What is the basis of when you switch back to polynomial in the daily death curve?

Do you think exponential decay is the best model for the tail? The deaths should lag the infections by a relatively fixed time. I don't really have a feel for anything better and a long tail on infections and deaths does make sense for something that is going to stick around but we can keep things at a low level.

PJYoung said:

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Most aren't "confirmed" COVID deaths in the US since most autopsies haven't been completed...and the US is counting every death, regardless of severity of underlying conditions, as a COVID death. Unlike most every country in the world.

I wonder why the US is approaching it this way?

Freeze Frame said:

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Most aren't "confirmed" COVID deaths in the US since most autopsies haven't been completed...and the US is counting every death, regardless of severity of underlying conditions, as a COVID death. Unlike most every country in the world.

I wonder why the US is approaching it this way?

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Would you source these claims?

so caveat: i could very well be wrong and don't want to seem like i am sure that I am right, but here is my reasoning behind each of these

BiochemAg97 said:

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What is the basis of when you switch back to polynomial in the daily death curve?

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short answer is my basis is what fits the data the best. I have cells where i can adjust that point back and forth and change the shape of each curve segment and just played with it until it seemed like a good match. the biggest unknown at this point is what do you call the "peak" in the polynomial curve (both date and quantity) as that is the single biggest influence in the final numbers. i chose 4/15 because my first simple "best fit" curve place it there and that matched the date the healthdata.org folks were predicting so i took that date and held it constant. my other basis was that on one of my other plots, i noticed the daily death total was starting to lay very nicely on a polynomial curve so i felt like that supported the case that we had already (if recently) made that transition

Quote:

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Do you think exponential decay is the best model for the tail? The deaths should lag the infections by a relatively fixed time. I don't really have a feel for anything better and a long tail on infections and deaths does make sense for something that is going to stick around but we can keep things at a low level.

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I think it is the best for a couple of reasons.
1) i don't know of a better option. unless we lock down 100% until all cases resolve, a steep decline isnt going to take us all the way to 0. now it could potentially be harmonic decline, but i haven't had the time yet to build that in.
2) china's tail is exponential decline. now there is a lot of reasonable doubt about their reported numbers, but that's the shape of their curve for whatever that's worth
3) that's the shape of the tail on seasonal flu after each season peaks. so my thinking is that as we open things back up, slowly enough to keep from causing a second peak, it would be reasonable to expect to see a long tail.

a lot of assumptions going on in this tail, and i'll be able to better forecast it once we see a decline (as a PETE decline forecasting is actually something i know a bit about). but for now this is my modeled forecast. hopefully worth slightly more than you paid for it.

ETFan said:

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Freeze Frame said:

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Most aren't "confirmed" COVID deaths in the US since most autopsies haven't been completed...and the US is counting every death, regardless of severity of underlying conditions, as a COVID death. Unlike most every country in the world.

I wonder why the US is approaching it this way?

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Would you source these claims?

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BlackGoldAg2011 said:

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so caveat: i could very well be wrong and don't want to seem like i am sure that I am right, but here is my reasoning behind each of these

BiochemAg97 said:

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What is the basis of when you switch back to polynomial in the daily death curve?

---

short answer is my basis is what fits the data the best. I have cells where i can adjust that point back and forth and change the shape of each curve segment and just played with it until it seemed like a good match. the biggest unknown at this point is what do you call the "peak" in the polynomial curve (both date and quantity) as that is the single biggest influence in the final numbers. i chose 4/15 because my first simple "best fit" curve place it there and that matched the date the healthdata.org folks were predicting so i took that date and held it constant. my other basis was that on one of my other plots, i noticed the daily death total was starting to lay very nicely on a polynomial curve so i felt like that supported the case that we had already (if recently) made that transition

Quote:

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Do you think exponential decay is the best model for the tail? The deaths should lag the infections by a relatively fixed time. I don't really have a feel for anything better and a long tail on infections and deaths does make sense for something that is going to stick around but we can keep things at a low level.

