trend .
Core Belief and policy-support is lower where GDPpC is lower within any religio-regional group .
Even responses to Weakly-Framed questions appear to mainly be determined by cultural influence , albeit occupying a wide envelope .
While prediction from religiosity @ @ @ @ @ @ @ not possible , that they smear between the two main cultural modes is good support itself of the overall cultural explanation .
Systemic excursions from the envelope are perhaps due to youth influence ; merely a culturally divergent sub-demographic .
Even the most objective climate survey question yields very little rationality in responses .
Table 1 summarizes findings .
While each of the mainstream Faiths is theoretically a separate cultural entity , their relationships with CCCC as presented in this series don ’ t appear to depend on the particulars of any faith @ @ @ @ @ @ @ .
At least purely in respect of reactions to the newcomer of CCCC , currently , all Faiths appear to act as though they ’ re part of a single culture .
Hence , what the presented charts are showing at heart is the interaction between two major cultures ( i.e .
religion and CCCC ) that have come under each other ’ s influence .
For an analogy , I ’ m reminded of those illustrations of two stars falling into each other ’ s orbit , with the occurrence of complex @ @ @ @ @ @ @ this analogy , one a bright young star ( CCCC ) and the other an old red giant ( mainstream religious faith ) .
Except we may know less about the cultural case right here upon Earth than the stellar one millions of light years distant .
Stretching the analogy , most people from the relevant social-science disciplines don ’ t actually recognize a CCCC ; it ’ s kind of ‘ invisible ’ .
But like a black hole orbiting the old red giant , we can tell it must be there @ @ @ @ @ @ @ sense if two bodies with mass and energy ( here , cultural mechanisms ) are interacting .
Hence a culture ( of catastrophe ) must be exerting powerful influence within the social domain of climate-change , and interacting with religion .
There are other bodies in this equation , in the US particularly the heavyweights of Rep/Con and Dem/Lib culture , which entangle old religion and new CCCC both ( and enough to locally disrupt the global trends shown here ; the US has a 4-way cultural dance ) .
Overall though , @ @ @ @ @ @ @ consistent the entanglement of religiosity and CCCC appears to be , globally .
Which also means we can use religiosity as a reliable lens to make the workings of CCCC clearer .
The false narratives of CCCC ( all strong cultural narratives are false , their ‘ purpose ’ requires this ) are powerfully affecting nations and faiths of all types across the globe .
Over the years , many commenters have articulated in some form that the movement against man-made climate-change is effectively ‘ a religion ’ in itself .
The effects @ @ @ @ @ @ @ the public domain at least , they ’ re right .
Such commenters are intuiting ‘ a cultural entity ’ , where religions happen to be the cultural entities they ’ re very familiar with .
Considering CCCC ’ s scale , the now generations-long trend , especially within Western societies , of less rule by the emotive and more by rationality , could well go into reverse through this single phenomenon alone .
The only thing holding off its irrationalities in many nations , ironically , is religious faith .
Covid-19 Addendum @ @ @ @ @ @ @ the effect that Covid-19 is likely to be fatal for catastrophic climate-change culture .
My money on this is no better than anyone else ’ s .
But it says that once Covid-19 is in the rear-view mirror , however long that takes , CCCC will still be a serious force .
Long evolved bio-cultural mechanisms make cultures tenacious , they can pivot to new circumstances and come back from heavy damage ; even turn adverse conditions into advantage ( there are already crude attempts , but they ’ ll get more sophisticated @ @ @ @ @ @ @ hooked to science , which ought to be fatal on its own one day .
But I doubt that day is here .
For guidance , the major faiths span a millennial scale and survived the Black Death plus many more real-world calamities , their fairy-tale fears plus hopes still intact .
This doesn ’ t mean the little secular sister of CCCC necessarily has similar staying power , but ultimately , it works on the same underlying mechanisms .
There are 3 posts in this series , all of which have the @ @ @ @ @ @ @ consist : 1 ) an expanded post , 2 ) a footnotes file , and 3 ) an Excel datafile .
The text below is a streamlined post version , geared to get the concepts across more readily and uncluttered regarding side-issues , detail on methodology , intricate depth , path my exploration took etc .
For folks who want more , the expanded post is ~4800 words .
Be aware that the footnotes file , also having various external references , relates to the expanded post ( though a couple are pointed @ @ @ @ @ @ @ the chart IDs within the Excel datafile are numbered for the expanded post .
However , all sources / data for the charts below can easily be found ( I provided SI IDs in the text ) .
The datafile includes various extra charts too .

by Andy West
Climate change affirmative responses to all survey questions are culturally determined, and across National Publics related to religiousity. Cultural attitudes inappropriately push climate policy.
Introduction
Post one of this series demonstrated a strong correlation across nations between religiosity, and their responses to unconstrained questions aligned to Catastrophic Climate Change Culture (CCCC), from a YouGov climate-change attitudes survey. The bold-blue series in Chart 1 below shows this, with the muted-pink for a less strong alignment. This expression of belief in CCCC I term Allied Belief (ABel); it’s caused by a (shallow) alliance of CCCC with (all) the main religious Faiths, which disables Innate Skepticism (ISk) of CCCC.
The second post showed that very different results are obtained for climate-change affirmative responses to reality-constrained questions (muted-orange and muted-red series), which across nations anti-correlate with their religiosity. The bold-orange series shows the (estimated) Core Belief (CBel) in CCCC, i.e. from individuals who still grant it top-priority in the presence of ‘ultimate’ constraint. The muted-red trend and red crosses bound this estimate somewhat with actual measurements. Reality clashes re-enable ISk about CCCC for religious people. The second post fully explains all Chart 1 features.
This ‘big picture’ chart is needed to better understand the following sections. All of the questions that produce linear responses with religiosity per above, I term as ‘Strongly-Framed’ questions. But we met some questions in Post 1, such as ‘Do you think that you personally could be doing more to tackle climate change?’, for which (as was confirmed) a linear response for ‘doing more’ wasn’t expected. However, this doesn’t mean such ‘Weakly-Framed’ questions necessarily have no relationship with religiosity; it turns out that they do, but it’s not linear. For clarity, Table 1 towards the end of this post lists which questions are Strongly/Weakly-Framed.
The Envelope of responses to Weakly-Framed questions
On the above chart, bold-orange to muted-red to muted-orange trends, represent responses to reality-constrained questions of decreasing constraint strength. Imagine a trend a little weaker still than the last in that sequence, so a bit higher up on the Y scale. Bold-blue to muted-pink trends represent responses to unconstrained questions with decreasing emotive / existential alignment to CCCC. Imagine a trend with somewhat weaker alignment still, so less gradient than pink. It seems that responses to Weakly-Framed questions are (in the main) anywhere between these two imagined trendlines, smeared as it were between pink and orange ‘modes’. For example, Chart 2 below show national responses for the ‘could be doing more’ option to the question quoted in Section 1 above.
Note: The superimposed envelope of expected responses (assuming the cultural modality explanation is true) is notional, drawn by using Chart 1 as a guideline for where the imagined trends described above would approximately sit, plus some margin for variability around the trends. In practice, I don’t know their precise positions and even less the legitimate variability of data-points relative to same [albeit the orange variability about trend is a lot larger than pink; I didn’t bother to depict this]. Yet the envelope covers most data, so is at least indicative of potential cause. National publics aren’t climate literate, so it seems unlikely that even where strong reality or strong CCCC alignment isn’t invoked, rationality could get purchase. It appears responses simply drift between the two main culturally-determined modes.
Given I don’t know where the edges of the envelope actually are, it seemed reasonable to speculate that Indonesia and Thailand might be legitimately covered, albeit an implication of noisy data. However, if Chart 2 has any meaning at all this couldn’t possibly be the case for Italy or Spain, which ought to have much lower climate concern scores, consistent with being closer to the low point between the two cones.
These two nations were noted in the last post to have a higher ‘Children’s Strike Weekly’ ranking than initially seemed likely for their religiosity level. For Spain at least, this is probably due to an unusually high religiosity gap between children and adults. Both nations also have very high youth unemployment levels, an open invitation for cultural causes claiming high moral ground, to which youths are more vulnerable. So, when Weakly-Framed questions don’t invoke more potent effects, might irreligious and disaffected youth wield sufficient influence to shift national attitudes? I don’t know. I figured looking at another Weakly-Framed question may help. Affirmative answers to: ‘The climate is changing and human activity is mainly responsible’ (the very first question mentioned in this series), are plotted below. The superimposed pink / orange trends and envelope are the same as on Chart 2 above.
