HamanitaMuscaria t1_j2qnsw1 wrote
"we estimate that unvaccinated Omicron cases had a 36% (95% confidence interval (CI): 31–42%) risk of transmitting infection to close contacts, as compared to a 28% (25–31%) risk among vaccinated cases"
um
AusCan531 t1_j2qxwcl wrote
A 22% reduction is a long way from perfect, but very helpful in a contagion.
Don_Ford t1_j2tskxe wrote
It's not with COVID
Tricky-Potato-851 t1_j2robbu wrote
In theory. In the wild, graphing cases, it doesn't matter at all. In the wild all that determines case count, which is why the cases count charts like a stock market traded financial instrument, is the innate points at which humans see risk and actually run from that risk. Having been boosted simply increases the number of boosted entering the contagion pool until the exact same point of risk occurs.
This is why year over year, omicron vs delta was a bug that was roughly 10x as promiscuous with a severity rate 1/10th previous year... overall view of risk is the same.
And so it will continue until you reach near ubiquity of the virus and near harmlessness.
This stuff ain't even a medical problem, it's a human psychology problem, hence the total failure of the medical establishment. Policy did near zero even short term with shut downs and vaccines. Look at the charts and try to guess when policy happened vs simple geometric expansion and contractions at the same points you'd expect if covid was a hot or falling stock in your IRA. I forget the details, having abandoned covid as a pursuit, but the periodicity is between 100 and 120 days, like most things related to people(seasons are innate, not a human invention) and the ball just bounces a certain amplitude based on perceived risk from the reported severity on tv/ observed severity among peers. The rest is not even significant in swaying that progression. Ie, you can determine future covid numbers as a function of hospitalization rates, but NOT vaccine numbers(a fact in the wild and a philosophical challenge as to why that is if you disagree with my premise).
DuckQueue t1_j2s3u5g wrote
> In the wild, graphing cases, it doesn't matter at all
This is wholly incorrect.
If you have a single case of a disease with an r0 of 2, after 20 generations of transmission you've got 2^20 - or just over 1 million cases.
If you reduce r0 by 22%, after that same 20 generations you have 1.56^20 - about 7000 - cases.
SnooPuppers1978 t1_j2txo5x wrote
R doesn't stay high like that throughout generations, it will proportionately go down the more recently infected/immune people there are.
The calculations must be more nuanced than that.
After each generation you should adapt the number of potential vulnerable candidates compared to what initial R had.
It would flatten the curve though and in total there would be around 24% fewer cases, based on that model. But this model is of course still to basic to exactly match real world. So here you can see for instance, that max cases amount to 187k per generation vs 86k per gen in terms of flattening the curve (good for hospitals).
Edit: as an example R2 vs R1.56 with 100 starting infected and a a population of 1,000,000 could be something like that:
| R2 Cases | R1.56 Cases | Total R2 Cases | Total R1.56 Cases |
|---|---|---|---|
| 100 | 100 | 100 | 100 |
| 200 | 156 | 300 | 256 |
| 400 | 243 | 700 | 499 |
| 799 | 379 | 1499 | 878 |
| 1596 | 591 | 3095 | 1469 |
| 3182 | 921 | 6277 | 2390 |
| 6324 | 1433 | 12601 | 3823 |
| 12489 | 2227 | 25090 | 6050 |
| 24351 | 3453 | 49441 | 9503 |
| 46294 | 5335 | 95735 | 14838 |
| 83724 | 8199 | 179459 | 23037 |
| 137398 | 12496 | 316857 | 35533 |
| 187725 | 18801 | 504582 | 54334 |
| 186005 | 27736 | 690587 | 82070 |
| 115105 | 39717 | 805692 | 121787 |
| 44732 | 54413 | 850424 | 176200 |