---

I think it is the best for a couple of reasons.
1) i don't know of a better option. unless we lock down 100% until all cases resolve, a steep decline isnt going to take us all the way to 0. now it could potentially be harmonic decline, but i haven't had the time yet to build that in.
2) china's tail is exponential decline. now there is a lot of reasonable doubt about their reported numbers, but that's the shape of their curve for whatever that's worth
3) that's the shape of the tail on seasonal flu after each season peaks. so my thinking is that as we open things back up, slowly enough to keep from causing a second peak, it would be reasonable to expect to see a long tail.

a lot of assumptions going on in this tail, and i'll be able to better forecast it once we see a decline (as a PETE decline forecasting is actually something i know a bit about). but for now this is my modeled forecast. hopefully worth slightly more than you paid for it.

---

I would try a linear fit on a week by week basis. Looking at the rate of change of m over discreet periods of time would give a pretty good idea of where we're headed. Using a single function to describe the system is tough because the system is being acted upon by changing external factors. Imagine trying to do first or second order kinetics with a temperature gradient. Now make the gradient somewhat random. Time intervals could then be used as a de facto smoothing function.

To me this is all about a need for data to inform future decisions.

I believe it's really important to know whether COVID19 solely caused the death or contributed to the death. We lose people every day to pneumonia who have significant health challenges and it's unlikely they would have gotten pneumonia without their health challenges (yes, I recognize that pneumonia is often developed from bacteria in the body vs. this contagious virus). How many autopsies are actually being done for those over 70?

My concern is that by just counting every death to coronavirus it will not paint an accurate picture of the true impact from the disease to inform future government policy decisions. Every life and every day with a loved one matters yet policy decisions impact lives every day. For example, someone in a car accident is much more likely to die at 75 mph vs. 55 mph yet some states elect to adopt a higher speed limit, thereby impacting lives. These decisions have to be made one way or the other and without having proper data the decisions might be ill-informed. there will not be any true way to know.

I'm hopeful that local municipalities, states and feds are accurately tracking co-morbidities but given our current political environment (on both sides) I'm highly skeptical.

ETFan said:

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Reading the comments to that tweet remind me why I avoid twitter. Good lord.

This is all an overlord, gates+fauci foundation, forced vaccine ploy, run on false models. Alrighty then.

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I only linked that tweet because it was unedited video vs. written word. I don't trust any news organization to accurately portray what someone says.

You're right, Twitter is a mess. If people were as smart in real life as they are on twitter we'd be unstoppable!

Oh, yeah I didn't mean anything towards you on that, I figured it was for the video.

KidDoc said:

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If they did not count these deaths as COVID deaths, instead counting them as heart attacks, COPD, etc then people would complain the government is hiding COVID deaths and it was a great cover up.

You just can't win either way. Do you only think they should count COVID deaths as COVID deaths in perfectly healthy people with no prior health issues? Do you realize how rare that person is in USA after age 12 or so?

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Exactly. I have seen both sides in the media. Over counting by counting everything with covid symptoms and under counting because we can't do the tests.

Doesn't seem like it matters for the purpose of modeling and predicting when we can leave our homes and go back to work again.

94chem said:

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BlackGoldAg2011 said:

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so caveat: i could very well be wrong and don't want to seem like i am sure that I am right, but here is my reasoning behind each of these

BiochemAg97 said:

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What is the basis of when you switch back to polynomial in the daily death curve?

---

short answer is my basis is what fits the data the best. I have cells where i can adjust that point back and forth and change the shape of each curve segment and just played with it until it seemed like a good match. the biggest unknown at this point is what do you call the "peak" in the polynomial curve (both date and quantity) as that is the single biggest influence in the final numbers. i chose 4/15 because my first simple "best fit" curve place it there and that matched the date the healthdata.org folks were predicting so i took that date and held it constant. my other basis was that on one of my other plots, i noticed the daily death total was starting to lay very nicely on a polynomial curve so i felt like that supported the case that we had already (if recently) made that transition

Quote:

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Do you think exponential decay is the best model for the tail? The deaths should lag the infections by a relatively fixed time. I don't really have a feel for anything better and a long tail on infections and deaths does make sense for something that is going to stick around but we can keep things at a low level.

---

I think it is the best for a couple of reasons.
1) i don't know of a better option. unless we lock down 100% until all cases resolve, a steep decline isnt going to take us all the way to 0. now it could potentially be harmonic decline, but i haven't had the time yet to build that in.
2) china's tail is exponential decline. now there is a lot of reasonable doubt about their reported numbers, but that's the shape of their curve for whatever that's worth
3) that's the shape of the tail on seasonal flu after each season peaks. so my thinking is that as we open things back up, slowly enough to keep from causing a second peak, it would be reasonable to expect to see a long tail.

a lot of assumptions going on in this tail, and i'll be able to better forecast it once we see a decline (as a PETE decline forecasting is actually something i know a bit about). but for now this is my modeled forecast. hopefully worth slightly more than you paid for it.