The first thing to note is that this question is slightly more CCCC-aligned than I guessed. There appears to be more grouping around the pink line than the orange, albeit this isn’t quite enough to have broken the smeared / dual-mode pattern. This could mean the true pink line ought to be a little steeper, which in turn means Thailand is possibly within the envelope. However, not only are Spain and Italy clearly outside again (and in similar positions), they’re now joined by Indonesia and India. Interestingly, Indonesia has recently seen a wave of mass youth protests against perceived threats to democracy and liberal values, in a country where conservatism and Islamist elites are gaining more power. Countering with accusations of blasphemy can only help open a religiosity gulf between secular youth and religious elites (very relevant here). The linked article notes regional support and even direct links to youth climate protest, with Thailand, Malaysia and the Philippines all named. India has a massive youth demographic, with 50% of its population below the age of 25, and has also featured mass youth protests over recent years. These have now coalesced against the new citizenship laws, but this wave started back in 2016 and is ultimately generic opposition to conservative religious power (this time Hindu), again seen as a perceived threat to liberal values and democracy.
All the nations mentioned in the above paragraph have national religiosity 50% or higher (however much less this is for youth), and are at the upper-edge of or above the envelope in either Chart 2 or Chart 3, or both. It seems something systemic is happening that can’t just be noise and is pretty likely linked to youth protest, but quite what?
If I assume a youth influence, however this works it may be a pointer to the future of the relevant nations, albeit interpreting that future isn’t so easy. It hinges upon what type of youth belief is the driver. Although some would represent an increase of core believers in CCCC, albeit occurring because more potent effects are absent the total belief is high, meaning much is likely Allied Belief. However, not this time through an alliance with religious faiths, but political culture, like the strong alliance between CCCC and Lib/Dem culture within the US. So, at the very least the relevant nations would shift leftwards on Chart 1, but could potentially fall out of the plot altogether if like the US (or Vietnam) a more complex local cultural jigsaw emerges, which needs a targeted analysis.
A search for Rationality
Interestingly, about half the nations hold a similar position in Chart 2 and 3. This plus the bounded area is enough for a fairish correlation between the two responses (SI Chart F5yx, r=0.68). If we needed another hint that it is not rationality driving affirmative responses to ‘The climate is changing and human activity is mainly responsible’, this is it. As the first post notes, publics can’t possibly give rational responses to the correlating Chart 2 question.
The apparent lack of rationality in the above responses prompted me to hunt for any rationality. I used the same ‘envelope’ charts as above, mapping responses to one of the most objective questions from the main YouGov climate-change attitudes survey. This Weakly-Framed question asks which countries have had the most negative impact on climate-change and, as demonstrated in the first post of the series, responses aren’t linear with religiosity. Answers are available from relatively common and culturally unconflicted knowledge. However, even in this case rationality plays a very modest role, very much second fiddle to cultural influence that occurs via the same two modes as above. Due to word-count limitation, I shunted this analysis to SI Footnote 2.
Elite attitudes
Similarly to children, another sub-demographic within irreligious nations at the LHS of Chart 1 where core belief in CCCC prospers more than in the general population, is the elite. Even within democracies, small elites can heavily sway policy to a direction not supported by the populace. For instance, the UK, Germany and Scandinavia, all have very strong emissions policies despite per the bold-blue series in Chart 1, having a very high national skepticism of existential climate issues (plus, all nations have very small Core Belief in climate catastrophism). This wouldn’t be a problem if the policies were aligned to mainstream science conclusions. But ultimately, being initiated by an emotive belief in CCCC, they are latterly and inevitably trending towards CCCC goals; i.e. the emergency avoidance of imminent global catastrophe. The easy acceptance of Greta/CSW by secular elites is not a coincidence.
In highly religious countries, much of the influence of elites and the functioning of society is still closely tied to religious expression. Notwithstanding the relatively new (and superficially high, i.e. from ABel) climate concerns, those elites and indeed society generally haven’t to date abandoned this model. Yet in countries where religion has long atrophied over generations, newer culture can more easily muscle into elite layers via the provision of high-moral-ground plus emotive persuasion. Subconsciously, the latter features are extremely desirable as shortcuts for promoting / extending an elite profile (see SI Footnote 3), when exhausted religion no longer supplies this service.
Major XR and CSW presence within irreligious nations (per the last post) are not expressions of what the local publics think, en-masse, but extreme frustration expressed by small minorities because for sure their local publics mostly don’t think like them. In mistakenly assuming such actions reflect popular feeling, and thus compliantly onboarding extreme demands (which also contradict mainstream science), already culturally compromised elites are marching dangerously further and further out of alignment with the mass of their own publics. Tension from such dislocations is already causing some significant backlash (e.g. SI Footnote 4). Highly religious nations are protected from similar extreme policy choices, by the strongly continuing commitment of their elites to much older irrational fairy stories, aka religions.
The expectation is that policy push from elite attitudes would occur most within nations from the LHS of Chart 1, much like XR and CSW presence. This expectation can be checked by looking at the penetration of highly challenging policies (socially or to infra-structure or both) that also have a high virtue-signaling aspect. Whether or not the policies truly provide major benefit to emissions reduction or the environment generally, is not particularly relevant. A suitable such policy is the promotion of Electric Vehicles (EVs).
Policy push case – EVs
Chart 4, introduced in the last post, represents either of the orange series on Chart 1 (depending on the scale), with many more nations thrown in. The Y scale happens to match estimated CBel, i.e. the original UN poll vote-share for action on climate-change, divided by 6. The blocks a) to d) and the color-coding, emphasize religio-regional groups. Significant variability about the main trend is largely due to GDP-per-Capita (GDPpC) within each religio-regional group.
So, we expect EV policy penetration to largely be dictated by cultural motivation, and hence be highest at the LHS. BUT… this won’t be wholly independent of economic issues; those countries that are motivated for this policy must also have a robust enough economy to create incentives plus charging infra-structure, plus a high enough GDPpC for the local market to afford EVs. Adapted to economic necessity, the above prediction suggests that nations with strong economies (in an absolute sense) plus at the top-leftmost, will have the greatest EV penetration.
The numbers trailing some of the nation labels derive from the Top 18 Electric Car Countries in 2020, showing penetration per nation by market-share of new EV sales. Eleven nations in Chart 4 also appear within that league table; I compressed the ranking into a scale 1 to 11, in order to skip the missing ones. While strict ranking order from top-left isn’t observed, all but one of the ranked nations are indeed at the top-left corner, as expected.
The only exception in that peer-group without a ranking, is the Czech Republic, which has the lowest absolute GDP (45th in IMF list) of the peer group. Conversely, the only nation not in the top-leftmost bunching, is Japan. This nation (in a unique religio-regional group unrelated to the dark blue coding), possess the highest absolute GDP (3rd in IMF list) on the chart. This data reasonably confirms the above expectations from cultural positioning, with secondary economic considerations.
As noted in section 4 of the last post and even in normal times, a huge problem for those governments trying to push this and other challenging policies, is that once the public grasp the reality issues associated with implementation, their support is unlikely to get beyond the thick orange Core Belief line in Chart 1, maybe at the most the muted-red Strongly-Constrained Belief line. Unless for special circumstances, like the immense amounts of hydro-electricity in Norway. And in current times, a huge new reality constraint has appeared in the form of COVID-19, which for a year or two at least will squeeze even the CBel line still further downwards regarding the choice of a true top priority.
What this series tells us
Assuming findings are confirmed, and that my explanations are the best fit for same.
Affirmative attitudes to climate-change in the public sphere are cultural. As such they’re also the product of net cultural interaction, mainly with wrt the long-established religious faiths. The surface alliance of CCCC with religion creates an impression of faith support, which flips into resistance for any reality- constrained circumstances. Overall, where religiosity is low, climate activism is higher (including child religiosity for child activism), likewise for main policy. A secondary influence in reality-constrained scenarios is GDP-per-Capita. This likely exacerbates a cultural factor, modulating the main religiosity trend. Core Belief and policy-support is lower where GDPpC is lower within any religio-regional group.
Even responses to Weakly-Framed questions appear to mainly be determined by cultural influence, albeit occupying a wide envelope. While prediction from religiosity of climate attitudes inside that envelope is not possible, that they smear between the two main cultural modes is good support itself of the overall cultural explanation. Systemic excursions from the envelope are perhaps due to youth influence; merely a culturally divergent sub-demographic. Even the most objective climate survey question yields very little rationality in responses. Table 1 summarizes findings.
