"This paper is head and shoulders above anything I found during my own literature review and just comes out and says everything (I?) painfully tried to piece together."
Regarding babies, I think there's also some inter-generational immunity that can be transferred from mom to baby either in-utero or through breastfeeding. So the population has some ongoing immunity that passes on and keeps the diseases in check. That's why new diseases that jump from animals to humans are specially devastating at first but eventually become more of a background issue as the population as a whole builds immunity and is able to pass it forward to its descendants.
I don't know the answer to the fire question but if i had to guess i'd say it's a combination of changing wind conditions and natural barriers. If the wind no longer goes south then the fire will more or less stop going south, and if there's a mountain or river along the way then you need pretty powerful wind to bypass it. Especially if the natural barrier is more wet than the original fire area.
> Assuming there is at least one continuous line of trees connecting (eg) Maine to Georgia, why didn’t every forest fire burn the entire East Coast to a crisp back before there were human firefighters?
uhhhhh, rain?
also having lived on the east coast, the climate is much wetter in general, to the point where live wood has enough water content to be incredibly difficult to light (even on purpose, as I can attest from my days as a Boy Scout), and any dead wood which builds up on the ground quickly becomes rotten and soggy
forest fires are rare on the East Coast, except in times/places going through truly exceptional droughts, and tend to be small localized affairs even then
What is with the hostility towards mask requirements? I take Rafal S. to be illustrative, though not necessarily typical. Anyway, the use of masks in public places was distinctive of a number of different east asian populations for quite a while before the current pandemic. It's not like this was an idea cooked up in an FDA boardroom or something.
In fact, the evidence that masks work has tended to overturn long-held orthodoxy vis-a-vis aerosol spread of respiratory illness; it's hardly a holdover of hidebound bureaucracy or pick your favorite dysfunction/conspiracy theory. And it makes total intuitive sense; covering your mouth when you cough has been a staple of western etiquette for much longer than I've been alive.
It's also, for what it's worth, a truly miniscule change in behavior that takes about a week to go from slightly strange to completely anodyne. And resistance is hardly universal among western countries; in Germany, there is plenty of kicking and screaming about Covid rules but as far as I can tell, comparatively little complaint about requirements to wear a mask in indoor public places.
So basically, what the heck is going on here? Why is "masking" being lumped in with lockdowns and vaccine requirements as if the two go hand in hand when in fact they're almost total opposites? Mask requirements are almost literally the least you could do, yet it's represented here as something approaching Soylent Green.
"I’m having trouble figuring out how to analyze this point. After thinking about it, maybe the problem is I don’t have a good sense of why fires ever stop. Assuming there is at least one continuous line of trees connecting (eg) Maine to Georgia, why didn’t every forest fire burn the entire East Coast to a crisp back before there were human firefighters?"
Having grown up on the west coast in a heavily wooded region, I remember learning about this in school. So I might have the details wrong, but this is what I remember.
Namely, fires keep on spreading until they
a) run across a natural roadblock they can't cross like a wide river or very tall mountain, an area that already burned fairly recently and had no fuel, or the ocean
b) the weather changes (rain, cool temperatures, etc) and it puts the fire out
c) it runs out of fuel.
This means that in many regions you'd have smaller fires fairly regularly that would burn slow but steady until the weather turned, and occasionally you'd have super fires that would spread thousands of miles and burn huge tracts of land before running into natural barriers and burning themselves out. The super fires tended to occur rarely, when there was enough fuel on the ground that hadn't burned and you got the perfect conditions for a huge burn (hot, dry, and high winds).
So that natural state of things for large, heavily forested regions in nature is for there to be some slow burning ground fires pretty much every summer that last until it rains, and the occasional really big fire. See for example the "Big Burn" of 1910 where three million acres of forest were burned to ashes in less than two days. The cause was a drought and unusually long dry spell. This led to many small slow burning fires like normal, but then one day hurricane force winds hit the region and whipped all the small fires into one huge inferno. It didn't really stop until a cold front moved in with lots of snow.
This is normal. Many times I've visited "The Grove of the Patriarchs" at Mt. Rainier National Park where some of the oldest trees in the region grow (some over 1,000 years old and 40 feet in diameter). The reason given for why they've survived so long is that they're on an island in the middle of the Ohanapacosh river, and apparently are situated just right to have survived all the megafires over the last 1,000 years.
Endemic diseases, avalanches, earthquakes, forest fires, and probably a million other things exhibit "self-organized criticality". You've got some thing that, if it happens, wants to spread to nearby units, but is more likely to spread to nearby units that haven't had it in a while. (An infection is more likely in a person with waning immunity than fresh immunity; the snow on a square inch of mountain slope is more likely to slide if there's several days of fresh snowfall on top than if it just slid; a bit of rock is more likely to slip if it's got more built up tension than if it's just been released; a square mile of forest is more likely to burn if it's got several years of unburnt underbrush than if it just burnt.) When you have lots of buildup and no immunity, so that R>1 everywhere in the network, then a spark anywhere burns/pandemics/avalanches everything. When you've got lots of immunity and no buildup, and the system is everywhere near some particular R<1, then your average outbreak infects 1/(1-R) total people before dying out. But when the average R in the system is close to 1, a lot will depend on the detailed network structure, and outbreaks/avalanches/earthquakes/forest fires can end up of any size, with a power law distribution of sizes, but on average they still leave most of the system right near that margin of 1 (unlike pandemics or global conflagrations).