---

I would try a linear fit on a week by week basis. Looking at the rate of change of m over discreet periods of time would give a pretty good idea of where we're headed. Using a single function to describe the system is tough because the system is being acted upon by changing external factors. Imagine trying to do first or second order kinetics with a temperature gradient. Now make the gradient somewhat random. Time intervals could then be used as a de facto smoothing function.

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a series of linear slopes with "m" values changing in a consistent enough manner that it is predictable? unless i'm misunderstanding you, you basically just described a series of tangent curves, which as you shrink the time periods down can be described by a 2nd order polynomial.

BlackGoldAg2011 said:

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94chem said:

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BlackGoldAg2011 said:

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so caveat: i could very well be wrong and don't want to seem like i am sure that I am right, but here is my reasoning behind each of these

BiochemAg97 said:

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What is the basis of when you switch back to polynomial in the daily death curve?

---

short answer is my basis is what fits the data the best. I have cells where i can adjust that point back and forth and change the shape of each curve segment and just played with it until it seemed like a good match. the biggest unknown at this point is what do you call the "peak" in the polynomial curve (both date and quantity) as that is the single biggest influence in the final numbers. i chose 4/15 because my first simple "best fit" curve place it there and that matched the date the healthdata.org folks were predicting so i took that date and held it constant. my other basis was that on one of my other plots, i noticed the daily death total was starting to lay very nicely on a polynomial curve so i felt like that supported the case that we had already (if recently) made that transition

Quote:

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Do you think exponential decay is the best model for the tail? The deaths should lag the infections by a relatively fixed time. I don't really have a feel for anything better and a long tail on infections and deaths does make sense for something that is going to stick around but we can keep things at a low level.

---

I think it is the best for a couple of reasons.
1) i don't know of a better option. unless we lock down 100% until all cases resolve, a steep decline isnt going to take us all the way to 0. now it could potentially be harmonic decline, but i haven't had the time yet to build that in.
2) china's tail is exponential decline. now there is a lot of reasonable doubt about their reported numbers, but that's the shape of their curve for whatever that's worth
3) that's the shape of the tail on seasonal flu after each season peaks. so my thinking is that as we open things back up, slowly enough to keep from causing a second peak, it would be reasonable to expect to see a long tail.

a lot of assumptions going on in this tail, and i'll be able to better forecast it once we see a decline (as a PETE decline forecasting is actually something i know a bit about). but for now this is my modeled forecast. hopefully worth slightly more than you paid for it.

---

I would try a linear fit on a week by week basis. Looking at the rate of change of m over discreet periods of time would give a pretty good idea of where we're headed. Using a single function to describe the system is tough because the system is being acted upon by changing external factors. Imagine trying to do first or second order kinetics with a temperature gradient. Now make the gradient somewhat random. Time intervals could then be used as a de facto smoothing function.

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a series of linear slopes with "m" values changing in a consistent enough manner that it is predictable? unless i'm misunderstanding you, you basically just described a series of tangent curves, which as you shrink the time periods down can be described by a 2nd order polynomial.

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Yes, but using larger time periods. Instead of a point of interest, you get an area/range of interest. Tangents may be a little too precise. I don't know. One is a series of derivatives taken at regular intervals; the other is a series of least square plots. Ideally they'd look about the same. Either way, m=0 or <0 for several days in a row is what we need

Freeze Frame said:

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To me this is all about a need for data to inform future decisions.

I believe it's really important to know whether COVID19 solely caused the death or contributed to the death. We lose people every day to pneumonia who have significant health challenges and it's unlikely they would have gotten pneumonia without their health challenges (yes, I recognize that pneumonia is often developed from bacteria in the body vs. this contagious virus). How many autopsies are actually being done for those over 70?

My concern is that by just counting every death to coronavirus it will not paint an accurate picture of the true impact from the disease to inform future government policy decisions. Every life and every day with a loved one matters yet policy decisions impact lives every day. For example, someone in a car accident is much more likely to die at 75 mph vs. 55 mph yet some states elect to adopt a higher speed limit, thereby impacting lives. These decisions have to be made one way or the other and without having proper data the decisions might be ill-informed. there will not be any true way to know.