| 13382 | 69928 | 863806 | 246128 |
| 3645 | 82238 | 867451 | 328366 |
| 966 | 86165 | 868417 | 414531 |
| 254 | 78697 | 868671 | 493228 |
| 67 | 62215 | 868738 | 555443 |
| 18 | 43147 | 868756 | 598590 |
| 5 | 27019 | 868761 | 625609 |
| 1 | 15780 | 868762 | 641389 |
| 0 | 8828 | 868762 | 650217 |
| 0 | 4817 | 868762 | 655034 |
| 0 | 2592 | 868762 | 657626 |
| 0 | 1384 | 868762 | 659010 |
| 0 | 736 | 868762 | 659746 |
| 0 | 391 | 868762 | 660137 |
| 0 | 207 | 868762 | 660344 |
| 0 | 110 | 868762 | 660454 |
| 0 | 58 | 868762 | 660512 |
| 0 | 31 | 868762 | 660543 |
| 0 | 16 | 868762 | 660559 |
| 0 | 8 | 868762 | 660567 |
| 0 | 4 | 868762 | 660571 |
| 0 | 2 | 868762 | 660573 |
With a slightly more accurate script and simulation I got the following:
| R0 | Gens before < 10 infections | Total Cases | Max Cases in a Gen |
|---|---|---|---|
| 0.78 | 10 | 428 | 78 |
| 1 | 2152 | 45472 | 100 |
| 1.28 | 63 | 403244 | 25961 |
| 1.64 | 35 | 662799 | 87996 |
| 2.1 | 24 | 822088 | 168399 |
| 2.68 | 18 | 913575 | 254938 |
| 3.44 | 14 | 963671 | 322040 |
| 4.4 | 12 | 987001 | 373786 |
| 5.63 | 10 | 996338 | 457475 |
| 7.21 | 8 | 999257 | 586940 |
| 9.22 | 7 | 999901 | 455211 |
| 11.81 | 7 | 999993 | 691460 |
| 15.11 | 6 | 1000000 | 684507 |
| 19.34 | 6 | 1000000 | 487709 |
DuckQueue t1_j2wnm2i wrote
> After each generation you should adapt the number of potential vulnerable candidates compared to what initial R had.
In the abstract your point isn't wrong, but in the real world population sizes are much larger, resistance is imperfect to begin with, mutation occurs, and we're talking about a disease where previous infection doesn't confer a high degree of resistance that persists over the long-term - like COVID - so that isn't going to have nearly as large an impact as you're suggesting with your example.
SnooPuppers1978 t1_j2woh6q wrote
> In the abstract your point isn't wrong, but in the real world population sizes are much larger, resistance is imperfect to begin with, mutation occurs, and we're talking about a disease where previous infection doesn't confer a high degree of resistance that persists over the long-term - like COVID - so that isn't going to have nearly as large an impact as you're suggesting with your example.
Yes, all of this can be adapted to the model, but eventual result will still be a wave like graph, where difference of 22% would get lower the higher the R0 is and the end results in terms of magnitudes would be very similar to what I showed above.
Whether the population is 1,000,000 here or 1,000,000,000 doesn't make that much of a difference though. It's just few generations more.
We could create a model that incorporates waning immunity based on the studies we've seen. And also run a vaccine like intervention to see how results would differ. We could try to use 8 billion people and try to roll out vaccine to all of them within certain timeframe. I might do it during the weekend if I have time.
The results with 1 billion population here - you can see that it's just few more gens, magnitude wise, proportionally not that much difference:
| R0 | Gens before < 10 infections | Total Cases | Max Cases in a Gen |
|---|---|---|---|
| 0.78 | 10 | 428 | 78 |
| 1 | 2153540 | 45454565 | 100 |
| 1.28 | 117 | 403004862 | 25885890 |
| 1.64 | 60 | 662734374 | 88055684 |
| 2.1 | 40 | 822064894 | 170459771 |
| 2.68 | 30 | 913564065 | 254590943 |
| 3.44 | 23 | 963666407 | 343953730 |
| 4.4 | 19 | 986999921 | 429451582 |
| 5.63 | 16 | 996336642 | 456685926 |
| 7.21 | 13 | 999256872 | 437456355 |
| 9.22 | 12 | 999900871 | 527835860 |
| 11.81 | 10 | 999992570 | 696393878 |
| 15.11 | 9 | 999999726 | 623729861 |
| 19.34 | 8 | 999999996 | 744938203 |
DuckQueue t1_j2wpnl4 wrote
> It's just few generations more.