I guess respiratory diseases and forest fires in temperate zones have lots of seasonality, so if they spend a lot of time far enough from 1 in either direction, then the fire season/flu season will end up having a characteristic size each year (proportional to the amount of immunity that is lost in the summer/winter while seasonality suppresses flu/fire). But earthquakes don't get this periodic forcing, so they stay near the critical edge.
Except that your thinking and everyone else's thinking on seasonality is wrong. Or rather it is fine but likely irrelevant, since this is a bioengineered lab-created virus. If this were Your virus, would you have made it seasonal? Maybe somewhat just to fool people. Let's remember that bioweapons do their best damage when they tie up resources and demoralize everyone and the more the better. Nevertheless, there will be some seasonality due to humidity, which is the primary cause of all seasonality. This virus was also engineered to accept add-on modules to be released down the road. People call it a "coronavirus" but it is much more. We need to adjust our thinking.
It strikes me as interesting that immunity tends to wane on the order of a year, and that lines up with the seasonal variation in R0. Any idea why the evolutionary equilibrium would find this timeline for immunity wane as optimal?
Can someone give intuition for why it must be that way? This seems like the crucial bit.
EDIT: ok, it makes sense that conditioned on the fact that the disease stays around, its R_t must be 1 on average. But doesn't that require careful tuning of R_0, how quickly immunity wanes and the length of the infection cycle?
As far as forests and population immunity, Taleb address this in Anti-Fragile. An anti-fragile system is one that gains from disorder. Small, frequent fires burn off fuel whereas modern forest management interrupts the natural order and allows huge amounts to accumulate.
The same thing happens in an economy. Lots of small bankruptcies over time strengthen the overall economy, but a prolonged period of constant growth and/or a lot of institutions that don't have skin-in-the-game (aka Too Big To Fail) lead to big blowups and deeper recessions.
It's more than just an explanatory analogy for the immune system as it relates to the Hygiene Theory of increased allergies in children and populations being exposed to non-fatal infections, either thru natural means or vaccinations.
Have you been waiting until this this is all over before trying to be smart about it. Smart per se (if looking smart is what everything is always about)
> Let’s say at some particular time that’s 90%, and maybe that implies an R of 0.5. As time goes on, immunity declines - 85%, 80%, etc - and r creeps up - 0.6, 0.7, etc.
<pedantry level="extreme">Ahem, R = 0.5 with 90% immunity means R0 = 5, meaning with 85% immunity R = 0.75 and with 80% immunity R = 1.0.</pedantry>
I always thought the "why does it stop?" question even more interesting and most people just ignore it. People will lecture about R and exponential growth but have little to say about an outbreak just dying out without any particular identifiable and repeatable reason.
Just like forest fires, they don't just burn everything. Experts have shown very little skill in predicting the end of an outbreak so I get pretty dismissive of the modeling effort in general. I'm sure this is complicated but I have come out of this convinced we just don't understand virus dynamics very well and I am pretty disappointed relative to what I thought about the field prior to this pandemic. Some of the lecturing on "trust the science" has been insufferable given this lack of actionable intelligence. This was a heaping spoonful of humility for the field and the CDC IMO.
"In South East Asia, we have two flu seasons ... in the summer, people coop themselves up at home with the air-conditioning on full blast.
....In South East Asia, the muggy air retains heat, requiring air-conditioning and reduced airflow."
Yep - why Louisiana got wrecked by Delta in August when we all retreated inside. Also why (largely GOP) hot southern states look like COVID geniuses after the winter, when the north was couped up and wrecked and we've been outside.
Regarding fire: I am a (country) firefighter, though my particular insight comes mostly just from having a fireplace. I think the thing you're missing is that wood is actually pretty hard to burn.
Put a big log in a fireplace and try to light it with a match. It won't burn. Try a phone book. Also won't burn. A match can light small sticks and grass, and those can burn hot enough to light bigger sticks, which in turn can burn hot enough to light solid logs.
Another experiment: Get a roaring fire started with a few big logs in the fireplace, nice and hot. Then separate out the logs so they aren't heating each other. There's a good chance they'll go out. Big solid pieces of wood need a *lot* of heat to keep burning. And this is with seasoned wood!
There's an "R0" for a forest fire that depends on the local environment. The biggest factors are fuel (type and quantity), weather, and terrain. Surprisingly, on a typical day in a typical forest, the R0 is <1, and even in crazy fires you might get a sudden drop in the R0 due to wind direction change, topography, or natural barriers (including low fuel load areas due to previous fires).
In summary: Forest fires stop naturally because forests are less flammable than you imagine, and the "R0" of even a big fire can be mercurial.
