I can't get chart to post. But link should get you there.
about Herd Immunity Threshold in detail, it’s becoming even more clear that the “H.I.T.” of COVID-19 is very likely in the 10-20% range, rather than the 60-70% range that was originally thought. It would be impossible to overstate the importance of this difference, because it supports exactly WHY COVID-19 has already reached herd immunity in most of Europe, and WHY we’re almost done here in the U.S., too. Here’s one new paper, Herd immunity thresholds for SARS-CoV-2 estimated from unfolding epidemics. Their conclusion:
about Herd Immunity Threshold in detail, it’s becoming even more clear that the “H.I.T.” of COVID-19 is very likely in the 10-20% range, rather than the 60-70% range that was originally thought. It would be impossible to overstate the importance of this difference, because it supports exactly WHY COVID-19 has already reached herd immunity in most of Europe, and WHY we’re almost done here in the U.S., too. Here’s one new paper, Herd immunity thresholds for SARS-CoV-2 estimated from unfolding epidemics. Their conclusion:
is Oxford’s Dr. Sunetra Gupta, check out this interview with her titled, “We may already have herd immunity – an interview with Professor Sunetra Gupta.” A quote:
is Oxford’s Dr. Sunetra Gupta, check out this interview with her titled, “We may already have herd immunity – an interview with Professor Sunetra Gupta.” A quote:
Lockdowns don’t work. Getting politicians involved in trying to fight the normal course of a viral illness will hopefully be seen by historians as one of the silliest things we ever chose to do. In simple terms, a virus is gonna be a virus. As Dr. Gupta explains, “The epidemic is an ecological relationship that we have to manage between ourselves and the virus. But instead, people are looking at it as a completely external thing.” Said differently, like every other virus, COVID-19 is here to stay. Lockdowns provide politicians with an “illusion of control” but the data is rolling in that they have been useless, and even The Lancet, one of the world’s most prestigious medical journals, has weighed in. Titled, A country level analysis measuring the impact of government actions, country preparedness and socioeconomic factors on COVID-19 mortality and related health outcomes, their conclusions are pretty stark, and depressing for those of us who have undergone lockdowns:
German scientists looked at the same topic just within the country of Germany and reached the same conclusion in this paper titled, Change points in the spread of COVID-19 question the effectiveness of nonpharmaceutical interventions in Germany. An excerpt:
Lockdowns don’t work. Getting politicians involved in trying to fight the normal course of a viral illness will hopefully be seen by historians as one of the silliest things we ever chose to do. In simple terms, a virus is gonna be a virus. As Dr. Gupta explains, “The epidemic is an ecological relationship that we have to manage between ourselves and the virus. But instead, people are looking at it as a completely external thing.” Said differently, like every other virus, COVID-19 is here to stay. Lockdowns provide politicians with an “illusion of control” but the data is rolling in that they have been useless, and even The Lancet, one of the world’s most prestigious medical journals, has weighed in. Titled, A country level analysis measuring the impact of government actions, country preparedness and socioeconomic factors on COVID-19 mortality and related health outcomes, their conclusions are pretty stark, and depressing for those of us who have undergone lockdowns:
German scientists looked at the same topic just within the country of Germany and reached the same conclusion in this paper titled, Change points in the spread of COVID-19 question the effectiveness of nonpharmaceutical interventions in Germany. An excerpt:
Viruses go up, and then down, and the death rate is the only reliable way to track them. A team at Oxford explains this way better than I ever can. In this post titled COVID-19: William Farr’s way out of the Pandemic, they explain how Farr, a UK epidemiologist from the mid-19th century, understood that all viruses follow a similar pattern, and that the slope of the death curve on the way up will roughly equal the slope on the way down, which means if you know when you have reached peak deaths, you have a very good idea of when the virus will be extinguished. As Farr wrote, “The death rate is a fact; anything beyond this is an inference.” The Oxford scientists write:
Viruses go up, and then down, and the death rate is the only reliable way to track them. A team at Oxford explains this way better than I ever can. In this post titled COVID-19: William Farr’s way out of the Pandemic, they explain how Farr, a UK epidemiologist from the mid-19th century, understood that all viruses follow a similar pattern, and that the slope of the death curve on the way up will roughly equal the slope on the way down, which means if you know when you have reached peak deaths, you have a very good idea of when the virus will be extinguished. As Farr wrote, “The death rate is a fact; anything beyond this is an inference.” The Oxford scientists write:
I do not know how much you read or like to read. But this is some of the info on this. Some is mine or ours. But I tried to use mostly research from others to demonstrate the points.
That is enough for now. But, obviously, I have a lot more data to back up the conclusions.