Some concluding thoughts
While each of the mainstream Faiths is theoretically a separate cultural entity, their relationships with CCCC as presented in this series don’t appear to depend on the particulars of any faith, only on national levels of belief. At least purely in respect of reactions to the newcomer of CCCC, currently, all Faiths appear to act as though they’re part of a single culture. Hence, what the presented charts are showing at heart is the interaction between two major cultures (i.e. religion and CCCC) that have come under each other’s influence.
For an analogy, I’m reminded of those illustrations of two stars falling into each other’s orbit, with the occurrence of complex gravitational and energy interactions. To further this analogy, one a bright young star (CCCC) and the other an old red giant (mainstream religious faith). Except we may know less about the cultural case right here upon Earth than the stellar one millions of light years distant. Stretching the analogy, most people from the relevant social-science disciplines don’t actually recognize a CCCC; it’s kind of ‘invisible’. But like a black hole orbiting the old red giant, we can tell it must be there because behaviors in the region only make sense if two bodies with mass and energy (here, cultural mechanisms) are interacting. Hence a culture (of catastrophe) must be exerting powerful influence within the social domain of climate-change, and interacting with religion.
There are other bodies in this equation, in the US particularly the heavyweights of Rep/Con and Dem/Lib culture, which entangle old religion and new CCCC both (and enough to locally disrupt the global trends shown here; the US has a 4-way cultural dance). Overall though, I’m surprised at just how consistent the entanglement of religiosity and CCCC appears to be, globally. Which also means we can use religiosity as a reliable lens to make the workings of CCCC clearer.
The false narratives of CCCC (all strong cultural narratives are false, their ‘purpose’ requires this) are powerfully affecting nations and faiths of all types across the globe. Over the years, many commenters have articulated in some form that the movement against man-made climate-change is effectively ‘a religion’ in itself. The effects presented here are more confirmation that for the public domain at least, they’re right. Such commenters are intuiting ‘a cultural entity’, where religions happen to be the cultural entities they’re very familiar with. Considering CCCC’s scale, the now generations-long trend, especially within Western societies, of less rule by the emotive and more by rationality, could well go into reverse through this single phenomenon alone. The only thing holding off its irrationalities in many nations, ironically, is religious faith.
Covid-19 Addendum: I’ve seen comment to the effect that Covid-19 is likely to be fatal for catastrophic climate-change culture. My money on this is no better than anyone else’s. But it says that once Covid-19 is in the rear-view mirror, however long that takes, CCCC will still be a serious force. Long evolved bio-cultural mechanisms make cultures tenacious, they can pivot to new circumstances and come back from heavy damage; even turn adverse conditions into advantage (there are already crude attempts, but they’ll get more sophisticated). CCCC’s wagon is hooked to science, which ought to be fatal on its own one day. But I doubt that day is here. For guidance, the major faiths span a millennial scale and survived the Black Death plus many more real-world calamities, their fairy-tale fears plus hopes still intact. This doesn’t mean the little secular sister of CCCC necessarily has similar staying power, but ultimately, it works on the same underlying mechanisms.
Admin notes
There are 3 posts in this series, all of which have the same style of Supplementary Information, which consist: 1) an expanded post, 2) a footnotes file, and 3) an Excel datafile. The text below is a streamlined post version, geared to get the concepts across more readily and uncluttered regarding side-issues, detail on methodology, intricate depth, path my exploration took etc. For folks who want more, the expanded post is ~4800 words. Be aware that the footnotes file, also having various external references, relates to the expanded post (though a couple are pointed at below). Likewise, all the chart IDs within the Excel datafile are numbered for the expanded post. However, all sources / data for the charts below can easily be found (I provided SI IDs in the text). The datafile includes various extra charts too.
Footnotes [Footnotes ]
Extended post [ Extended Post]
Datafile [Datafile]
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climateetc--2020-05-14--Greening the planet and slouching towards Paris?

A new paper finds higher than expected CO fertilization inferred from leaf to global observations .
The paper predicts that the Earth is going to gain nearly three times as much green matter as was predicted by the IPCC AR5 .
Earlier this month , I posted a short piece about an explosive paper on planetary greening that appeared in the journal Global Change Biology .
I ’ ve since mused that it deserves a considerably longer , more contextual post .
The innocuously titled paper , “ Higher than expected CO fertilization inferred from leaf to global observations ” @ @ @ @ @ @ @ ’ s CSIRO ) and eight coauthors uses a biophysical model and observed climate to back-calculate global primary productivity ( GPP ; the net change in standing vegetation per year ) , and to forward-calculate it using climate model forecasts .
Abstract .
“ Several lines of evidence point to an increase in the activity of the terrestrial biosphere over recent decades , impacting the global net land carbon sink ( NLS ) and its control on the growth of atmospheric carbon dioxide ( c ) .
Global terrestrial gross primary production ( @ @ @ @ @ @ @ by photosynthesis—is estimated to have risen by ( 31 ± 5 ) % since 1900 , but the relative contributions of different putative drivers to this increase are not well known .
Here we identify the rising atmospheric CO concentration as the dominant driver .
We reconcile leaf‐level and global atmospheric constraints on trends in modeled biospheric activity to reveal a global CO fertilization effect on photosynthesis of 30 % since 1900 , or 47 % for a doubling of c above the pre‐industrial level .
Our historic value is nearly twice as @ @ @ @ @ @ @ 4 ) % that do not use the full range of available constraints .
Consequently , under a future low‐emission scenario , we project a land carbon sink ( 174 PgC , 2006–2099 ) that is 57 PgC larger than if a lower CO fertilization effect comparable with current estimates is assumed .
These findings suggest a larger beneficial role of the land carbon sink in modulating future excess anthropogenic CO consistent with the target of the Paris Agreement to stay below 2°C warming , and underscore the importance of preserving terrestrial carbon @ @ @ @ @ @ @ earth is going to gain nearly three times as much green matter as was forecast in the last ( 2013 ) IPCC report .
It is noteworthy that Haverd ’ s model very faithfully reproduced the satellite-sensed changes in leaf area index shown by Zhu et al .
( 2016 ) , which found the greatest greenings to be in the world ’ s semiarid tropics , tropical forests , and a smaller ( but significant ) increase in temperate latitudes .
( I noted that paper here in 2018 ) .
It @ @ @ @ @ @ @ different methods—satellite sensing ( Zhu ) and a biophysical model ( Haverd ) come up with pretty much the same answer : we are greening up the earth fast , especially in critical tropical ecosystems .
Under a plausible emissions pathway , this will pull so much carbon dioxide out of the air that we could meet the Paris Accord of keeping surface warming below 2⁰C .
Specifically , the authors wrote , “ [ t ] hese findings suggest a larger beneficial role of the land carbon sink in modulating future excess @ @ @ @ @ @ @ the Paris Agreement to stay below 2°C warming… ” But they leave it the reader to do the math to see just how much their findings move the world toward Paris ( which of course I will do later in this post ) .
Here are the amounts and causes of changes in past GPP : Figure 1 .
Historical annual GPP according Haverd et al .
Plotted here are the effects of leaf-level physiological changes directly stimulated by carbon dioxide ( dark green ) , the overall increase in leaf matter i @ @ @ @ @ @ @ effects of climate change ( tan ) —i.e .
the increase in temperature since 1900 .
Haverd et al .
give the previously accepted 1900-2006 increase in GPP as 17 % +/- 4 % .
They used a model with land use , observed climate , and an interaction between changing CO and climate and found GPP likely increased 31 % +/- 4 % , or statistically speaking , roughly twice the increase in planetary green-ness that was previously accepted .
Figure 2 .
The left-hand image is Haverd et al ’ s @ @ @ @ @ @ @ Productivity ( the units are grams of carbon per meter squared per year ) , for 1980-2016 .
The right figures break down the causes : direct carbon dioxide effect ( C ) , temperature effect ( T ) , the interaction between the two ( CxT ) , precipitation ( P ) and land use change ( LUC ) .
Of most interest here is the left-hand image which is very similar to Zhu et al ’ s satellite greening .
Obviously , if increasing atmospheric carbon dioxide caused so much planetary @ @ @ @ @ @ @ , it stands to reason that there ’ s going to be a much bigger change during the remainder of this century .
Using a similar approach to what they applied to the past ( but now climate forecasts are substituted for observations ) , they estimated the increase in green-ness that would result from either doubling atmospheric carbon dioxide from its preindustrial background , or putting the world on a low-emission pathway in which its concentration peaks at 440 parts per million ( ppm ) around 2050 .
( For reference , @ @ @ @ @ @ @ to be around 410ppm ) .
The emissions scenario in Haverd is the UN ’ s Representative Concentration Pathway ( RCP ) 2.6 , their lowest one .