Re: seasonality of polio - yes, swimming pools, but also summer fruits and vegetables. Think strawberries, lettuce, anything that would be hand-picked and not cooked.
I don't have the source, but it used to be A Thing in Victorian times to not feed kids fresh greens in the summer 'because it upset their systems' - in other words, because they would pick up a food-borne illness.
Our current era is *amazing* and I like it quite a lot.
This model feels satisfying for endemic viruses which have reached an equilibrium state, but now I feel a bit confused again about COVID. In Hungary (where I am; and I think this applies to most of Europe, but haven't double-checked), in both 2020 and 2021, it essentially died out over the summer, started ticking back up more-or-less literally the day the calendar turned over to September, and raged during the winter. Since this hasn't been around long enough to have been entrained into a yearly cycle around an R=1 equilibrium, it *must* be the physical factors themselves -- heat, humidity, UV, indoors, whatever -- causing that directly?
Interestingly, our local Covid wave crested (with a fairly high daily count of new infections) in the last week of November and is now clearly falling in Czechia, even though the weather corresponds to our usual December standards. It caught the experts a bit off-guard, many of them predicted a steady worsening of the situation, but the virus obviously did not read their opinions.
Last winter, in very similar weather, the wave wasn't falling at all. It was growing fast.
That argument from the forest fire analogy is really fundamentally wrong. For one thing, forests start in a minimally vulnerable state (new forests have zero deadfall) so if you let nature run its course, they will stay in that state with minimal fire damage. Human populations on the other hand start out in a maximally vulnerable state against a new virus; if you let nature run its course, you get maximum damage (health care system overload, etc.)
For another, in a forest-fire-prone area, deadfall will burn eventually; there isn't really any other process that would make it go away. So by doing large-scale fire supression you are only delaying the inevitable. Immunity, on the other hand, can be gained both by infection and vaccination; suppressing an epidemic while vaccines are being researched and rolled out makes perfect sense.
I'm not sure why, but no one yet seems to have mentioned the concept of an *excitable medium*, a standard concept in dynamical systems that's used in understanding wildfires, disease, heart and brain tissue, and some fancy cyclical chemical reactions.
This isn't an answer by itself, but seems like an important term to be throwing around in these conversations. :-)
Regarding warmer regions possibly having somewhat less flu overall:
Let's say r=(50-t)(d/2)/180, where t is the temperature in °C and d is the average interval between two incidences of the flu in years (so at any given time, d/2 is approximately the time since the average person had the flu for the last time). Let's say the year-round average temperature is 5°C in Alaska, 20°C in Florida, and 26°C in Panama. The year-round average r should be 1, which gives d=8 in Alaska, d=12 in Florida and d=15 in Panama.
Though the long-term average r may actually be different from 1 in locations with high seasonal differences. In the summer, the flu may go locally extinct, then restart from imported cases in the fall. Or even if it doesn't go extinct, imported cases may make up a significant fraction of all cases in the summer and the fall. These cause deviations from the simple model. In the simple model, the derivative of the logarithm of the case count is proportional to r, however this fails to be a good approximation when the case count is very low. When the case count drops from 1 to 0, the log of the case count drops to -∞. And when the case count is low, imported cases increase the case count significantly above what r would predict. Assuming that there is a steady stream of imported cases, so the case count never actually drops to 0, this implies that the long-term average r is somewhere below 1, with the imported cases keeping the disease from going extinct. With a year-round average r below 1, the formula above gives a lower d: e.g. if the average r in Alaska is 0.75, Alaskans get the flu every 6 years instead of 8, increasing the difference compared to Panama. None of this changes that during the Alaskan summer, case counts are negligible compared to any time in Panama.
"(something like this might also be why the Native Americans had such a hard time with European diseases)"
Yes and no. Any explanation for why the American Indians were nearly wiped out by European diseases (estimates range from 95-98%) has to explain why the same thing didn't happen in the other direction. In grad school, the explanation we learned about was the limited HLA (human leukocyte antigen) diversity in the American populations because they came from a small founder population.
In order to form antibodies, your immune system has to 'present' the antigen it collects. It does this using antigen presenting cells, which grab ahold of short peptide sequences and display them on their cell surface for T- and B-cells to sample. HLA is like the 'hands' that grab onto these peptide strands. But unlike human hands they can only grab certain sequence shapes. A few of these is enough to cover most shapes, but not all.
Not everyone has the same set of HLA. The ones you have are hereditary, and they dictate the kind of thing you can mount an immune response to. This is one reason why certain populations are more susceptible to some infections and more resistant to others.
There's a lot of intermixing that has happened these past few millennia from Africa to Asia, so no sub-population has only one set of HLA. Except in pre-Columbian America. Mostly isolated, and derived from a small founder population, the limited HLA in the Americas meant any disease that didn't have strong HLA binding (and hence was difficult for the immune system to 'see') would propogate particularly well through the population, since everyone's HLA were the same.