Therefore, if you need more info or additional links or need clarification -- just let me know.
I do not know how much you read or like to read. But this is some of the info on this. Some is mine or ours. But I tried to use mostly research from others to demonstrate the points.
That is enough for now. But, obviously, I have a lot more data to back up the conclusions.
Therefore, if you need more info or additional links or need clarification -- just let me know.
Herd immunity was achieved in Europe with lock down standards and process of sewage correctly.
Achieving a purification system neutralizing the enivatable cycles. Corona feeds on sewage of animal waste it also infects the animal first recognized in Europe. The virus can attach easily to water vapor and other vapors being airborne in cloud systems. It can fall as rain if enough infected vapor exists within our sewage system evoparatuon pond reduction systems.
Burning human solids as a Cano hydrate after evaporation Europe's model presses sewage slury realileasing pure h20 trapping the virus for.furnance electric.generation precept systems.
Methane powered.auros.or.much more common.
And methane is diverted to natural gas creating the smell. Our sewage.systems.like.most of infrastructure is greatly need of an upgrade.
The emerging facts is that without protocols and hospital treatments our death count would exceed 10 million Americans from this virus alone. Hence a possible .5 percent decrease within the general population death vs live birth rates... it would be the first such declination since the civil war.
Herd immunity was achieved in Europe with lock down standards and process of sewage correctly.
Achieving a purification system neutralizing the enivatable cycles. Corona feeds on sewage of animal waste it also infects the animal first recognized in Europe. The virus can attach easily to water vapor and other vapors being airborne in cloud systems. It can fall as rain if enough infected vapor exists within our sewage system evoparatuon pond reduction systems.
Burning human solids as a Cano hydrate after evaporation Europe's model presses sewage slury realileasing pure h20 trapping the virus for.furnance electric.generation precept systems.
Methane powered.auros.or.much more common.
And methane is diverted to natural gas creating the smell. Our sewage.systems.like.most of infrastructure is greatly need of an upgrade.
The emerging facts is that without protocols and hospital treatments our death count would exceed 10 million Americans from this virus alone. Hence a possible .5 percent decrease within the general population death vs live birth rates... it would be the first such declination since the civil war.
The next continent of discussion will be those who succumb to serious side effects area which not immediate but consistent. Then the cause of these re noevirus scientist believe the strain of bubonic plague that is infected squirrels mice and rodents is a very old stage of the original virus. This seems to be roughing from the tundra region shared by Siberia katxmcha Mongolia and the Ming provinces of northern china.... literally it's melting out of previous glacier.lock.
These begin a new set of message me vaccine sequences as such a old strain of the original virus able to infect pigs rodents and man efficiently.
Vaccine process need to begin a new set strains of the aboriginal life and modern plagues construction engineering must be suppressed.
The next continent of discussion will be those who succumb to serious side effects area which not immediate but consistent. Then the cause of these re noevirus scientist believe the strain of bubonic plague that is infected squirrels mice and rodents is a very old stage of the original virus. This seems to be roughing from the tundra region shared by Siberia katxmcha Mongolia and the Ming provinces of northern china.... literally it's melting out of previous glacier.lock.
These begin a new set of message me vaccine sequences as such a old strain of the original virus able to infect pigs rodents and man efficiently.
Vaccine process need to begin a new set strains of the aboriginal life and modern plagues construction engineering must be suppressed.
With a time of mutations to infection the study was released in Japan on the outbreak of corona 19 she had the virus recovered and felt as a Nurse on cruise ship to he reinforced and still reinfected within 3 weeks with a different strain of this virus.
the difference within the strains cause alarm as antibodies of one seem to be inefctive of another.
The mrna 1273 vaccine is proceeding on schedual. 82 sites with a potential 120. Thousand candidates should be receiving vaccination in the fall with 2 billion doses are being manufactured for a jan1st delivery schedual. Oxford university has a seemingly better vaccine as.astra zaneca has entered a 16 thousand person study within epicenter of there vaccine for a 2.billion dose schedual in January. That will cover the population of earth if both vaccines are proven effective.
With a time of mutations to infection the study was released in Japan on the outbreak of corona 19 she had the virus recovered and felt as a Nurse on cruise ship to he reinforced and still reinfected within 3 weeks with a different strain of this virus.
the difference within the strains cause alarm as antibodies of one seem to be inefctive of another.
The mrna 1273 vaccine is proceeding on schedual. 82 sites with a potential 120. Thousand candidates should be receiving vaccination in the fall with 2 billion doses are being manufactured for a jan1st delivery schedual. Oxford university has a seemingly better vaccine as.astra zaneca has entered a 16 thousand person study within epicenter of there vaccine for a 2.billion dose schedual in January. That will cover the population of earth if both vaccines are proven effective.