University of Guelph Economist Ross McKitrick recently demonstrated that global carbon dioxide concentrations have been below every UN scenario generated from the 1990s onward , so the lower-peaking scenario isn ’ t just fantasy .
( My own opinion , consistent with many others , is that we are currently running around RCP 6.0 . )
In the doubling scenario ( from a nominal 300 @ @ @ @ @ @ @ 47 % increase in green biomass from 2006-2099 .
That ’ s over and above the 37 % increase already observed since 1900 ( Figure 1 ) .
So we are going to come darned close to doubling the earth ’ s green vegetation since 1900 with no particular conservation effort .
Doubling of the CO concentration ( relative to preindustrial ) will likely occur sometime around 2070 or so .
The changes in green matter increase projected for 2006-2099 using RCP 2.6 are still huge .
Read their words ( and I @ @ @ @ @ @ @ …we estimate a cumulative biophysical sink…equivalent to 17 years of anthropogenic emissions at current rates [ emphasis added ] .
RCP 2.6 is associated with 2.4⁰C of warming ( since preindustrial ) by 2100 .
The goal of the Paris Agreement is to hold warming to two degrees or below .
The reduction in warming from the equivalent of 17 years of zero emissions is , of course , spread through the century , but if it took place now ( according to the UN ’ s models ) it would reduce 0.5⁰C @ @ @ @ @ @ @ models have us warming at roughly 0.3⁰C/decade in the near term , but Haverd et al .
tell us we will effectively have 1.7 decades of zero emissions thanks to greening .
A little math : 2.4⁰ ( the UN ’ s expected RCP 2.6 warming to 2100 ) minus 0.5⁰ ( the reduction in warming from 17 years of zero emissions ) = 1.9⁰C of warming .
Thanks to the wonders of photosynthesis on God ’ s getting-greener earth , we meet the Paris Accord .
That should have been front-page news @ @ @ @ @ @ @ google , there hasn ’ t been one story about this astounding paper .
Moderation note : As with all guest posts , please keep your comments civil and relevant .

by Patrick J. Michaels
A new paper finds higher than expected CO 2 fertilization inferred from leaf to global observations. The paper predicts that the Earth is going to gain nearly three times as much green matter as was predicted by the IPCC AR5.
Earlier this month, I posted a short piece about an explosive paper on planetary greening that appeared in the journal Global Change Biology. I’ve since mused that it deserves a considerably longer, more contextual post.
The innocuously titled paper, “Higher than expected CO 2 fertilization inferred from leaf to global observations”, by Vanessa Haverd (of Australia’s CSIRO) and eight coauthors uses a biophysical model and observed climate to back-calculate global primary productivity (GPP; the net change in standing vegetation per year), and to forward-calculate it using climate model forecasts.
Abstract. “Several lines of evidence point to an increase in the activity of the terrestrial biosphere over recent decades, impacting the global net land carbon sink (NLS) and its control on the growth of atmospheric carbon dioxide (c a ). Global terrestrial gross primary production (GPP)—the rate of carbon fixation by photosynthesis—is estimated to have risen by (31 ± 5)% since 1900, but the relative contributions of different putative drivers to this increase are not well known. Here we identify the rising atmospheric CO 2 concentration as the dominant driver. We reconcile leaf‐level and global atmospheric constraints on trends in modeled biospheric activity to reveal a global CO 2 fertilization effect on photosynthesis of 30% since 1900, or 47% for a doubling of c a above the pre‐industrial level. Our historic value is nearly twice as high as current estimates (17 ± 4)% that do not use the full range of available constraints. Consequently, under a future low‐emission scenario, we project a land carbon sink (174 PgC, 2006–2099) that is 57 PgC larger than if a lower CO 2 fertilization effect comparable with current estimates is assumed. These findings suggest a larger beneficial role of the land carbon sink in modulating future excess anthropogenic CO 2 consistent with the target of the Paris Agreement to stay below 2°C warming, and underscore the importance of preserving terrestrial carbon sinks.”
The paper predicted that the earth is going to gain nearly three times as much green matter as was forecast in the last (2013) IPCC report. It is noteworthy that Haverd’s model very faithfully reproduced the satellite-sensed changes in leaf area index shown by Zhu et al. (2016), which found the greatest greenings to be in the world’s semiarid tropics, tropical forests, and a smaller (but significant) increase in temperate latitudes. (I noted that paper here in 2018).
It’s very reassuring when two radically different methods—satellite sensing (Zhu) and a biophysical model (Haverd) come up with pretty much the same answer: we are greening up the earth fast, especially in critical tropical ecosystems.
Under a plausible emissions pathway, this will pull so much carbon dioxide out of the air that we could meet the Paris Accord of keeping surface warming below 2⁰C. Specifically, the authors wrote,
“[t]hese findings suggest a larger beneficial role of the land carbon sink in modulating future excess anthropogenic CO 2 consistent with the target of the Paris Agreement to stay below 2°C warming…”
But they leave it the reader to do the math to see just how much their findings move the world toward Paris (which of course I will do later in this post).
Here are the amounts and causes of changes in past GPP:
Figure 1. Historical annual GPP according Haverd et al. Plotted here are the effects of leaf-level physiological changes directly stimulated by carbon dioxide (dark green), the overall increase in leaf matter i(light green), and the effects of climate change (tan)—i.e. the increase in temperature since 1900.
Haverd et al. give the previously accepted 1900-2006 increase in GPP as 17% +/- 4%. They used a model with land use, observed climate, and an interaction between changing CO 2 and climate and found GPP likely increased 31%+/- 4%, or statistically speaking, roughly twice the increase in planetary green-ness that was previously accepted.
Figure 2. The left-hand image is Haverd et al’s map of model-calculated trends in Global Primary Productivity (the units are grams of carbon per meter squared per year), for 1980-2016. The right figures break down the causes: direct carbon dioxide effect (C), temperature effect (T), the interaction between the two (CxT), precipitation (P) and land use change (LUC). Of most interest here is the left-hand image which is very similar to Zhu et al’s satellite greening.
Obviously, if increasing atmospheric carbon dioxide caused so much planetary greening in 1980-2016 (Figure 2), it stands to reason that there’s going to be a much bigger change during the remainder of this century. Using a similar approach to what they applied to the past (but now climate forecasts are substituted for observations), they estimated the increase in green-ness that would result from either doubling atmospheric carbon dioxide from its preindustrial background, or putting the world on a low-emission pathway in which its concentration peaks at 440 parts per million (ppm) around 2050. (For reference, the annual average for 2020 is likely to be around 410ppm). The emissions scenario in Haverd is the UN’s Representative Concentration Pathway (RCP) 2.6, their lowest one.
University of Guelph Economist Ross McKitrick recently demonstrated that global carbon dioxide concentrations have been below every UN scenario generated from the 1990s onward, so the lower-peaking scenario isn’t just fantasy. (My own opinion, consistent with many others, is that we are currently running around RCP 6.0.)
In the doubling scenario (from a nominal 300 to 600ppm) they project a whopping 47% increase in green biomass from 2006-2099. That’s over and above the 37% increase already observed since 1900 (Figure 1). So we are going to come darned close to doubling the earth’s green vegetation since 1900 with no particular conservation effort. Doubling of the CO 2 concentration (relative to preindustrial) will likely occur sometime around 2070 or so.
The changes in green matter increase projected for 2006-2099 using RCP 2.6 are still huge. Read their words (and I hope your sitting down): “…we estimate a cumulative biophysical sink…equivalent to 17 years of anthropogenic emissions at current rates [emphasis added].
RCP 2.6 is associated with 2.4⁰C of warming (since preindustrial) by 2100. The goal of the Paris Agreement is to hold warming to two degrees or below. The reduction in warming from the equivalent of 17 years of zero emissions is, of course, spread through the century, but if it took place now (according to the UN’s models) it would reduce 0.5⁰C of the expected warming. The IPCC models have us warming at roughly 0.3⁰C/decade in the near term, but Haverd et al. tell us we will effectively have 1.7 decades of zero emissions thanks to greening.
A little math: 2.4⁰ (the UN’s expected RCP 2.6 warming to 2100) minus 0.5⁰ (the reduction in warming from 17 years of zero emissions) = 1.9⁰C of warming. Thanks to the wonders of photosynthesis on God’s getting-greener earth, we meet the Paris Accord.
That should have been front-page news. Instead, at least according to google, there hasn’t been one story about this astounding paper.
Moderation note: As with all guest posts, please keep your comments civil and relevant.
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climateetc--2020-05-10--Why herd immunity to COVID-19 is reached much earlier than thought

A study published in March by the COVID-19 Response Team from Imperial College ( Ferguson20 [ 1 ] ) appears to have been largely responsible for driving government actions in the UK and , to a fair extent , in the US and some other countries .