Children are "weirdly resilient" in large part because of Original Antigenic Sin. The name sounds kooky and religious but it's actually a well-observed phenomenon in epidemiology:
Children have no previous immune experience with a given virus, so their entire immune system can figure out the best way to fight it and follow that plan. T-cells, B-cells, macrophages, etc are all involved in the most effective ways possible.
Once that "plan" is established it can only change to a certain extent when later infections are encountered. When an immune system first familiarized with the Wuhan strain of SARS-COV-2 encounters the omicron strain, it follows the relatively ineffective Wuhan-strain plan and then, very importantly, can only partially update that plan on contact with omicron. This effect is at least semi-permanent, and it explains much of why our original 2019-era vaccines are so useless against 2022-era COVID.
You write: This paper [ Projecting The Transmission Dynamics Of SARS-CoV2 ] is head and shoulders above anything I found during my own literature review...
Sorry to disillusion you, but this is actually a rather poor paper. The apparent sophistication of regression analysis and simulation is all flawed. To the extent that the conclusions are reasonable at all, they are simply the result of intuition, with a false veneer of mathematics lending them more apparent credibility.
I comment in detail on this paper in a series of four blog posts, starting at
These posts actually only cover the first part of the paper. I never got around to the posts on the second part. But it too is deeply flawed. As far as I can tell, their procedure to find optimal parameter values does not do anything sensible.
I corresponded a bit with Marc Lipsitch about this paper, and he pointed me to some further code. But in the end I was not able to pin down what exactly they do in the second part of the paper. Here is an excerpt from my last email to him (to which I haven't gotten a reply):
---------
After looking at this code, I'm just as puzzled as I was before about what you did, but in a different way.
First of all, I should mention that the fitted parameter values for the SEIRS model in the figuremaker.R file (rounded versions of which are in your Table S8) seem odd to me. 1/sigma1 is 44.948, 1/sigma2 is 44.961, 1/nu is 2.99975, 1/gamma is 5.04 - all quite close to integer values. Before looking at the code, my guess had been that you used some version of LHS that looked only at values on some coarse grid, obtaining an estimate with integer values for these parameters, which you then used as initial values for Nelder-Mead optimization, and that this optimization procedure did not do much, leaving these values very close to integers.
I see now that the LHS procedure does not use a coarse grid, so there would be no reason for it to produce an optimum at or near integers. Also, it appears that you do not specify initial values for the Nelder-Mead optimization, so that isn't how information was transferred from the LHS part to the N-M part.
My current guess is that you used the results of LHS merely to narrow down the parameter ranges for the N-M optimization somewhat - the ranges for parameters in the "Do a maximization" code from the notebook are narrower than those in Table S8. That the results of N-M optimization give values for 1/nu and 1/gamma that are near integers could then be explained if the Mathematica N-M procedure itself searches for initial values on some coarse grid, and then fails to move much from these initial values. In the case of 1/sigma1 and 1/sigma2, the upper bound in the "Do a maximization" code is 45 (Table S8 has an upper bound of 100), so it appears that the N-M optimization may have simply been prevented from moving beyond this constraint.
But perhaps this guess isn't correct. I'd appreciate further clarification.
I note that the LHS procedure optimizes the sum of squared errors between the actual incidence and the predicted incidence, but the N-M procedure optimizes the sum of squared errors between the log of the actual incidence and the log of the predicted incidence (ignoring weeks when the actual incidence is zero). Is this difference deliberate?
To be frank, the whole concept of fitting the SEIRS model in this way does not make much sense to me. The model is deterministic, but as you
note, its results can change drastically with small parameter changes, due to "bifurcations". The model is also much simpler than reality, so one would not expect particularly close matches to the data. The real process also has aspects that can only reasonably be modelled as random. If randomness were added to the model, one would fit it by maximimizing the probability of the observed data, which would change smoothly with parameter values.
"'In this model, warmer regions should have less flu overall, since a longer interval between incidences corresponds to a long-term average r of 1. Maybe Alaskans get a flu, say, once in 8 years on average, Floridians every 12 years (still seasonally) and Panamans every 15 years (without seasonality).'
That last paragraph sounds fascinating but I’m not sure I understand why it’s true; can someone explain?"
---
I think I see the argument, but if so I think the argument's wrong? (Sources would have helped; was 10240 citing a known result or thinking on their own?) Here's what I think it was going for:
"For a disease at equilibrium, long-run average R=1. You can think of R=(transmission rate while infected)×(length of infection). So if transmission-rate-while-infected is lower in warmer climates, length-of-infection has to be longer, for the product to still be 1."
The fallacy would be in switching out "time infected" (per infection) for "time between infections"; those would only be equal if everyone always got re-infected right after clearing the last one.
"This paper is head and shoulders above anything I found during my own literature review and just comes out and says everything (I?) painfully tried to piece together."
Regarding babies, I think there's also some inter-generational immunity that can be transferred from mom to baby either in-utero or through breastfeeding. So the population has some ongoing immunity that passes on and keeps the diseases in check. That's why new diseases that jump from animals to humans are specially devastating at first but eventually become more of a background issue as the population as a whole builds immunity and is able to pass it forward to its descendants.