Stumptownstu is right. Key difference is that other countries can afford to open schools earlier because they are farther ahead in controlling coronavirus spread. According to Fauci, US level of infection is still unacceptably high. Also public health experts don't ignore hospitalization and other data to focus only on death rate.
Stumptownstu is right. Key difference is that other countries can afford to open schools earlier because they are farther ahead in controlling coronavirus spread. According to Fauci, US level of infection is still unacceptably high. Also public health experts don't ignore hospitalization and other data to focus only on death rate.
Just popped up the first link. I'll eventually read through all of what you posted though It may take a day or so, possibly more as there seems to be full studies and I cross reference A LOT! Plus now that there is some semblance of American sports to wager on I can't really justifying laying right next to my wife tinkering on my phone for too long of stretches and NOT capping. 10 minutes here, 20 minutes there, then I gotta put it down.
I will say this. I am skeptical. I have read a lot of scientific writing over the years including many published full studies and one thing I can say definitively without even reading any of it is that we haven't had a large enough window of data collection to be fully conclusive of anything. And when it comes to children it's even less because, as of now, the only people really getting tested are those exhibiting symptoms. So we really don't know if children aren't contracting this, or if they are just typically asymptomatic. Another thing I know is that most of America shut schools down rather swiftly. And children these days are increasingly antisocial, in the conventional sense. We really don't know ANYTHING about the proliferation of this virus amongst children in this country, and very little about such in other countries. What do we really honestly have to go on?
Just popped up the first link. I'll eventually read through all of what you posted though It may take a day or so, possibly more as there seems to be full studies and I cross reference A LOT! Plus now that there is some semblance of American sports to wager on I can't really justifying laying right next to my wife tinkering on my phone for too long of stretches and NOT capping. 10 minutes here, 20 minutes there, then I gotta put it down.
I will say this. I am skeptical. I have read a lot of scientific writing over the years including many published full studies and one thing I can say definitively without even reading any of it is that we haven't had a large enough window of data collection to be fully conclusive of anything. And when it comes to children it's even less because, as of now, the only people really getting tested are those exhibiting symptoms. So we really don't know if children aren't contracting this, or if they are just typically asymptomatic. Another thing I know is that most of America shut schools down rather swiftly. And children these days are increasingly antisocial, in the conventional sense. We really don't know ANYTHING about the proliferation of this virus amongst children in this country, and very little about such in other countries. What do we really honestly have to go on?
I gotcha. Believe me when I tell you that I sent only a teeny portion to give you some idea. But we have way more data than you realize and we have been looking at it in-depth for a while.
No need to read the whole thing -- just glance at the charts. Look at the countries they show and look at the states they show. I can't recall if I posted it for sure. But it is easy to find. All indicate that it is mostly over now.
But if you get interested in anything in particular you want more information on -- I can post it.
I gotcha. Believe me when I tell you that I sent only a teeny portion to give you some idea. But we have way more data than you realize and we have been looking at it in-depth for a while.
No need to read the whole thing -- just glance at the charts. Look at the countries they show and look at the states they show. I can't recall if I posted it for sure. But it is easy to find. All indicate that it is mostly over now.
But if you get interested in anything in particular you want more information on -- I can post it.
This is addressed in a couple of the links as well. It is easily tracked and predictable by the IFR. It was more the timeframe and geographic location. The countries that locked down vs the ones that did not -- have the same chart. The states early on that are recovered and the ones later on that are recovering -- have the same chart.
This is addressed in a couple of the links as well. It is easily tracked and predictable by the IFR. It was more the timeframe and geographic location. The countries that locked down vs the ones that did not -- have the same chart. The states early on that are recovered and the ones later on that are recovering -- have the same chart.
Back to topic. I live in a town of 20,000 and think the local board came up with a feasible answer. The choice will be left with the parent whether
or not to send their child to school. Class will be both at school and virtually. Same goes for the teachers and other non-teaching positions. It will
be their decision. Seems pretty simple and logical. Eliminates the "blame" game. What say all?
Back to topic. I live in a town of 20,000 and think the local board came up with a feasible answer. The choice will be left with the parent whether
or not to send their child to school. Class will be both at school and virtually. Same goes for the teachers and other non-teaching positions. It will
be their decision. Seems pretty simple and logical. Eliminates the "blame" game. What say all?