Like... twice as many. Yes, not multiple orders of magnitude but still enough to make a huge difference, especially when you account for the other factors I mentioned.
And that still wouldn't account for how diseases actually spread in real populations, where not everyone has an equal chance of being exposed to any given other person. There's a reason actual models of the spread of disease are much more complex than the model you're providing. And a reason why observational estimates of the R0 for COVID haven't been appreciably declining over time.
SnooPuppers1978 t1_j2wqqe5 wrote
Yes, but there's also factors to the other side. As the OP above mentioned people will adapt their behaviour depending on how they perceive the risk for themselves. If people have vaccinated and perceive the risk as lower, they will be more likely to go out. If there's a huge wave currently ongoing, people will be less likely to go out. If there's little threat, people will go out more likely, making the likelihood of new wave to start higher. Risk behaviour will be another balancing factor that will make the wave smooth out whether you have the intervention or not. If people see death around them, they get scared and start to avoid, if people see no danger, they will increase their risk behaviour. Behaviour will influence the R0 so much. Imagine being in contact with 50% fewer people than you were previously. That would be halving the R.
So in the end with all those factors together, unless the efficacy is enough to create herd immunity it's going to be waves with not much differing total amount of cases. Efficacy has to be enough for herd immunity or very close to that, otherwise yeah, it would just be something like that.
Main effect will be for risk groups for whom the risk of the disease will be much lower in terms of hospitalisations and death thanks to their immune systems being prepared from the vaccine. And in addition less overload on hospitals due to flattening the curve, but in the end total amount of infections are not going to be magnitudes away due to inherent characteristics of this virus.
DuckQueue t1_j2ws3t1 wrote
> So in the end with all those factors together, unless the efficacy is enough to create herd immunity it's going to be waves with not much differing total amount of cases.
You seem to be assuming that the disease will exhaust itself and run out of people to infect, but as the real world shows, that isn't generally how infectious diseases - especially ones this effective at escaping the immune system - work.
It's only meaningful to talk about the total number of cases up to a given point in time - if you're trying to talk about the total where the number of new infections permamently drops to 0 you're talking about circumstances that might apply to some newly-arising zoonotic diseases but decidedly does not apply to the disease we're talking about.
SnooPuppers1978 t1_j2wsv97 wrote
> You seem to be assuming that the disease will exhaust itself and run out of people to infect
For certain amount of time, hence the waves. There will be smaller amount of population still having the virus, until the virus mutates or immunity wanes enough after which it will start all over again.
After certain amount of time like a year or two years, the total cases amount would be similar in terms of magnitude. They won't be 10x based on 22% efficacy.
Because you were suggesting 7k vs 1 million which is different in magnitudes.
I'm suggesting that difference would probably be less than 2x after 2 years for example. And if I had to guess it would probably be something like 25% difference similarly, if we tried to make our model more comprehensive.
Immoralist86 t1_j2rnslb wrote
But also:
“Index cases with a history of prior SARS-CoV-2 infection (that is, reinfection) had a lower risk of transmitting to close contacts (23% (19–27%)) than index cases with no history of prior infection (33% (30–37%)”
“Prior SARS-CoV-2 infection was similarly associated with a 23% reduction (3–39%) in risk of transmission from the index case. Having both prior vaccination and SARS-CoV-2 infection was associated with a 40% (20–55%) reduction in risk of transmission by the index case, based on a linear combination of regression coefficients.”
“for every five additional weeks since last vaccine dose, SARS-CoV-2 breakthrough infections were 6% (2–11%) more likely to transmit infection to close contacts. We did not observe a statistically significant relationship between time since last SARS-CoV-2 infection and risk of transmission”
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