I don't know the answer to the fire question but if i had to guess i'd say it's a combination of changing wind conditions and natural barriers. If the wind no longer goes south then the fire will more or less stop going south, and if there's a mountain or river along the way then you need pretty powerful wind to bypass it. Especially if the natural barrier is more wet than the original fire area.
> Assuming there is at least one continuous line of trees connecting (eg) Maine to Georgia, why didn’t every forest fire burn the entire East Coast to a crisp back before there were human firefighters?
uhhhhh, rain?
also having lived on the east coast, the climate is much wetter in general, to the point where live wood has enough water content to be incredibly difficult to light (even on purpose, as I can attest from my days as a Boy Scout), and any dead wood which builds up on the ground quickly becomes rotten and soggy
forest fires are rare on the East Coast, except in times/places going through truly exceptional droughts, and tend to be small localized affairs even then
What is with the hostility towards mask requirements? I take Rafal S. to be illustrative, though not necessarily typical. Anyway, the use of masks in public places was distinctive of a number of different east asian populations for quite a while before the current pandemic. It's not like this was an idea cooked up in an FDA boardroom or something.
In fact, the evidence that masks work has tended to overturn long-held orthodoxy vis-a-vis aerosol spread of respiratory illness; it's hardly a holdover of hidebound bureaucracy or pick your favorite dysfunction/conspiracy theory. And it makes total intuitive sense; covering your mouth when you cough has been a staple of western etiquette for much longer than I've been alive.
It's also, for what it's worth, a truly miniscule change in behavior that takes about a week to go from slightly strange to completely anodyne. And resistance is hardly universal among western countries; in Germany, there is plenty of kicking and screaming about Covid rules but as far as I can tell, comparatively little complaint about requirements to wear a mask in indoor public places.
So basically, what the heck is going on here? Why is "masking" being lumped in with lockdowns and vaccine requirements as if the two go hand in hand when in fact they're almost total opposites? Mask requirements are almost literally the least you could do, yet it's represented here as something approaching Soylent Green.
"I’m having trouble figuring out how to analyze this point. After thinking about it, maybe the problem is I don’t have a good sense of why fires ever stop. Assuming there is at least one continuous line of trees connecting (eg) Maine to Georgia, why didn’t every forest fire burn the entire East Coast to a crisp back before there were human firefighters?"
Having grown up on the west coast in a heavily wooded region, I remember learning about this in school. So I might have the details wrong, but this is what I remember.
Namely, fires keep on spreading until they
a) run across a natural roadblock they can't cross like a wide river or very tall mountain, an area that already burned fairly recently and had no fuel, or the ocean
b) the weather changes (rain, cool temperatures, etc) and it puts the fire out
c) it runs out of fuel.
This means that in many regions you'd have smaller fires fairly regularly that would burn slow but steady until the weather turned, and occasionally you'd have super fires that would spread thousands of miles and burn huge tracts of land before running into natural barriers and burning themselves out. The super fires tended to occur rarely, when there was enough fuel on the ground that hadn't burned and you got the perfect conditions for a huge burn (hot, dry, and high winds).
So that natural state of things for large, heavily forested regions in nature is for there to be some slow burning ground fires pretty much every summer that last until it rains, and the occasional really big fire. See for example the "Big Burn" of 1910 where three million acres of forest were burned to ashes in less than two days. The cause was a drought and unusually long dry spell. This led to many small slow burning fires like normal, but then one day hurricane force winds hit the region and whipped all the small fires into one huge inferno. It didn't really stop until a cold front moved in with lots of snow.
https://en.wikipedia.org/wiki/Great_Fire_of_1910#Origin
This is normal. Many times I've visited "The Grove of the Patriarchs" at Mt. Rainier National Park where some of the oldest trees in the region grow (some over 1,000 years old and 40 feet in diameter). The reason given for why they've survived so long is that they're on an island in the middle of the Ohanapacosh river, and apparently are situated just right to have survived all the megafires over the last 1,000 years.
Endemic diseases, avalanches, earthquakes, forest fires, and probably a million other things exhibit "self-organized criticality". You've got some thing that, if it happens, wants to spread to nearby units, but is more likely to spread to nearby units that haven't had it in a while. (An infection is more likely in a person with waning immunity than fresh immunity; the snow on a square inch of mountain slope is more likely to slide if there's several days of fresh snowfall on top than if it just slid; a bit of rock is more likely to slip if it's got more built up tension than if it's just been released; a square mile of forest is more likely to burn if it's got several years of unburnt underbrush than if it just burnt.) When you have lots of buildup and no immunity, so that R>1 everywhere in the network, then a spark anywhere burns/pandemics/avalanches everything. When you've got lots of immunity and no buildup, and the system is everywhere near some particular R<1, then your average outbreak infects 1/(1-R) total people before dying out. But when the average R in the system is close to 1, a lot will depend on the detailed network structure, and outbreaks/avalanches/earthquakes/forest fires can end up of any size, with a power law distribution of sizes, but on average they still leave most of the system right near that margin of 1 (unlike pandemics or global conflagrations).