Raiders the glitch you have privy 2 may exist. Ad is known is thoae who suffered mild symptoms. 50 percent of all infected may never have ask for or received treatment and abated the symptoms with this is a cold. Need sime day will night quill and maybe a little Imodium ad for the dysentery keeping the fact if they were infected to be known.
Areas such as new York should be ballooning dealing with the first wave causality counts. And could have abated the virus.
But within this consideration students cared for entering school sheltered from the infection being cared for nit raised ferral. Today's student population it is also likely they were not exposed and now exposure gives a higher chance of a more damaging virus...
I agree with Sundance that localities sgould make decisions based on how they feel. Known or not that instinct of mothers protective nature should not be challenged here. Obviously they aren't signing waivers from a Tulsa rally in this context.
Raiders the glitch you have privy 2 may exist. Ad is known is thoae who suffered mild symptoms. 50 percent of all infected may never have ask for or received treatment and abated the symptoms with this is a cold. Need sime day will night quill and maybe a little Imodium ad for the dysentery keeping the fact if they were infected to be known.
Areas such as new York should be ballooning dealing with the first wave causality counts. And could have abated the virus.
But within this consideration students cared for entering school sheltered from the infection being cared for nit raised ferral. Today's student population it is also likely they were not exposed and now exposure gives a higher chance of a more damaging virus...
I agree with Sundance that localities sgould make decisions based on how they feel. Known or not that instinct of mothers protective nature should not be challenged here. Obviously they aren't signing waivers from a Tulsa rally in this context.
federal funding was never needed. With the closure of all interscolastic competition a great wealth of funding does exist locally. The federal education money is an unneeded supplement tell the pig to keep it. We dont do sports this year at a high school level. That funding alone gives is more than a surplus.
federal funding was never needed. With the closure of all interscolastic competition a great wealth of funding does exist locally. The federal education money is an unneeded supplement tell the pig to keep it. We dont do sports this year at a high school level. That funding alone gives is more than a surplus.
World health organization condemns the idea of pursing natural herd immunity as dangerous. Medxiv.org disclaimer states that theorical research hasn't been peer reviewed and shouldn't be used for clinical practice. No country pursues strategy of allowing coronavirus to infect as many people to develop herd immunity because the price is too high in thousands more hospitalizations and deaths. It is unethical and unachievable. Much better to end pandemic with a safe vaccine.
Problem with herd immunity is that enough people must develop antibodies. 70% to 90% of population is a fair estimate. But Lancet study estimates only 5% of the population is immune in Sweden and Spain after thousands of coronavirus cases. Sweden's no lockdown has proven to be a failed experiment. Resulting in more infections, deaths and economic damage than neighbours. South Korea avoids a lockdown of economy because of early extensive testing and contact tracing. However testing and contact tracing are still inadequate in the US.
According to Imperial college London, immunity is temporary. Level of antibodies required to resist infection vanish within months. Besides, waiting for herd immunity isn't necessary because restrictions are effective. Lockdowns, social distancing, hygiene, masks, testing and contact tracing have proven successful in reducing virus spread in many countries.
World health organization condemns the idea of pursing natural herd immunity as dangerous. Medxiv.org disclaimer states that theorical research hasn't been peer reviewed and shouldn't be used for clinical practice. No country pursues strategy of allowing coronavirus to infect as many people to develop herd immunity because the price is too high in thousands more hospitalizations and deaths. It is unethical and unachievable. Much better to end pandemic with a safe vaccine.
Problem with herd immunity is that enough people must develop antibodies. 70% to 90% of population is a fair estimate. But Lancet study estimates only 5% of the population is immune in Sweden and Spain after thousands of coronavirus cases. Sweden's no lockdown has proven to be a failed experiment. Resulting in more infections, deaths and economic damage than neighbours. South Korea avoids a lockdown of economy because of early extensive testing and contact tracing. However testing and contact tracing are still inadequate in the US.
According to Imperial college London, immunity is temporary. Level of antibodies required to resist infection vanish within months. Besides, waiting for herd immunity isn't necessary because restrictions are effective. Lockdowns, social distancing, hygiene, masks, testing and contact tracing have proven successful in reducing virus spread in many countries.
I think you are completely misunderstanding the context or thesis they are using to arrive at this figure and the data that they are using.
This is the one we reviewed a couple of weeks ago. I am going to print it since it is fairly short and explains how they are arriving at this. I omitted the graphs because they don’t come out right. But they are necessary to get the picture of what they are saying. I don’t expect you to worry with the formulae and methodology — just know they are widely accepted.
Several of the sources used include the WHO and Lancet papers, along with 20 others.
I think you are completely misunderstanding the context or thesis they are using to arrive at this figure and the data that they are using.
