12 ms·

Small but important correction: nothing can make epidemiological spread non-exponential. Driving base reproduction below one additional infection per infected p

Small but important correction: nothing can make epidemiological spread non-exponential. Driving base reproduction below one additional infection per infected patient means the exponent is less than one, so the incidence of the disease rapidly decreases. This decrease is also exponential by definition: infection is simply an exponential process, and an exponential equation doesn't stop being what it is when the exponent is less than one. The steady state is exactly 1, which is like balancing a pencil on its point. It's plausible that two things happened here: the various local restrictions reduced the R0 of flu below 1, and the border closures kept mutations from traveling: and influenza is notoriously mutation-prone. These can combine to practically extirpate influenza. Unfortunately, the effect is temporary, and the next flu season is likely to be a real doozy. Which will be "fun" because our societies now have a hyperactive immune system, and there will be considerable political pressure to "do something" about the next flu wave. This must be resisted but I'm not optimistic.

Majromax 6y ago
> The steady state is exactly 1, which is like balancing a pencil on its point. At exactly one, it's indeterminate; you could see a subexponential growth or decay. With no exponential terms remaining, lower-order terms that are ordinarily hidden by exponential growth become the dominant observables. (Since epidemic spread is also random, you're much more likely to see the stochastic terms show up in the overall statistics in these cases. You really can be lucky or unlucky with Rt ~= 1, but there's no persistent luck with Rt >> 1.) This is also important before community spreading sets in, and it is the mechanism by which contact tracing can work. Rather than change the general susceptibility of the population to the disease (changing the effective reproduction number), contact tracing tries to operate at the level of individual cases in ways that cannot be scaled to uncontrolled community spreading (even if Rt is close to 1). > and the border closures kept mutations from traveling: and influenza is notoriously mutation-prone. Perhaps, but are influenza mutations an important effect within a single flu season? I know the determination of to-be-dominant strains has a great effect on the composition of each season's flu vaccine, but as far as I am aware we don't see declining flu vaccine efficacy over a season.
- Pyramus 6y ago
  By the way, now that we are already talking about R ~= 1 ... Over pretty much the last year you could observe, in different countries all around the world, that the reproduction number was 'magically' floating around 1. Only recently did I learn that this effect was puzzling for epidemiologists as well and was only solved around 2012 (?) in a model that assumes a network of information about the disease in parallel to the network of disease transmission. The resulting feedback loops lead to the meta-stability of R=1. Super interesting how society acts as this distributed information processor, similar to 'the market' in economics.
  - marvin 6y ago
    A well-known Norwegian economic commentator pointed this out in a newspaper article a few weeks ago. You'll eventually be forced to maintain an R~=1 no matter what you do, so it's best for everyone if your cases have a low baseline when that happens. The measures will be the same, but the baseline risk can either be terrible or okay. You can almost see the phenomenon in real time during this pandemic. Countries that have low trust in authorities will still freak out when the epidemic hits biblical proportions, and do various forms of impromptu distancing measures which will bring the R number down. Then when the signs of panic subside, they'll loosen them. And so on. Societies with high trust in authorities will still pressure their authorities to loosen up when things feel safe, with predictible results, leading to further lockdowns.
    - LeCow 6y ago
      The economic deviation caused by governments over reacting is your biggest pressure. Unless you shut down all travel, bars, restaurants, schools, universities and dating. Then all of this will come back in the future and kick you in the teeth. Either we're going to have to accept this as a way of life, which is more detrimental. Or we're pushing off the inevitable.
      - marvin 6y ago
        No one has overreacted, unless you accept an outcome that both leads to improvised individual social distancing and the even worse worse economic devastation that follows. This was uncertain to most people last year, but now we’ve seen so many examples that it really shouldn’t be so controversial any longer. But if it wasn’t, we wouldn’t be discussing it. The covid virus is evolved to fit exactly into the niche of societal behavior where it will be a big fucking problem but not so bad that it’s immediately obvious to enough people.
toss1 6y ago
>> there will be considerable political pressure to "do something" about the next flu wave. This must be resisted Why on earth does it make sense to resist sensible public health measures to reduce the influenza to R0<1? The measures would not need to be nearly as drastic as those for COVID ("normal" R0 of 2 vs 2.5+), so more handwashing (good to minimize a broad spectrum of pathogens), masks (already culturally ordinary in many countries), and especially better indoor ventilation systems would be a long-term benefit to everyone. I'm mostly hoping that the success of better sequencing, mRNA vaccine technology, and the rapid development deployed for CV-19 will also be applicable to influenza and help minimize or practically eliminate it. Are you assuming other measures?