I guess respiratory diseases and forest fires in temperate zones have lots of seasonality, so if they spend a lot of time far enough from 1 in either direction, then the fire season/flu season will end up having a characteristic size each year (proportional to the amount of immunity that is lost in the summer/winter while seasonality suppresses flu/fire). But earthquakes don't get this periodic forcing, so they stay near the critical edge.
Except that your thinking and everyone else's thinking on seasonality is wrong. Or rather it is fine but likely irrelevant, since this is a bioengineered lab-created virus. If this were Your virus, would you have made it seasonal? Maybe somewhat just to fool people. Let's remember that bioweapons do their best damage when they tie up resources and demoralize everyone and the more the better. Nevertheless, there will be some seasonality due to humidity, which is the primary cause of all seasonality. This virus was also engineered to accept add-on modules to be released down the road. People call it a "coronavirus" but it is much more. We need to adjust our thinking.
It strikes me as interesting that immunity tends to wane on the order of a year, and that lines up with the seasonal variation in R0. Any idea why the evolutionary equilibrium would find this timeline for immunity wane as optimal?
> rt should be 1 on average in the long run
Can someone give intuition for why it must be that way? This seems like the crucial bit.
EDIT: ok, it makes sense that conditioned on the fact that the disease stays around, its R_t must be 1 on average. But doesn't that require careful tuning of R_0, how quickly immunity wanes and the length of the infection cycle?
As far as forests and population immunity, Taleb address this in Anti-Fragile. An anti-fragile system is one that gains from disorder. Small, frequent fires burn off fuel whereas modern forest management interrupts the natural order and allows huge amounts to accumulate.
The same thing happens in an economy. Lots of small bankruptcies over time strengthen the overall economy, but a prolonged period of constant growth and/or a lot of institutions that don't have skin-in-the-game (aka Too Big To Fail) lead to big blowups and deeper recessions.
It's more than just an explanatory analogy for the immune system as it relates to the Hygiene Theory of increased allergies in children and populations being exposed to non-fatal infections, either thru natural means or vaccinations.
Have you been waiting until this this is all over before trying to be smart about it. Smart per se (if looking smart is what everything is always about)
> Let’s say at some particular time that’s 90%, and maybe that implies an R of 0.5. As time goes on, immunity declines - 85%, 80%, etc - and r creeps up - 0.6, 0.7, etc.
<pedantry level="extreme">Ahem, R = 0.5 with 90% immunity means R0 = 5, meaning with 85% immunity R = 0.75 and with 80% immunity R = 1.0.</pedantry>
I always thought the "why does it stop?" question even more interesting and most people just ignore it. People will lecture about R and exponential growth but have little to say about an outbreak just dying out without any particular identifiable and repeatable reason.
Just like forest fires, they don't just burn everything. Experts have shown very little skill in predicting the end of an outbreak so I get pretty dismissive of the modeling effort in general. I'm sure this is complicated but I have come out of this convinced we just don't understand virus dynamics very well and I am pretty disappointed relative to what I thought about the field prior to this pandemic. Some of the lecturing on "trust the science" has been insufferable given this lack of actionable intelligence. This was a heaping spoonful of humility for the field and the CDC IMO.
"In South East Asia, we have two flu seasons ... in the summer, people coop themselves up at home with the air-conditioning on full blast.
....In South East Asia, the muggy air retains heat, requiring air-conditioning and reduced airflow."
Yep - why Louisiana got wrecked by Delta in August when we all retreated inside. Also why (largely GOP) hot southern states look like COVID geniuses after the winter, when the north was couped up and wrecked and we've been outside.
Regarding fire: I am a (country) firefighter, though my particular insight comes mostly just from having a fireplace. I think the thing you're missing is that wood is actually pretty hard to burn.
Put a big log in a fireplace and try to light it with a match. It won't burn. Try a phone book. Also won't burn. A match can light small sticks and grass, and those can burn hot enough to light bigger sticks, which in turn can burn hot enough to light solid logs.
Another experiment: Get a roaring fire started with a few big logs in the fireplace, nice and hot. Then separate out the logs so they aren't heating each other. There's a good chance they'll go out. Big solid pieces of wood need a *lot* of heat to keep burning. And this is with seasoned wood!
There's an "R0" for a forest fire that depends on the local environment. The biggest factors are fuel (type and quantity), weather, and terrain. Surprisingly, on a typical day in a typical forest, the R0 is <1, and even in crazy fires you might get a sudden drop in the R0 due to wind direction change, topography, or natural barriers (including low fuel load areas due to previous fires).
In summary: Forest fires stop naturally because forests are less flammable than you imagine, and the "R0" of even a big fire can be mercurial.
Re: seasonality of polio - yes, swimming pools, but also summer fruits and vegetables. Think strawberries, lettuce, anything that would be hand-picked and not cooked.
I don't have the source, but it used to be A Thing in Victorian times to not feed kids fresh greens in the summer 'because it upset their systems' - in other words, because they would pick up a food-borne illness.