This is the one we reviewed a couple of weeks ago. I am going to print it since it is fairly short and explains how they are arriving at this. I omitted the graphs because they don’t come out right. But they are necessary to get the picture of what they are saying. I don’t expect you to worry with the formulae and methodology — just know they are widely accepted.
Several of the sources used include the WHO and Lancet papers, along with 20 others.
Abstract
It is widely believed that the herd immunity threshold (HIT) required to prevent a resurgence of SARS-CoV-2 is in excess of 50% for any epidemiological setting. Here, we demonstrate that HIT may be greatly reduced if a fraction of the population is unable to transmit the virus due to innate resistance or cross-protection from exposure to seasonal coronaviruses. The drop in HIT is proportional to the fraction of the population resistant only when that fraction is effectively segregated from the general population; however, when mixing is random, the drop in HIT is more precipitous. Significant reductions in expected mortality can also be observed in settings where a fraction of the population is resistant to infection. These results help to explain the large degree of regional variation observed in seroprevalence and cumulative deaths and suggest that sufficient herd-immunity may already be in place to substantially mitigate a potential second wave.
Main Text
It has been evident from the outset that the risk of severe disease and death from COVID-19 is not uniformly distributed across all age classes, with the bulk of deaths among the +12 million cases reported worldwide (by 12 July 2020, ?(?1?)?) occurring among older age classes and those with comorbidities ?(?2?, ?3?)?. It is further becoming clear that risk of infection is also not uniformly distributed across the population ?(?4?–?9?)?. T-cell and IgG antibody activity have been reported in non-exposed individuals to SARS-CoV-2, suggesting that resistance to infection may accrue from previous exposure to endemic corona viruses ?(?7?, ?10?, ?11?)?. A fraction of the population may also already be intrinsically resistant to infection as a consequence of high functioning innate immunity and such mechanistic reasons as reduced expression of Angiotensin Converting Enzyme 2 (ACE2) ?(?12?)?. Here we present a general framework which can be used to systematically explore the impact of these differences in vulnerability to disease and resistance to infection by SARS-CoV-2 on its epidemiology.
Abstract
It is widely believed that the herd immunity threshold (HIT) required to prevent a resurgence of SARS-CoV-2 is in excess of 50% for any epidemiological setting. Here, we demonstrate that HIT may be greatly reduced if a fraction of the population is unable to transmit the virus due to innate resistance or cross-protection from exposure to seasonal coronaviruses. The drop in HIT is proportional to the fraction of the population resistant only when that fraction is effectively segregated from the general population; however, when mixing is random, the drop in HIT is more precipitous. Significant reductions in expected mortality can also be observed in settings where a fraction of the population is resistant to infection. These results help to explain the large degree of regional variation observed in seroprevalence and cumulative deaths and suggest that sufficient herd-immunity may already be in place to substantially mitigate a potential second wave.
Main Text
It has been evident from the outset that the risk of severe disease and death from COVID-19 is not uniformly distributed across all age classes, with the bulk of deaths among the +12 million cases reported worldwide (by 12 July 2020, ?(?1?)?) occurring among older age classes and those with comorbidities ?(?2?, ?3?)?. It is further becoming clear that risk of infection is also not uniformly distributed across the population ?(?4?–?9?)?. T-cell and IgG antibody activity have been reported in non-exposed individuals to SARS-CoV-2, suggesting that resistance to infection may accrue from previous exposure to endemic corona viruses ?(?7?, ?10?, ?11?)?. A fraction of the population may also already be intrinsically resistant to infection as a consequence of high functioning innate immunity and such mechanistic reasons as reduced expression of Angiotensin Converting Enzyme 2 (ACE2) ?(?12?)?. Here we present a general framework which can be used to systematically explore the impact of these differences in vulnerability to disease and resistance to infection by SARS-CoV-2 on its epidemiology.
Our model (see ?Supplementary Text File?) links two subpopulations (groups 1 and 2) by means of an interaction matrix in which d ( 0 < d < 1 ) specifies the degree of within-group mixing in a subpopulation of proportion ? . Thus, all contacts are within the respective groups (i.e. mixing is fully assortative) when d = 1 , and between-group mixing is maximised at d = 0 . Random or proportionate mixing occurs when d = ? . We define the basic reproduction number ( R0 ) for each group as the fundamental transmission potential of the virus within a homogenous population consisting of members of that group. Rates of loss of infection and immunity are given respectively as s and ? .