Until that report came out , the strategy of the UK government , at least , seems to have been to rely on the build up of ‘ herd immunity ’ to slow the growth of the epidemic and eventually cause it to peter out .
The ‘ herd immunity threshold ’ ( @ @ @ @ @ @ @ basic reproduction rate of the epidemic , R – a measure of how many people , on average , each infected individual infects .
Standard simple compartmental models of epidemic growth imply that the HIT equals { 1 – 1/R } .
Once the HIT is passed , the rate of new infections starts to decline , which should ensure that health systems will not thereafter be overwhelmed and makes it more practicable to take steps to eliminate the disease .
However , the Ferguson20 report estimated that relying on herd immunity would @ @ @ @ @ @ @ and US populations becoming infected during the epidemic , mainly over a two-month period , based on an R estimate of 2.4 .
These figures imply that the HIT is between 50 % and 60 % .
[ 2 ] Their report implied that health systems would be overwhelmed , resulting in far more deaths .
It claimed that only draconian government interventions could prevent this occurring .
Such interventions were rapidly implemented in the UK , in most states of the US , and in various other countries , via highly disruptive @ @ @ @ @ @ @ A notable exception was Sweden , which has continued to pursue a herd immunity-based strategy , relying on relatively modest social distancing policies .
The Imperial College team estimated that , after those policies were introduced in mid-March , R in Sweden was 2.5 , with only a 2.5 % probability that it was under 1.5 .
[ 3 ] The rapid spread of COVID-19 in the country in the second half of March suggests that R is unlikely to have been significantly under 2.0 .
[ 4 ] Very sensibly , the @ @ @ @ @ @ @ prevalence of infections by the SARS-COV-2 virus in Stockholm County , the earliest in Sweden hit by COVID-19 .
They thereby estimated that 17 % of the population would have been infected by 11 April , rising to 25 % by 1 May 2020 .
[ 5 ] Yet recorded new cases had stopped increasing by 11 April ( Figure 1 ) , as had net hospital admissions , [ 6 ] and both measures have fallen significantly since .
That pattern indicates that the HIT had been reached by 11April , at @ @ @ @ @ @ @ population appear to have been infected .
How can it be true that the HIT has been reached in Stockholm County with only about 17 % of the population having been infected , while an R of 2.0 is normally taken to imply a HIT of 50 % ?
A recent paper ( Gomes et al .
[ 7 ] ) provides the answer .
It shows that variation between individuals in their susceptibility to infection and their propensity to infect others can cause the HIT to be much lower than it is @ @ @ @ @ @ @ compartmental epidemic models take no account of such variability .
And the model used in the Ferguson20 study , while much more complex , appears only to take into account inhomogeneity arising from a very limited set of factors – notably geographic separation from other individuals and household size – with only a modest resulting impact on the growth of the epidemic .
[ 8 ] Using a compartmental model modified to take such variability into account , with co-variability between susceptibility and infectivity arguably handled in a more realistic way than by @ @ @ @ @ @ @ finding that the HIT is indeed reached at a much lower level than when the population is homogeneous .
That would explain why the HIT appears to have been passed in Stockholm by mid April .
The same seems likely to be the case in other major cities and regions that have been badly affected by COVID-19 .
Figure 1 .
New COVID-19 cases reported in Stockholm County , Sweden , over the 7 days up to the date shown .
Note that in Sweden testing for COVID-19 infection was narrowed on 12 @ @ @ @ @ @ @ hospital care , so from then on only a tiny proportion of infections were recorded as cases .
This would account for the lack of growth in cases during the first week plotted .
Since hospitalisation usually occurs several days after symptom onset , this change also increases the lag between infection and recording as a case .
Accordingly , from mid- March on the 7-day trailing average new cases figure will reflect new infections that on average occurred approximately two weeks earlier .
Like Gomes et al.
, I use a simple @ @ @ @ @ @ @ 9 ] in which the population is divided into four compartments : Susceptible ( uninfected ) , Exposed ( latent : infected but not yet infectious ) , Infectious ( typically when diseased ) , and Recovered ( and thus immune and harmless ) .
This is shown in Figure 2 .
In reality , the Recovered compartment includes people who instead die , which has the same effect on the model dynamics .
The entire population starts in the Susceptible compartment , save for a tiny proportion that are transferred to the @ @ @ @ @ @ @ The seed infectious individuals infect Susceptible individuals , who move to the Exposed compartment .
Exposed individuals gradually transfer to the Infectious compartment , on average remaining as Exposed for the chosen latent period .
Infectious individuals in turn gradually transfer to the Recovered compartment , on average remaining as Infectious for the selected infectious period .
In the case of COVID-19 , the diseased ( symptomatic ) stage is typically reached about 5 days after infection , but an infected individual starts to become infectious about 2 days earlier .
I therefore @ @ @ @ @ @ @ days .
[ 10 ] The infectious period depends mainly on the delay between infectiousness and symptoms appearing and on how quickly an individual reduces contacts with others once they become symptomatic , as well as on how infectious asymptomatic cases are .
In an SEIR model , the infective period can be derived by subtracting the latent period from the generation time – the mean interval between the original infection of a person and the infections that they then cause .
The Ferguson20 model assumed a generation time of 6.5 days , @ @ @ @ @ @ @ 7.5 days .
[ 11 ] I use 7 days , which is consistent with growth rates near the start of COVID-19 outbreaks .
[ 12 ] The infectious period is therefore 4 ( =7 − 3 ) days .
I set R =2.4 , the same value Ferguson20 use .
On average , while an individual is in the Infectious compartment , the number of Susceptible individuals they infect is R × { the proportion of the population that remains in the Susceptible compartment } .
With these settings , the progression @ @ @ @ @ @ @ standard SEIR model , in which all individuals have identical characteristics , is as shown in Figure 3 .
The HIT is reached once 58 % of the population has been infected , and ultimately 88 % of the population become infected .
Figure 3 .
Epidemic progression in an SEIR model with R =2.4 and a homogeneous population .
The time to reach the herd immunity threshold , which depends on the strength of the seeding at time zero , is arbitrary .
Modifying the basic SEIR model for variability in individual @ @ @ @ @ @ @ COVID-19 transmission is thought to occur directly from symptomatic and pre-symptomatic infected individuals , with little transmission from asymptomatic cases or from the environment .
[ 13 ] There is strong evidence that a small proportion of individuals account for most infections – the ‘ superspreaders ’ .
A good measure of the dispersion of transmission – the extent to which infection happens through many spreaders or just a few – is the coefficient of variation ( CV ) .
[ 14 ] Two different estimates of this figure have been published for @ @ @ @ @ @ @ ] estimated that 8.9 % of cases were responsible for 80 % of total infections , while a multi-country study [ 16 ] estimated that 10 % were so responsible .
In both cases a gamma probability distribution was assumed , as is standard for this purpose .
The corresponding CV best estimates and 95 % uncertainty ranges are 3.3 ( 3.0–5.6 ) and 3.1 ( 2.2–5.0 ) .
These figures are slightly higher than the 2.5 estimated for the 2003 epidemic of SARS .
[ 17 ] CV estimates indicate the probability @ @ @ @ @ @ @ reflect population inhomogeneity regarding individuals ’ differing tendency to infect others , but it is unclear to what extent they also reflect susceptibility differences between individuals .
However , since COVID-19 transmission is very largely person-to-person , much of the inhomogeneity in transmission rates will reflect how socially connected individuals are , and how close and prolonged their interactions with other individuals are .
As these factors affect the probability of transmission both from and to an individual , as well as causing variation in an individual ’ s infectivity they should cause @ @ @ @ @ @ @ infection .
A common social connectivity related factor implies that an individual ’ s susceptibility and infectivity are positively correlated , and it is not unreasonable to assume a quite strong correlation .
However , it seems unrealistic to assume , as Gomes et al .
do in one case , that an individual ’ s infectivity is directly proportional to their personal susceptibility .
( In the other case that they model , they assume that an individual ’ s infectivity is unrelated to their susceptibility . )
Some of the variability @ @ @ @ @ @ @ susceptible individual during an interaction will undoubtedly be unrelated to social connectivity , for example the size of their viral load .
Likewise , susceptibility will vary with the strength of an individual ’ s immune system as well as with their social connectivity .
I use unit-median lognormal distributions to reflect such social-connectivity unrelated variability in infectivity and susceptibility .
Their standard deviations determine the strength of the factor they represent .
I model an individual ’ s overall infectivity as the product of their common social-connectivity related factor and their unrelated @ @ @ @ @ @ @ susceptibility in a corresponding manner .