- pmoriarty 6y ago
  "so more handwashing (good to minimize a broad spectrum of pathogens), masks (already culturally ordinary in many countries), and especially better indoor ventilation systems" Let's not forget a substantial portion of the population working from home, using less public transportation (choosing to travel by car when traveling at all), a huge decrease in tourism and large public gatherings, much less eating out at restaurants, contactless food delivery becoming the norm, etc. So many factors figure in to why much of the (wealthy, developed) world is a lot more resistant to contagious pathogens today than it was a year ago.
- Mountain_Skies 6y ago
  Politicians have shown themselves throughout this pandemic to be opportunistic authoritarians who obviously don't believe in their mandates since they break them themselves so frequently. There's no reason to expect that these sociopaths won't jump at the opportunity to drink more from the fountain of power again given the chance. Since they've gotten away with so much this time, they might even be tempted to go even further next time.
  - toss1 6y ago
    Are you serious? If anything, politicians have vastly under-managed the situation, timidly afraid of offending constituents' offense at any inconvenience, and only partially at best following sound science. In states that did issue orders for masks and stay-at-home, the orders were weak, late, and lifted early, resulting in multiple waves that only abate now because of the rapid deployment of vaccines. Most importantly, there was very little and late funding to cover the costs of those who should most have been shut down, group travel, entertainment, dining, etc. - should have been fully shut down immediately, and everyone's costs covered. 6-10 weeks of hard shutdown, while standing up a full masking, test/trace/isolate protocol would have handled it, yet few countries did it. A few countries did implement early, strong, and effective measures, such as New Zealand. They also then opened up many months earlier than the rest of the world with near-normal life. Where are the politicians "drunk with power" who are restarting lockdowns for their own gratification? Where is the advantage for such a "drunk on power" politician? What could they possible gain by unnecessarily implementing measures that are seen at best by the smart ones who understand it as a necessary inconvenience, and by the rest as an assault on them? Even flat-out authoritarians do no such thing. E.g., China, who is unashamed to run literal concentration camps for Uyghur minorities, and who did hard lockdowns at the start, is not opening up as soon as scientifically feasible. Unless you can show some citations of evidence, this looks a lot less like a real phenomenon, and more like a pseudo-libertarian teenager's trope.
im3w1l 6y ago
At a super fundamental level, epidemics take place on a social graph. In a well connected graph spread will be exponential, but depending on graph shape it could be something else. In particular you could imagine that if people never venture outside their own block that the social network is an euclidean graph. In an ideal case where people are evenly spaced in the plane and only interact with neighbors, the disease would spread as a circle expanding outwards, so total infections would be proportional to ~ t^2, and current infections ~ t.
- biomcgary 6y ago
  You are essentially describing a supersized plaque assay (https://en.wikipedia.org/wiki/Virus_quantification#Plaque_assay https://en.wikipedia.org/wiki/Virus_quantification#Plaque_as...).
- dTal 6y ago
  I'm perplexed why anyone would downvote this comment; it seems very interesting and insightful to me.
  - Fomite 6y ago
    I'm perplexed as well. That the perfect mixing models most people think of for infectious diseases are an imperfect approximation of the actual dynamics on a graph is well known in epidemiology.
dragonwriter 6y ago
>>Small but important correction: nothing can make epidemiological spread non-exponential. “Exponential with R varying over time” and “not exponential” differ only in interpretation imposed by an observer. > infection is simply an exponential process No, in the hyperidealized perfect mixing scenario, its a logistic process, like most other resource constrained processed that look exponential when analyzed over a dhort period. In the real world, its neither exponential nor even perfectly logistic, even before considering changes to the environment in which the disease spreads (including those induced by the disease, including people’s response to knowledge of it.)
javagram 6y ago
> Which will be "fun" because our societies now have a hyperactive immune system, and there will be considerable political pressure to "do something" about the next flu wave. So, do something by taking a flu vaccine like is already available and recommended for annual use by the CDC?
- makomk 6y ago
  The flu vaccine isn't hugely effective at the best of times, and with flu disappearing worldwide and global travel locked down I don't see how they'll even be able to figure out what strains to target for the next one.
  - enkid 6y ago
    Even when not perfectly matched, the flu vaccine does offer some protection.
    - jogundas 6y ago
      Both @makomk and @enkid seem to be right [0]. [0] https://www.cochrane.org/CD001269/ARI_vaccines-prevent-influenza-healthy-adults https://www.cochrane.org/CD001269/ARI_vaccines-prevent-influ...