The incidence of deaths can be derived from this general framework by assigning appropriate infection fatality rates to the different subpopulations, and factoring in a delay between infection and death. For SARS-CoV-2, this can be achieved by defining a vulnerable fraction to which deaths are confined (see ?Supplementary Text File?). However, since the vulnerable fraction is likely to be small, the level of population-wide immunity required to reverse the growth rate of infections may be expected to remain at 1 - 1/R0 , where R0 is the basic reproduction number in the general population. By contrast, if a fraction ? of the population is resistant to infection ( R01 = 0) , the herd immunity threshold (HIT) is given as (1 - ?)(1 - 1 [1/(1 - (1-d)? )]) , for all values of ? . This suggests that a wide variation in HIT can be R0 (1-?) observed depending on the proportion resistant, the R0 within the non-resistant group and the degree of mixing between resistant and non-resistant groups.
When mixing is fully assortative, HIT = (1 - ?)(1 - 1/R0 ) . In other words, the HIT declines in proportion to the size of the resistant group (?Figure 1A?). For example, when R0 = 2 , HIT will be reached at 25% if half the population is resistant. By contrast, under proportionate (i.e. random) mixing, HIT = 1 - 1/R0 - ? (?Figure 1B?). This implies that the pathogen will not spread unless the proportion immune is below 1 - 1/R0 . Thus, under the same condition of half the population being resistant, no epidemic will occur unless R0 > 2 . The dependence of HIT on the degree of within-group mixing ( d ) increases with the proportion resistant ? (?Figures 2 A & C?), exhibiting their lowest values in a disassortative extreme ( d = 0 ). We expect that, in most populations, the resistant and non-resistant groups will mix proportionately (represented by the white line in ?Figure 2?) but, even in the assortative extreme, the values for HIT we obtain (?Table 1?) are well below those reported by Britton et al ?(?13?) in relation to the effects of age and activity structure on HIT. Our results are in broad agreement with those of Gomes et al. ?(?14?) under substantial individual variation in susceptibility or connectivity, and the two exercises should be seen to reinforce each other. Our binary approach of resistant versus susceptible with structured mixing has the advantage that we can display the entire range of possible outcomes without needing to explicitly measure the coefficient of variation in susceptibility and exposure to infection. Incomplete resistance can be implemented within this framework by allowing R01 = F × R02 where 0 < F < 1 (?Figure S1?); our simulations indicate that under incomplete resistance, the reduction in HIT is roughly proportional to F (for example, 50% of the population being 50% resistant is roughly equivalent 25% with complete resistance, under proportionate mixing, when R0 = 1.5 ).
Our model (see ?Supplementary Text File?) links two subpopulations (groups 1 and 2) by means of an interaction matrix in which d ( 0 < d < 1 ) specifies the degree of within-group mixing in a subpopulation of proportion ? . Thus, all contacts are within the respective groups (i.e. mixing is fully assortative) when d = 1 , and between-group mixing is maximised at d = 0 . Random or proportionate mixing occurs when d = ? . We define the basic reproduction number ( R0 ) for each group as the fundamental transmission potential of the virus within a homogenous population consisting of members of that group. Rates of loss of infection and immunity are given respectively as s and ? .
The incidence of deaths can be derived from this general framework by assigning appropriate infection fatality rates to the different subpopulations, and factoring in a delay between infection and death. For SARS-CoV-2, this can be achieved by defining a vulnerable fraction to which deaths are confined (see ?Supplementary Text File?). However, since the vulnerable fraction is likely to be small, the level of population-wide immunity required to reverse the growth rate of infections may be expected to remain at 1 - 1/R0 , where R0 is the basic reproduction number in the general population. By contrast, if a fraction ? of the population is resistant to infection ( R01 = 0) , the herd immunity threshold (HIT) is given as (1 - ?)(1 - 1 [1/(1 - (1-d)? )]) , for all values of ? . This suggests that a wide variation in HIT can be R0 (1-?) observed depending on the proportion resistant, the R0 within the non-resistant group and the degree of mixing between resistant and non-resistant groups.