[ 18 ] I consider the cases of CV=1 and CV=2 for the common social connectivity factor that causes inhomogeneity in both susceptibility and infectivity .
For unrelated lognormally-distributed inhomogeneity in susceptibility I take standard deviations of either 0.4 or 0.8 , corresponding to a CV of 0.417 or 0.947 respectively .
Where their gamma-distributed common factor inhomogeneity is set at 1 , the resulting total inhomogeneity in susceptibility is respectively 1.17 or 1.65 when the lower or higher unrelated inhomogeneity standard deviations respectively are used ; @ @ @ @ @ @ @ inhomogeneity in susceptibility is respectively 2.17 or 2.98 .
The magnitude of variability in individuals ’ social-connectivity unrelated infectivity-specific inhomogeneity factor does not affect the progression of an epidemic or the HIT , so for simplicity I ignore it here .
[ 19 ] Figure 4 shows the progression of a COVID-19 epidemic in the case of CV=1 for the common social connectivity factor inhomogeneity , with unrelated inhomogeneity in susceptibility having a standard deviation of 0.4 .
The HIT is 60 % lower than for a homogeneous population , at 23.6 % @ @ @ @ @ @ @ .
And 43 % rather than 88 % of the population ultimately becomes infected .
If the standard deviation of unrelated inhomogeneity in susceptibility is increased to 0.8 , the HIT becomes 18.9 % , and 35 % of the population are ultimately infected .
Figure 4 .
Epidemic progression in an SEIR model with R =2.4 and a population with CV=1 common factor inhomogeneity in susceptibility and infectivity and also unrelated multiplicative inhomogeneity in susceptibility with a standard deviation of 0.4 .
Figure 5 shows the progression of a COVID-19 epidemic in @ @ @ @ @ @ @ social connectivity factor inhomogeneity , with unrelated inhomogeneity in susceptibility having a standard deviation of 0.8 .
The HIT is only 6.9 % of the population , and only 14 % of the population ultimately becoming infected .
If the standard deviation of unrelated inhomogeneity in susceptibility is reduced to 0.4 , those figures become respectively 8.6 % and 17 % .
Figure 5 .
Epidemic progression in an SEIR model with R =2.4 and a population with CV=2 common factor inhomogeneity in susceptibility and infectivity and also unrelated multiplicative inhomogeneity in susceptibility @ @ @ @ @ @ @ Incorporating , in a reasonable manner , inhomogeneity in susceptibility and infectivity in a standard SEIR epidemiological model , rather than assuming a homogeneous population , causes a very major reduction in the herd immunity threshold , and also in the ultimate infection level if the epidemic thereafter follows an unconstrained path .
Therefore , the number of fatalities involved in achieving herd immunity is much lower than it would otherwise be .
In my view , the true herd immunity threshold probably lies somewhere between the 7 % and 24 % implied @ @ @ @ @ @ @ and 5 .
If it were around 17 % , which evidence from Stockholm County suggests the resulting fatalities from infections prior to the HIT being reached should be a very low proportion of the population .
The Stockholm infection fatality rate appears to be approximately 0.4 % , [ 20 ] considerably lower than per the Verity et al .
[ 21 ] estimates used in Ferguson20 , with a fatality rate of under 0.1 % from infections until the HIT was reached .
The fatality rate to reach the HIT in @ @ @ @ @ @ @ , because R is positively related to population density .
[ 22 ] Accordingly , total fatalities should be well under 0.1 % of the population by the time herd immunity is achieved .
Although there would be subsequent further fatalities , as the epidemic shrinks it should be increasingly practicable to hasten its end by using testing and contact tracing to prevent infections spreading , and thus substantially reduce the number of further fatalities below those projected by the SEIR model in a totally unmitigated scenario .
[ 1 ] Neil M @ @ @ @ @ @ @ interventions ( NPIs ) to reduce COVID-19 mortality and healthcare demand .
Imperial College COVID-19 Response Team Report 9 , 16 March 2020 , https : //spiral.imperial.ac.uk:8443/handle/10044/1/77482 [ 2 ] A final infection rate of 81 % implies , in the context of a simple compartmental model with a fixed , homogeneous population , that the ‘ effective R ‘ is between 2.0 and 2.1 , and that the HIT is slightly over 50 % .
Ferguson20 use a more complex model , so it is not surprising that the implied effective R @ @ @ @ @ @ @ that Ferguson20 state they assume .
[ 3 ] Flaxman , S. et al.
, Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries .
Imperial College COVID-19 Response Team Report 13 , 30 March 2020 , https : //www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/report-13-europe-npi-impact/ [ 4 ] Based on the Ferguson20 estimate of a mean generation time of 6.5 days , which appears to be in line with existing evidence , an R of 2.0 would result in a daily growth rate of 2.0^ ( 1/6.5 ) = 11 @ @ @ @ @ @ @ the peak growth rate in cases in late March in Stockholm County , and in early April in the two regions with the next highest number of cases , in both of which the epidemic took off slightly later than in Stockholm , and in line with the growth rate in Swedish COVID-19 deaths in early April [ 7 ] Gomes , M. G. M. , et al .
Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold .
medRxiv 2 May 2020. https : //www.medrxiv.org/content/10.1101/2020.04.27.20081893v1 [ 8 ] @ @ @ @ @ @ @ that Ferguson20 estimated would eventually become infected is only slightly lower than the 88 % level implied by their R estimate of 2.4 in the case of a homogeneous population .
[ 10 ] Gomes et al .
instead set the latent period slightly longer , to 4 days and treated it as a partly infectious period , unlike in the standard SEIR model .
[ 11 ] Li Q , Guan X , Wu P , et al .
: Early Transmission Dynamics in Wuhan , China , of Novel Coronavirus-Infected Pneumonia @ @ @ @ @ @ @ ; 382 ( 13 ) :1199–1207.https : //www.nejm.org/doi/10.1056/NEJMoa2001316 [ 12 ] Once a SEIR model has passed its start up phase , and while a negligible proportion susceptible individuals have been infected , the epidemic daily growth factor is R ^ ( 1/generation time ) , or 1.10–1.13 for R =2.0–2.4 if the generation time is 7 days .
[ 14 ] The coefficient of variation is the ratio of the standard deviation to the mean of its probability distribution .
It is usual to assume a gamma distribution for infectivity , the @ @ @ @ @ @ @ [ 15 ] Bi , Qifang , et al .
“ Epidemiology and transmission of COVID-19 in 391 cases and 1286 of their close contacts in Shenzhen , China : a retrospective cohort study.
” The Lancet Infectious Diseases 27 April 2020. https : //doi.org/10.1016/S1473-3099 ( 20 ) 30287-5 [ 16 ] Endo , Akira , et al .
“ Estimating the overdispersion in COVID-19 transmission using outbreak sizes outside China.
” Wellcome Open Research 5.67 ( 2020 ) : 67. https : //wellcomeopenresearch.org/articles/5-67 [ 17 ] Lloyd-Smith , J O et al @ @ @ @ @ @ @ individual variation on disease emergence.
” Nature 438.7066 ( 2005 ) : 355-359. https : //www.nature.com/articles/nature04153 [ 18 ] For computational efficiency , I divide the population into 10,000 equal sized segments with their common social connectivity factor increasing according to its assumed probability distribution , and allocate each population segment values for unrelated variability in susceptibility and infectivity randomly , according to their respective probability distributions .
[ 19 ] A highly susceptible but averagely infectious person is more likely to be removed from the susceptible pool early in an epidemic , @ @ @ @ @ @ @ .
However , no such selective removal occurs for a highly infectious person of averagely susceptibility .
Therefore , as Gomes et al .
point out , variability in susceptibility lowers the HIT , but variability in infectivity does not do so except to the extent that it is correlated with variability in susceptibility .
[ 20 ] On 8 May 2020 reported total COVID-19 deaths in Stockholm County were 1,660 , which is 0.40 % of the estimated 413,000 of its population who had been infected by 11 April 2020 .
COVID-19 @ @ @ @ @ @ @ May that relate to infections by 11 April 2020 are likely to be approximately balanced by deaths reported by 8 May 2020 that related to post 11 April 2020 infections .
[ 21 ] Verity R , Okell LC , Dorigatti I , et al .
Estimates of the severity of COVID-19 disease .
medRxiv 13 March 2020 ; https : //www.medrxiv.org/content/10.1101/2020.03.09.20033357v1 .
[ 22 ] Similarly , the HIT may be significantly higher in areas that are very densely populated , have much less inhomogenous populations and/or are repeatedly reseeded from other @ @ @ @ @ @ @ high prevalence of COVID-19 infection that has been found in , for instance , some prisons and residential institutions or in city districts .