Majromax 6y ago

> The steady state is exactly 1, which is like balancing a pencil on its point. At exactly one, it's indeterminate; you could see a subexponential growth or decay. With no exponential terms remaining, lower-order terms that are ordinarily hidden by exponential growth become the dominant observables. (Since epidemic spread is also random, you're much more likely to see the stochastic terms show up in the overall statistics in these cases. You really can be lucky or unlucky with Rt ~= 1, but there's no persistent luck with Rt >> 1.) This is also important before community spreading sets in, and it is the mechanism by which contact tracing can work. Rather than change the general susceptibility of the population to the disease (changing the effective reproduction number), contact tracing tries to operate at the level of individual cases in ways that cannot be scaled to uncontrolled community spreading (even if Rt is close to 1). > and the border closures kept mutations from traveling: and influenza is notoriously mutation-prone. Perhaps, but are influenza mutations an important effect within a single flu season? I know the determination of to-be-dominant strains has a great effect on the composition of each season's flu vaccine, but as far as I am aware we don't see declining flu vaccine efficacy over a season.

Pyramus 6y ago
By the way, now that we are already talking about R ~= 1 ... Over pretty much the last year you could observe, in different countries all around the world, that the reproduction number was 'magically' floating around 1. Only recently did I learn that this effect was puzzling for epidemiologists as well and was only solved around 2012 (?) in a model that assumes a network of information about the disease in parallel to the network of disease transmission. The resulting feedback loops lead to the meta-stability of R=1. Super interesting how society acts as this distributed information processor, similar to 'the market' in economics.
- marvin 6y ago
  A well-known Norwegian economic commentator pointed this out in a newspaper article a few weeks ago. You'll eventually be forced to maintain an R~=1 no matter what you do, so it's best for everyone if your cases have a low baseline when that happens. The measures will be the same, but the baseline risk can either be terrible or okay. You can almost see the phenomenon in real time during this pandemic. Countries that have low trust in authorities will still freak out when the epidemic hits biblical proportions, and do various forms of impromptu distancing measures which will bring the R number down. Then when the signs of panic subside, they'll loosen them. And so on. Societies with high trust in authorities will still pressure their authorities to loosen up when things feel safe, with predictible results, leading to further lockdowns.
  - LeCow 6y ago
    The economic deviation caused by governments over reacting is your biggest pressure. Unless you shut down all travel, bars, restaurants, schools, universities and dating. Then all of this will come back in the future and kick you in the teeth. Either we're going to have to accept this as a way of life, which is more detrimental. Or we're pushing off the inevitable.
    - marvin 6y ago
      No one has overreacted, unless you accept an outcome that both leads to improvised individual social distancing and the even worse worse economic devastation that follows. This was uncertain to most people last year, but now we’ve seen so many examples that it really shouldn’t be so controversial any longer. But if it wasn’t, we wouldn’t be discussing it. The covid virus is evolved to fit exactly into the niche of societal behavior where it will be a big fucking problem but not so bad that it’s immediately obvious to enough people.

toss1 6y ago

>> there will be considerable political pressure to "do something" about the next flu wave. This must be resisted Why on earth does it make sense to resist sensible public health measures to reduce the influenza to R0<1? The measures would not need to be nearly as drastic as those for COVID ("normal" R0 of 2 vs 2.5+), so more handwashing (good to minimize a broad spectrum of pathogens), masks (already culturally ordinary in many countries), and especially better indoor ventilation systems would be a long-term benefit to everyone. I'm mostly hoping that the success of better sequencing, mRNA vaccine technology, and the rapid development deployed for CV-19 will also be applicable to influenza and help minimize or practically eliminate it. Are you assuming other measures?