When mixing is fully assortative, HIT = (1 - ?)(1 - 1/R0 ) . In other words, the HIT declines in proportion to the size of the resistant group (?Figure 1A?). For example, when R0 = 2 , HIT will be reached at 25% if half the population is resistant. By contrast, under proportionate (i.e. random) mixing, HIT = 1 - 1/R0 - ? (?Figure 1B?). This implies that the pathogen will not spread unless the proportion immune is below 1 - 1/R0 . Thus, under the same condition of half the population being resistant, no epidemic will occur unless R0 > 2 . The dependence of HIT on the degree of within-group mixing ( d ) increases with the proportion resistant ? (?Figures 2 A & C?), exhibiting their lowest values in a disassortative extreme ( d = 0 ). We expect that, in most populations, the resistant and non-resistant groups will mix proportionately (represented by the white line in ?Figure 2?) but, even in the assortative extreme, the values for HIT we obtain (?Table 1?) are well below those reported by Britton et al ?(?13?) in relation to the effects of age and activity structure on HIT. Our results are in broad agreement with those of Gomes et al. ?(?14?) under substantial individual variation in susceptibility or connectivity, and the two exercises should be seen to reinforce each other. Our binary approach of resistant versus susceptible with structured mixing has the advantage that we can display the entire range of possible outcomes without needing to explicitly measure the coefficient of variation in susceptibility and exposure to infection. Incomplete resistance can be implemented within this framework by allowing R01 = F × R02 where 0 < F < 1 (?Figure S1?); our simulations indicate that under incomplete resistance, the reduction in HIT is roughly proportional to F (for example, 50% of the population being 50% resistant is roughly equivalent 25% with complete resistance, under proportionate mixing, when R0 = 1.5 ).
Herd-immunity threshold and associated percentage decrease in mortality. ?Herd-immunity threshold (A) and percent decrease in mortality (B) ?for R0 = 1.5 under different combinations of proportion resistant ( ? ) and levels of within-group mixing ( d ). Panels C and D present the same output but for R0 = 2.5. Simulations ran for 365 days with1/s= 5 days, ? = 0, R01 = 0 and R0 = R02 . Each color band in the color scales equates to a 0.125 change, and black covers the range 0-0.01 in panels A, C and the range 99-100 in panels B, D. For visualisation purposes the percent decrease in mortality is 100 × (1 - z/z?=0) , where z is the proportion exposed at the end of the simulation. The white line designates proportionate mixing ( ? = d) separating an area of assortative (higher within group) mixing above from disassortative (higher between groups) mixing in the area below.
Maintaining the proportion immune above the threshold of herd immunity prevents the associated pathogen from establishing and spreading within a population. Otherwise, infections will continue to increase until the HIT is reached. Thereafter, the incidence of new infections will fall but the proportion exposed will overshoot HIT and settle eventually at a value often much in excess of HIT (?Figure S2?). Substantial reductions in cumulative mortality can be obtained as the resistant proportion increases (?Figures 2 B & D?) which could provide a simple explanation for the wide variation in death rates reported across various regions.
Provided the proportion of the population exposed is in excess of the HIT, any subsequent epidemic will not occur until the susceptible population is replenished through births and/or loss of immunity. Non-pharmaceutical interventions preventing the proportion exposed from exceeding the HIT, will leave the population open to further growth in infections once these measures are eased. We further stress that HIT is independent of the rate of loss of immunity ( ? ) although the latter will affect the timing and magnitude of the subsequent epidemic peaks (?Figure S3?). Moreover, the public health impact of subsequent peaks will depend on the degree to which previous exposure reduces severity of disease, and not just whether infection-blocking immunity is lost. Given the mounting evidence that exposure to seasonal coronaviruses offers protection against clinical symptoms ?(?9?)?, it would be reasonable to assume that exposure to SARS-CoV-2 itself would confer a significant degree of clinical immunity. Thus, a second peak may result in far fewer deaths, particularly among those with comorbidities in the younger age classes.
Determining the proportion exposed for SARS-CoV-2 is not possible through tracking clinical cases since the majority of infections are likely to be asymptomatic ?(?15?)?, although symptom tracking and other proxies such as excess influenza-like-illness provide a promising alternative route ?(?16?, ?17)? ?. Obtaining these data through serological surveys has proved to be a challenge, principally due to the variability in both antibody and cellular immune responses among exposed individuals and their kinetics ?(?18)? ?. Reported levels of seroprevalence have not come close to what people believe to be necessary for herd immunity ?(?18–? ?22?)?. Our results indicate that a wide variation in reported levels of exposure to SARS-CoV-2 can arise as a result of differences in the proportion of the population resistant to infection ( ? ). High levels of seropositivity can arise under a reasonable range of ? and R0 where HIT is nonetheless lower than the proportion of the population already exposed (?Figure S2?).
Herd-immunity threshold and associated percentage decrease in mortality. ?Herd-immunity threshold (A) and percent decrease in mortality (B) ?for R0 = 1.5 under different combinations of proportion resistant ( ? ) and levels of within-group mixing ( d ). Panels C and D present the same output but for R0 = 2.5. Simulations ran for 365 days with1/s= 5 days, ? = 0, R01 = 0 and R0 = R02 . Each color band in the color scales equates to a 0.125 change, and black covers the range 0-0.01 in panels A, C and the range 99-100 in panels B, D. For visualisation purposes the percent decrease in mortality is 100 × (1 - z/z?=0) , where z is the proportion exposed at the end of the simulation. The white line designates proportionate mixing ( ? = d) separating an area of assortative (higher within group) mixing above from disassortative (higher between groups) mixing in the area below.