Originally posted here , where a pdf copy is also available

By Nic Lewis
Introduction
A study published in March by the COVID-19 Response Team from Imperial College (Ferguson20[1]) appears to have been largely responsible for driving government actions in the UK and, to a fair extent, in the US and some other countries. Until that report came out, the strategy of the UK government, at least, seems to have been to rely on the build up of ‘herd immunity’ to slow the growth of the epidemic and eventually cause it to peter out.
The ‘herd immunity threshold’ (HIT) can be estimated from the basic reproduction rate of the epidemic, R 0 – a measure of how many people, on average, each infected individual infects. Standard simple compartmental models of epidemic growth imply that the HIT equals {1 – 1/R 0 }. Once the HIT is passed, the rate of new infections starts to decline, which should ensure that health systems will not thereafter be overwhelmed and makes it more practicable to take steps to eliminate the disease.
However, the Ferguson20 report estimated that relying on herd immunity would result in 81% of the UK and US populations becoming infected during the epidemic, mainly over a two-month period, based on an R 0 estimate of 2.4. These figures imply that the HIT is between 50% and 60%.[2] Their report implied that health systems would be overwhelmed, resulting in far more deaths. It claimed that only draconian government interventions could prevent this occurring. Such interventions were rapidly implemented in the UK, in most states of the US, and in various other countries, via highly disruptive and restrictive enforced ‘lockdowns’.
A notable exception was Sweden, which has continued to pursue a herd immunity-based strategy, relying on relatively modest social distancing policies. The Imperial College team estimated that, after those policies were introduced in mid-March, R 0 in Sweden was 2.5, with only a 2.5% probability that it was under 1.5.[3] The rapid spread of COVID-19 in the country in the second half of March suggests that R 0 is unlikely to have been significantly under 2.0.[4]
Very sensibly, the Swedish public health authority has surveyed the prevalence of infections by the SARS-COV-2 virus in Stockholm County, the earliest in Sweden hit by COVID-19. They thereby estimated that 17% of the population would have been infected by 11 April, rising to 25% by 1 May 2020.[5] Yet recorded new cases had stopped increasing by 11 April (Figure 1), as had net hospital admissions,[6] and both measures have fallen significantly since. That pattern indicates that the HIT had been reached by 11April, at which point only 17% of the population appear to have been infected.
How can it be true that the HIT has been reached in Stockholm County with only about 17% of the population having been infected, while an R 0 of 2.0 is normally taken to imply a HIT of 50%?
The importance of population inhomogeneity
A recent paper (Gomes et al.[7]) provides the answer. It shows that variation between individuals in their susceptibility to infection and their propensity to infect others can cause the HIT to be much lower than it is in a homogeneous population. Standard simple compartmental epidemic models take no account of such variability. And the model used in the Ferguson20 study, while much more complex, appears only to take into account inhomogeneity arising from a very limited set of factors – notably geographic separation from other individuals and household size – with only a modest resulting impact on the growth of the epidemic.[8] Using a compartmental model modified to take such variability into account, with co-variability between susceptibility and infectivity arguably handled in a more realistic way than by Gomes et al., I confirm their finding that the HIT is indeed reached at a much lower level than when the population is homogeneous. That would explain why the HIT appears to have been passed in Stockholm by mid April. The same seems likely to be the case in other major cities and regions that have been badly affected by COVID-19.
Figure 1. New COVID-19 cases reported in Stockholm County, Sweden, over the 7 days up to the date shown. Note that in Sweden testing for COVID-19 infection was narrowed on 12 March, to focus on people needing hospital care, so from then on only a tiny proportion of infections were recorded as cases. This would account for the lack of growth in cases during the first week plotted. Since hospitalisation usually occurs several days after symptom onset, this change also increases the lag between infection and recording as a case. Accordingly, from mid- March on the 7-day trailing average new cases figure will reflect new infections that on average occurred approximately two weeks earlier.
The epidemiological model used
Like Gomes et al., I use a simple ‘SEIR’ epidemiological model,[9] in which the population is divided into four compartments: Susceptible (uninfected), Exposed (latent: infected but not yet infectious), Infectious (typically when diseased), and Recovered (and thus immune and harmless). This is shown in Figure 2. In reality, the Recovered compartment includes people who instead die, which has the same effect on the model dynamics. The entire population starts in the Susceptible compartment, save for a tiny proportion that are transferred to the Infectious compartment to seed the epidemic. The seed infectious individuals infect Susceptible individuals, who move to the Exposed compartment. Exposed individuals gradually transfer to the Infectious compartment, on average remaining as Exposed for the chosen latent period. Infectious individuals in turn gradually transfer to the Recovered compartment, on average remaining as Infectious for the selected infectious period.
Figure 2. SEIR compartment epidemiological model diagram.
In the case of COVID-19, the diseased (symptomatic) stage is typically reached about 5 days after infection, but an infected individual starts to become infectious about 2 days earlier. I therefore set the average latent period as 3 days.[10]
The infectious period depends mainly on the delay between infectiousness and symptoms appearing and on how quickly an individual reduces contacts with others once they become symptomatic, as well as on how infectious asymptomatic cases are. In an SEIR model, the infective period can be derived by subtracting the latent period from the generation time – the mean interval between the original infection of a person and the infections that they then cause.
The Ferguson20 model assumed a generation time of 6.5 days, slightly lower than a subsequent estimate of 7.5 days.[11] I use 7 days, which is consistent with growth rates near the start of COVID-19 outbreaks.[12] The infectious period is therefore 4 (=7 − 3) days.
I set R 0 =2.4, the same value Ferguson20 use. On average, while an individual is in the Infectious compartment, the number of Susceptible individuals they infect is R 0 × {the proportion of the population that remains in the Susceptible compartment}.
With these settings, the progression of a COVID-19 epidemic projected by a standard SEIR model, in which all individuals have identical characteristics, is as shown in Figure 3. The HIT is reached once 58% of the population has been infected, and ultimately 88% of the population become infected.
Figure 3. Epidemic progression in an SEIR model with R 0 =2.4 and a homogeneous population. The time to reach the herd immunity threshold, which depends on the strength of the seeding at time zero, is arbitrary.
Modifying the basic SEIR model for variability in individual susceptibility and infectivity
The great bulk of COVID-19 transmission is thought to occur directly from symptomatic and pre-symptomatic infected individuals, with little transmission from asymptomatic cases or from the environment.[13] There is strong evidence that a small proportion of individuals account for most infections – the ‘superspreaders’.
A good measure of the dispersion of transmission – the extent to which infection happens through many spreaders or just a few – is the coefficient of variation (CV).[14] Two different estimates of this figure have been published for COVID-19. A Shenzhen-based study[15] estimated that 8.9% of cases were responsible for 80% of total infections, while a multi-country study[16] estimated that 10% were so responsible. In both cases a gamma probability distribution was assumed, as is standard for this purpose. The corresponding CV best estimates and 95% uncertainty ranges are 3.3 (3.0–5.6) and 3.1 (2.2–5.0). These figures are slightly higher than the 2.5 estimated for the 2003 epidemic of SARS.[17]
CV estimates indicate the probability of transmission of an infection. They reflect population inhomogeneity regarding individuals’ differing tendency to infect others, but it is unclear to what extent they also reflect susceptibility differences between individuals. However, since COVID-19 transmission is very largely person-to-person, much of the inhomogeneity in transmission rates will reflect how socially connected individuals are, and how close and prolonged their interactions with other individuals are. As these factors affect the probability of transmission both from and to an individual, as well as causing variation in an individual’s infectivity they should cause the same variation in their susceptibility to infection.
A common social connectivity related factor implies that an individual’s susceptibility and infectivity are positively correlated, and it is not unreasonable to assume a quite strong correlation. However, it seems unrealistic to assume, as Gomes et al. do in one case, that an individual’s infectivity is directly proportional to their personal susceptibility. (In the other case that they model, they assume that an individual’s infectivity is unrelated to their susceptibility.)