Our current era is *amazing* and I like it quite a lot.
What about Original Antigenetic Sin?
This model feels satisfying for endemic viruses which have reached an equilibrium state, but now I feel a bit confused again about COVID. In Hungary (where I am; and I think this applies to most of Europe, but haven't double-checked), in both 2020 and 2021, it essentially died out over the summer, started ticking back up more-or-less literally the day the calendar turned over to September, and raged during the winter. Since this hasn't been around long enough to have been entrained into a yearly cycle around an R=1 equilibrium, it *must* be the physical factors themselves -- heat, humidity, UV, indoors, whatever -- causing that directly?
Interestingly, our local Covid wave crested (with a fairly high daily count of new infections) in the last week of November and is now clearly falling in Czechia, even though the weather corresponds to our usual December standards. It caught the experts a bit off-guard, many of them predicted a steady worsening of the situation, but the virus obviously did not read their opinions.
Last winter, in very similar weather, the wave wasn't falling at all. It was growing fast.
Covid dynamic is complicated.
That argument from the forest fire analogy is really fundamentally wrong. For one thing, forests start in a minimally vulnerable state (new forests have zero deadfall) so if you let nature run its course, they will stay in that state with minimal fire damage. Human populations on the other hand start out in a maximally vulnerable state against a new virus; if you let nature run its course, you get maximum damage (health care system overload, etc.)
For another, in a forest-fire-prone area, deadfall will burn eventually; there isn't really any other process that would make it go away. So by doing large-scale fire supression you are only delaying the inevitable. Immunity, on the other hand, can be gained both by infection and vaccination; suppressing an epidemic while vaccines are being researched and rolled out makes perfect sense.
So why does immunity to chickenpox last a lifetime, but immunity to some other diseases only last a year? What's different about chickenpox?
I'm not sure why, but no one yet seems to have mentioned the concept of an *excitable medium*, a standard concept in dynamical systems that's used in understanding wildfires, disease, heart and brain tissue, and some fancy cyclical chemical reactions.
This isn't an answer by itself, but seems like an important term to be throwing around in these conversations. :-)
If polio is spread through swimming pools, perhaps we should be playing “Marco-Polio” instead?
Regarding warmer regions possibly having somewhat less flu overall:
Let's say r=(50-t)(d/2)/180, where t is the temperature in °C and d is the average interval between two incidences of the flu in years (so at any given time, d/2 is approximately the time since the average person had the flu for the last time). Let's say the year-round average temperature is 5°C in Alaska, 20°C in Florida, and 26°C in Panama. The year-round average r should be 1, which gives d=8 in Alaska, d=12 in Florida and d=15 in Panama.
Though the long-term average r may actually be different from 1 in locations with high seasonal differences. In the summer, the flu may go locally extinct, then restart from imported cases in the fall. Or even if it doesn't go extinct, imported cases may make up a significant fraction of all cases in the summer and the fall. These cause deviations from the simple model. In the simple model, the derivative of the logarithm of the case count is proportional to r, however this fails to be a good approximation when the case count is very low. When the case count drops from 1 to 0, the log of the case count drops to -∞. And when the case count is low, imported cases increase the case count significantly above what r would predict. Assuming that there is a steady stream of imported cases, so the case count never actually drops to 0, this implies that the long-term average r is somewhere below 1, with the imported cases keeping the disease from going extinct. With a year-round average r below 1, the formula above gives a lower d: e.g. if the average r in Alaska is 0.75, Alaskans get the flu every 6 years instead of 8, increasing the difference compared to Panama. None of this changes that during the Alaskan summer, case counts are negligible compared to any time in Panama.
"(something like this might also be why the Native Americans had such a hard time with European diseases)"
Yes and no. Any explanation for why the American Indians were nearly wiped out by European diseases (estimates range from 95-98%) has to explain why the same thing didn't happen in the other direction. In grad school, the explanation we learned about was the limited HLA (human leukocyte antigen) diversity in the American populations because they came from a small founder population.
In order to form antibodies, your immune system has to 'present' the antigen it collects. It does this using antigen presenting cells, which grab ahold of short peptide sequences and display them on their cell surface for T- and B-cells to sample. HLA is like the 'hands' that grab onto these peptide strands. But unlike human hands they can only grab certain sequence shapes. A few of these is enough to cover most shapes, but not all.
Not everyone has the same set of HLA. The ones you have are hereditary, and they dictate the kind of thing you can mount an immune response to. This is one reason why certain populations are more susceptible to some infections and more resistant to others.
There's a lot of intermixing that has happened these past few millennia from Africa to Asia, so no sub-population has only one set of HLA. Except in pre-Columbian America. Mostly isolated, and derived from a small founder population, the limited HLA in the Americas meant any disease that didn't have strong HLA binding (and hence was difficult for the immune system to 'see') would propogate particularly well through the population, since everyone's HLA were the same.