Maintaining the proportion immune above the threshold of herd immunity prevents the associated pathogen from establishing and spreading within a population. Otherwise, infections will continue to increase until the HIT is reached. Thereafter, the incidence of new infections will fall but the proportion exposed will overshoot HIT and settle eventually at a value often much in excess of HIT (?Figure S2?). Substantial reductions in cumulative mortality can be obtained as the resistant proportion increases (?Figures 2 B & D?) which could provide a simple explanation for the wide variation in death rates reported across various regions.
Provided the proportion of the population exposed is in excess of the HIT, any subsequent epidemic will not occur until the susceptible population is replenished through births and/or loss of immunity. Non-pharmaceutical interventions preventing the proportion exposed from exceeding the HIT, will leave the population open to further growth in infections once these measures are eased. We further stress that HIT is independent of the rate of loss of immunity ( ? ) although the latter will affect the timing and magnitude of the subsequent epidemic peaks (?Figure S3?). Moreover, the public health impact of subsequent peaks will depend on the degree to which previous exposure reduces severity of disease, and not just whether infection-blocking immunity is lost. Given the mounting evidence that exposure to seasonal coronaviruses offers protection against clinical symptoms ?(?9?)?, it would be reasonable to assume that exposure to SARS-CoV-2 itself would confer a significant degree of clinical immunity. Thus, a second peak may result in far fewer deaths, particularly among those with comorbidities in the younger age classes.
Determining the proportion exposed for SARS-CoV-2 is not possible through tracking clinical cases since the majority of infections are likely to be asymptomatic ?(?15?)?, although symptom tracking and other proxies such as excess influenza-like-illness provide a promising alternative route ?(?16?, ?17)? ?. Obtaining these data through serological surveys has proved to be a challenge, principally due to the variability in both antibody and cellular immune responses among exposed individuals and their kinetics ?(?18)? ?. Reported levels of seroprevalence have not come close to what people believe to be necessary for herd immunity ?(?18–? ?22?)?. Our results indicate that a wide variation in reported levels of exposure to SARS-CoV-2 can arise as a result of differences in the proportion of the population resistant to infection ( ? ). High levels of seropositivity can arise under a reasonable range of ? and R0 where HIT is nonetheless lower than the proportion of the population already exposed (?Figure S2?).
Equally, seropositivity measures of 10-20% are entirely compatible with local levels of immunity having approached or even exceeded the HIT, in which case the risk and scale of resurgence is lower than currently perceived.
Equally, seropositivity measures of 10-20% are entirely compatible with local levels of immunity having approached or even exceeded the HIT, in which case the risk and scale of resurgence is lower than currently perceived.
Yes. This is standard in this situation for it to be released as a ‘preprint’ while being evaluated.
They are arriving at this from several angles. The Peru, ICE, Princess Diamond, are all called into question at some point. T-cells and age stratification are examined. Basically, 4 types of Coronaviruses with cold symptoms play into the T-cell exposure as well. Asymptotic situations have to be factored in.
Vaccine would be ideal. Sure. But you have to keep in mind two or three thing. No vaccine has been developed effectively for a Coronavirus yet. This is UR — basically an external situation. So, that makes it tricky. And, the effectiveness of a vaccine throughout progression.
So, no one is advocating just letting everyone get exposed. That is never the plan. It is a matter of determining the true HIT needed. Etc. Etc.
Yes. This is standard in this situation for it to be released as a ‘preprint’ while being evaluated.
They are arriving at this from several angles. The Peru, ICE, Princess Diamond, are all called into question at some point. T-cells and age stratification are examined. Basically, 4 types of Coronaviruses with cold symptoms play into the T-cell exposure as well. Asymptotic situations have to be factored in.
Vaccine would be ideal. Sure. But you have to keep in mind two or three thing. No vaccine has been developed effectively for a Coronavirus yet. This is UR — basically an external situation. So, that makes it tricky. And, the effectiveness of a vaccine throughout progression.
So, no one is advocating just letting everyone get exposed. That is never the plan. It is a matter of determining the true HIT needed. Etc. Etc.
So with the earlier Farr explanation coupled with this — you can see the timeframe makes it almost impossible to have the higher HIT that most were predicting or anticipating.
So with the earlier Farr explanation coupled with this — you can see the timeframe makes it almost impossible to have the higher HIT that most were predicting or anticipating.
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