pmoriarty 6y ago
"so more handwashing (good to minimize a broad spectrum of pathogens), masks (already culturally ordinary in many countries), and especially better indoor ventilation systems" Let's not forget a substantial portion of the population working from home, using less public transportation (choosing to travel by car when traveling at all), a huge decrease in tourism and large public gatherings, much less eating out at restaurants, contactless food delivery becoming the norm, etc. So many factors figure in to why much of the (wealthy, developed) world is a lot more resistant to contagious pathogens today than it was a year ago.
Mountain_Skies 6y ago
Politicians have shown themselves throughout this pandemic to be opportunistic authoritarians who obviously don't believe in their mandates since they break them themselves so frequently. There's no reason to expect that these sociopaths won't jump at the opportunity to drink more from the fountain of power again given the chance. Since they've gotten away with so much this time, they might even be tempted to go even further next time.
- toss1 6y ago
  Are you serious? If anything, politicians have vastly under-managed the situation, timidly afraid of offending constituents' offense at any inconvenience, and only partially at best following sound science. In states that did issue orders for masks and stay-at-home, the orders were weak, late, and lifted early, resulting in multiple waves that only abate now because of the rapid deployment of vaccines. Most importantly, there was very little and late funding to cover the costs of those who should most have been shut down, group travel, entertainment, dining, etc. - should have been fully shut down immediately, and everyone's costs covered. 6-10 weeks of hard shutdown, while standing up a full masking, test/trace/isolate protocol would have handled it, yet few countries did it. A few countries did implement early, strong, and effective measures, such as New Zealand. They also then opened up many months earlier than the rest of the world with near-normal life. Where are the politicians "drunk with power" who are restarting lockdowns for their own gratification? Where is the advantage for such a "drunk on power" politician? What could they possible gain by unnecessarily implementing measures that are seen at best by the smart ones who understand it as a necessary inconvenience, and by the rest as an assault on them? Even flat-out authoritarians do no such thing. E.g., China, who is unashamed to run literal concentration camps for Uyghur minorities, and who did hard lockdowns at the start, is not opening up as soon as scientifically feasible. Unless you can show some citations of evidence, this looks a lot less like a real phenomenon, and more like a pseudo-libertarian teenager's trope.

im3w1l 6y ago

At a super fundamental level, epidemics take place on a social graph. In a well connected graph spread will be exponential, but depending on graph shape it could be something else. In particular you could imagine that if people never venture outside their own block that the social network is an euclidean graph. In an ideal case where people are evenly spaced in the plane and only interact with neighbors, the disease would spread as a circle expanding outwards, so total infections would be proportional to ~ t^2, and current infections ~ t.

biomcgary 6y ago
You are essentially describing a supersized plaque assay (https://en.wikipedia.org/wiki/Virus_quantification#Plaque_assay https://en.wikipedia.org/wiki/Virus_quantification#Plaque_as...).
dTal 6y ago
I'm perplexed why anyone would downvote this comment; it seems very interesting and insightful to me.
- Fomite 6y ago
  I'm perplexed as well. That the perfect mixing models most people think of for infectious diseases are an imperfect approximation of the actual dynamics on a graph is well known in epidemiology.

dragonwriter 6y ago

>>Small but important correction: nothing can make epidemiological spread non-exponential. “Exponential with R varying over time” and “not exponential” differ only in interpretation imposed by an observer. > infection is simply an exponential process No, in the hyperidealized perfect mixing scenario, its a logistic process, like most other resource constrained processed that look exponential when analyzed over a dhort period. In the real world, its neither exponential nor even perfectly logistic, even before considering changes to the environment in which the disease spreads (including those induced by the disease, including people’s response to knowledge of it.)

javagram 6y ago

> Which will be "fun" because our societies now have a hyperactive immune system, and there will be considerable political pressure to "do something" about the next flu wave. So, do something by taking a flu vaccine like is already available and recommended for annual use by the CDC?

makomk 6y ago
The flu vaccine isn't hugely effective at the best of times, and with flu disappearing worldwide and global travel locked down I don't see how they'll even be able to figure out what strains to target for the next one.
- enkid 6y ago
  Even when not perfectly matched, the flu vaccine does offer some protection.
  - jogundas 6y ago
    Both @makomk and @enkid seem to be right [0]. [0] https://www.cochrane.org/CD001269/ARI_vaccines-prevent-influenza-healthy-adults https://www.cochrane.org/CD001269/ARI_vaccines-prevent-influ...