Some of the variability in the likelihood of someone infecting a susceptible individual during an interaction will undoubtedly be unrelated to social connectivity, for example the size of their viral load. Likewise, susceptibility will vary with the strength of an individual’s immune system as well as with their social connectivity. I use unit-median lognormal distributions to reflect such social-connectivity unrelated variability in infectivity and susceptibility. Their standard deviations determine the strength of the factor they represent. I model an individual’s overall infectivity as the product of their common social-connectivity related factor and their unrelated infectivity-specific factor, and calculate their overall susceptibility in a corresponding manner.[18]
I consider the cases of CV=1 and CV=2 for the common social connectivity factor that causes inhomogeneity in both susceptibility and infectivity. For unrelated lognormally-distributed inhomogeneity in susceptibility I take standard deviations of either 0.4 or 0.8, corresponding to a CV of 0.417 or 0.947 respectively. Where their gamma-distributed common factor inhomogeneity is set at 1, the resulting total inhomogeneity in susceptibility is respectively 1.17 or 1.65 when the lower or higher unrelated inhomogeneity standard deviations respectively are used; where set at 2 the resulting total inhomogeneity in susceptibility is respectively 2.17 or 2.98. The magnitude of variability in individuals’ social-connectivity unrelated infectivity-specific inhomogeneity factor does not affect the progression of an epidemic or the HIT, so for simplicity I ignore it here.[19]
Results
Figure 4 shows the progression of a COVID-19 epidemic in the case of CV=1 for the common social connectivity factor inhomogeneity, with unrelated inhomogeneity in susceptibility having a standard deviation of 0.4. The HIT is 60% lower than for a homogeneous population, at 23.6% rather than 58.3% of the population. And 43% rather than 88% of the population ultimately becomes infected. If the standard deviation of unrelated inhomogeneity in susceptibility is increased to 0.8, the HIT becomes 18.9%, and 35% of the population are ultimately infected.
Figure 4. Epidemic progression in an SEIR model with R 0 =2.4 and a population with CV=1 common factor inhomogeneity in susceptibility and infectivity and also unrelated multiplicative inhomogeneity in susceptibility with a standard deviation of 0.4.
Figure 5 shows the progression of a COVID-19 epidemic in the case of CV=2 for the common social connectivity factor inhomogeneity, with unrelated inhomogeneity in susceptibility having a standard deviation of 0.8. The HIT is only 6.9% of the population, and only 14% of the population ultimately becoming infected. If the standard deviation of unrelated inhomogeneity in susceptibility is reduced to 0.4, those figures become respectively 8.6% and 17%.
Figure 5. Epidemic progression in an SEIR model with R 0 =2.4 and a population with CV=2 common factor inhomogeneity in susceptibility and infectivity and also unrelated multiplicative inhomogeneity in susceptibility with a standard deviation of 0.8.
Conclusions
Incorporating, in a reasonable manner, inhomogeneity in susceptibility and infectivity in a standard SEIR epidemiological model, rather than assuming a homogeneous population, causes a very major reduction in the herd immunity threshold, and also in the ultimate infection level if the epidemic thereafter follows an unconstrained path. Therefore, the number of fatalities involved in achieving herd immunity is much lower than it would otherwise be.
In my view, the true herd immunity threshold probably lies somewhere between the 7% and 24% implied by the cases illustrated in Figures 4 and 5. If it were around 17%, which evidence from Stockholm County suggests the resulting fatalities from infections prior to the HIT being reached should be a very low proportion of the population. The Stockholm infection fatality rate appears to be approximately 0.4%,[20] considerably lower than per the Verity et al.[21] estimates used in Ferguson20, with a fatality rate of under 0.1% from infections until the HIT was reached. The fatality rate to reach the HIT in less densely populated areas should be lower, because R 0 is positively related to population density.[22] Accordingly, total fatalities should be well under 0.1% of the population by the time herd immunity is achieved. Although there would be subsequent further fatalities, as the epidemic shrinks it should be increasingly practicable to hasten its end by using testing and contact tracing to prevent infections spreading, and thus substantially reduce the number of further fatalities below those projected by the SEIR model in a totally unmitigated scenario.
Nicholas Lewis 10 May 2020
[1] Neil M Ferguson et al., Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand. Imperial College COVID-19 Response Team Report 9, 16 March 2020, https://spiral.imperial.ac.uk:8443/handle/10044/1/77482
[2] A final infection rate of 81% implies, in the context of a simple compartmental model with a fixed, homogeneous population, that the ‘effective R 0 ‘ is between 2.0 and 2.1, and that the HIT is slightly over 50%. Ferguson20 use a more complex model, so it is not surprising that the implied effective R 0 differs slightly from the basic 2.4 value that Ferguson20 state they assume.
[3] Flaxman, S. et al., Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries. Imperial College COVID-19 Response Team Report 13, 30 March 2020, https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/report-13-europe-npi-impact/
[4] Based on the Ferguson20 estimate of a mean generation time of 6.5 days, which appears to be in line with existing evidence, an R 0 of 2.0 would result in a daily growth rate of 2.0^(1/6.5)= 11%. That is slightly lower than the peak growth rate in cases in late March in Stockholm County, and in early April in the two regions with the next highest number of cases, in both of which the epidemic took off slightly later than in Stockholm, and in line with the growth rate in Swedish COVID-19 deaths in early April
[5] https://www.folkhalsomyndigheten.se/contentassets/2da059f90b90458d8454a04955d1697f/skattning-peakdag-antal-infekterade-covid-19-utbrottet-stockholms-lan-februari-april-2020.pdf
[6] John Burn-Murdoch, Financial Times Research, 2 May 2020. http://web.archive.org/web/20200507075628/https:/twitter.com/jburnmurdoch/status/1256712090028576768
[7] Gomes, M. G. M., et al. Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold. medRxiv 2 May 2020. https://www.medrxiv.org/content/10.1101/2020.04.27.20081893v1
[8] The 81% proportion of the population that Ferguson20 estimated would eventually become infected is only slightly lower than the 88% level implied by their R 0 estimate of 2.4 in the case of a homogeneous population.
[9] https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SEIR_model
[10] Gomes et al. instead set the latent period slightly longer, to 4 days and treated it as a partly infectious period, unlike in the standard SEIR model.
[11] Li Q, Guan X, Wu P, et al.: Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus-Infected Pneumonia. N Engl J Med. 2020; 382(13):1199–1207.https://www.nejm.org/doi/10.1056/NEJMoa2001316
[12] Once a SEIR model has passed its start up phase, and while a negligible proportion susceptible individuals have been infected, the epidemic daily growth factor is R 0 ^(1/generation time), or 1.10–1.13 for R 0 =2.0–2.4 if the generation time is 7 days.
[13] L. Ferretti et al., Science 10.1126/science.abb6936 (2020).
[14] The coefficient of variation is the ratio of the standard deviation to the mean of its probability distribution. It is usual to assume a gamma distribution for infectivity, the shape parameter of which equals 1/CV2.
[15] Bi, Qifang, et al. “Epidemiology and transmission of COVID-19 in 391 cases and 1286 of their close contacts in Shenzhen, China: a retrospective cohort study.” The Lancet Infectious Diseases 27 April 2020. https://doi.org/10.1016/S1473-3099(20)30287-5
[16] Endo, Akira, et al. “Estimating the overdispersion in COVID-19 transmission using outbreak sizes outside China.” Wellcome Open Research 5.67 (2020): 67. https://wellcomeopenresearch.org/articles/5-67
[17] Lloyd-Smith, J O et al. “Superspreading and the effect of individual variation on disease emergence.” Nature 438.7066 (2005): 355-359. https://www.nature.com/articles/nature04153
[18] For computational efficiency, I divide the population into 10,000 equal sized segments with their common social connectivity factor increasing according to its assumed probability distribution, and allocate each population segment values for unrelated variability in susceptibility and infectivity randomly, according to their respective probability distributions.
[19] A highly susceptible but averagely infectious person is more likely to be removed from the susceptible pool early in an epidemic, reducing the average susceptibility of the pool. However, no such selective removal occurs for a highly infectious person of averagely susceptibility. Therefore, as Gomes et al. point out, variability in susceptibility lowers the HIT, but variability in infectivity does not do so except to the extent that it is correlated with variability in susceptibility.
[20] On 8 May 2020 reported total COVID-19 deaths in Stockholm County were 1,660, which is 0.40% of the estimated 413,000 of its population who had been infected by 11 April 2020. COVID-19 deaths reported for Stockholm County after 8 May that relate to infections by 11 April 2020 are likely to be approximately balanced by deaths reported by 8 May 2020 that related to post 11 April 2020 infections.
[21] Verity R, Okell LC, Dorigatti I, et al. Estimates of the severity of COVID-19 disease. medRxiv 13 March 2020; https://www.medrxiv.org/content/10.1101/2020.03.09.20033357v1.
[22] Similarly, the HIT may be significantly higher in areas that are very densely populated, have much less inhomogenous populations and/or are repeatedly reseeded from other areas. That would account for the high prevalence of COVID-19 infection that has been found in, for instance, some prisons and residential institutions or in city districts.
Originally posted here, where a pdf copy is also available
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