Children are "weirdly resilient" in large part because of Original Antigenic Sin. The name sounds kooky and religious but it's actually a well-observed phenomenon in epidemiology:
https://www.jstor.org/stable/985534
Children have no previous immune experience with a given virus, so their entire immune system can figure out the best way to fight it and follow that plan. T-cells, B-cells, macrophages, etc are all involved in the most effective ways possible.
Once that "plan" is established it can only change to a certain extent when later infections are encountered. When an immune system first familiarized with the Wuhan strain of SARS-COV-2 encounters the omicron strain, it follows the relatively ineffective Wuhan-strain plan and then, very importantly, can only partially update that plan on contact with omicron. This effect is at least semi-permanent, and it explains much of why our original 2019-era vaccines are so useless against 2022-era COVID.
You write: This paper [ Projecting The Transmission Dynamics Of SARS-CoV2 ] is head and shoulders above anything I found during my own literature review...
Sorry to disillusion you, but this is actually a rather poor paper. The apparent sophistication of regression analysis and simulation is all flawed. To the extent that the conclusions are reasonable at all, they are simply the result of intuition, with a false veneer of mathematics lending them more apparent credibility.
I comment in detail on this paper in a series of four blog posts, starting at
https://radfordneal.wordpress.com/2020/05/27/critique-of-projecting-the-transmission-dynamics-of-sars-cov-2-through-the-postpandemic-period-part-1-reproducing-the-results/
These posts actually only cover the first part of the paper. I never got around to the posts on the second part. But it too is deeply flawed. As far as I can tell, their procedure to find optimal parameter values does not do anything sensible.
I corresponded a bit with Marc Lipsitch about this paper, and he pointed me to some further code. But in the end I was not able to pin down what exactly they do in the second part of the paper. Here is an excerpt from my last email to him (to which I haven't gotten a reply):
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After looking at this code, I'm just as puzzled as I was before about what you did, but in a different way.
First of all, I should mention that the fitted parameter values for the SEIRS model in the figuremaker.R file (rounded versions of which are in your Table S8) seem odd to me. 1/sigma1 is 44.948, 1/sigma2 is 44.961, 1/nu is 2.99975, 1/gamma is 5.04 - all quite close to integer values. Before looking at the code, my guess had been that you used some version of LHS that looked only at values on some coarse grid, obtaining an estimate with integer values for these parameters, which you then used as initial values for Nelder-Mead optimization, and that this optimization procedure did not do much, leaving these values very close to integers.
I see now that the LHS procedure does not use a coarse grid, so there would be no reason for it to produce an optimum at or near integers. Also, it appears that you do not specify initial values for the Nelder-Mead optimization, so that isn't how information was transferred from the LHS part to the N-M part.
My current guess is that you used the results of LHS merely to narrow down the parameter ranges for the N-M optimization somewhat - the ranges for parameters in the "Do a maximization" code from the notebook are narrower than those in Table S8. That the results of N-M optimization give values for 1/nu and 1/gamma that are near integers could then be explained if the Mathematica N-M procedure itself searches for initial values on some coarse grid, and then fails to move much from these initial values. In the case of 1/sigma1 and 1/sigma2, the upper bound in the "Do a maximization" code is 45 (Table S8 has an upper bound of 100), so it appears that the N-M optimization may have simply been prevented from moving beyond this constraint.
But perhaps this guess isn't correct. I'd appreciate further clarification.
I note that the LHS procedure optimizes the sum of squared errors between the actual incidence and the predicted incidence, but the N-M procedure optimizes the sum of squared errors between the log of the actual incidence and the log of the predicted incidence (ignoring weeks when the actual incidence is zero). Is this difference deliberate?
To be frank, the whole concept of fitting the SEIRS model in this way does not make much sense to me. The model is deterministic, but as you
note, its results can change drastically with small parameter changes, due to "bifurcations". The model is also much simpler than reality, so one would not expect particularly close matches to the data. The real process also has aspects that can only reasonably be modelled as random. If randomness were added to the model, one would fit it by maximimizing the probability of the observed data, which would change smoothly with parameter values.
"'In this model, warmer regions should have less flu overall, since a longer interval between incidences corresponds to a long-term average r of 1. Maybe Alaskans get a flu, say, once in 8 years on average, Floridians every 12 years (still seasonally) and Panamans every 15 years (without seasonality).'
That last paragraph sounds fascinating but I’m not sure I understand why it’s true; can someone explain?"
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I think I see the argument, but if so I think the argument's wrong? (Sources would have helped; was 10240 citing a known result or thinking on their own?) Here's what I think it was going for:
"For a disease at equilibrium, long-run average R=1. You can think of R=(transmission rate while infected)×(length of infection). So if transmission-rate-while-infected is lower in warmer climates, length-of-infection has to be longer, for the product to still be 1."
The fallacy would be in switching out "time infected" (per infection) for "time between infections"; those would only be equal if everyone always got re-infected right after clearing the last one.
So does this analysis imply that dressing up warm does not protect you against the flu? How about "the common cold"?
Relatedly, why does my nose start running as soon as I'm exposed to low temperature and wind, while also being a symptom of the common cold?