I'm hopeful that local municipalities, states and feds are accurately tracking co-morbidities but given our current political environment (on both sides) I'm highly skeptical.

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I get the impression that some don't really want to know the actual number. I'm sure some researchers down the road would want actual numbers, but likely will never get them.

It seems simple to me to take a sample and freeze it so it could be tested later if you don't want to waste the tests now.

k2aggie07 said:

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I think people are misunderstanding what she said, or at least the implication.

I don't think the CDC is wanting doctors to overrule what they feel is the underlying cause of death and put COVID19 instead. I think they're wanting to make sure that IF covid19 is the underlying cause of death, then covid19 is what is recorded. Not "viral infection" not "pneumonia" but also not putting cancer if cancer wasn't what actually lead to death.

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I agree with this assessment. If you look at was she is saying specifically, I don't think she is saying if a death has a positive test it gets counted as a COVID death. Obviously someone dying in a auto accident whith COVID won't get recorded as COVID cause of death. If you look at the full CDC description you get further confirmation of that
https://www.cdc.gov/nchs/nvss/vsrr/COVID19/index.htm
based on her wording and the CDC description I believe a fair characterization of the intent of what she said would be that we as a country are not downplaying the COVID deaths by attributing it to the "under lying condition" when there is one. the data backs this up as well, because if we were massively over identifying COVID deaths you would expect our CFR to be more towards the upper echelon of countries, not the lower group. additionally, if it was being so over identified that the data was completely unreliable, you also wouldn't be hearing stories from ER Drs of hospitals being nearly overwhelmed even with everything else shut down and deferred.

My takeaway is that the argument that we are over identifying deaths attributable to COVID has some merit. We probably are, and it may even be enough that it will make comparisons to other causes of death difficult when they are close. That said though, the number is not so inflated that it makes the data usefulness. Her statements, the CDC description, other interviews around her comments, and the data itself would all point to the conclusion, that the data is in the ballpark of the "correct" number, and is close enough to be useful for rough modeling and forecasting purposes.

updated charts. I had to push the peak date out 3 days and the quantity up a bit to maintain a reasonable looking fit. 2 days at 1900+ deaths threw a wrench in my lower forecast. Also added data labels to each case load estimate showing what the value is at the last number based on real rather than forecast death counts.

PJYoung said:

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Wow that is a great graph to give perspective.

KidDoc said:

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PJYoung said:

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Wow that is a great graph to give perspective.

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It would have been much better if seasonal flu each year was included or at least the worst flu since 2000. People need to see that data point if only because seasonal flu is what many compare against.

as promised:


flu estimates from here:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6815659/

with no bending over in the daily death rate there is a lot of uncertainty still in the assumptions that go into this, but as you can see, a 2 week difference in when we hit our peak (1 week from now vs 3 weeks from now) means the difference in coming in just under the lower bound of uncertainty for annual flu deaths, and blowing out the top end.


edit to add, and just as a spot.sanity check, it seems my curve selection is working for italy's data so far. haven't gotten to exp decay yet, but so far so good. and the decay phase doesn't actually shift the final total all that much.

BlackGoldAg2011 said:

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AustinScubaAg said:

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KidDoc said:

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PJYoung said:

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Wow that is a great graph to give perspective.

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It would have been much better if seasonal flu each year was included or at least the worst flu since 2000. People need to see that data point if only because seasonal flu is what many compare against.

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if only there were a thread somewhere where someone had put together a bunch of graphs comparing seasonal flu to covid-19... [/sarcasm]

seriously though that would be a completely different look than what this graphic is displaying. it is comparing epidemics to each other and it's really not fair to compare most epidemics to something like flu that has basically reached a steady state balance in the environment. seasonal flu (especially on a global scale) never has a 0 day. you can get a sense for that in my graphs when you just look at the week one data point for each of COVID vs flu, and that's just in the US where flu is very seasonal. but i'm already working on a global covid forecast plot so i'll add it and show a line for seasonal flu too

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I only made the flu reference because there has not been a new virus with the same efficacy as the flu in years. The plot of deaths over time of the other epidemics vs covid19 can be pretty misleading since many of these epidemics were much harder to spread.

BlackGoldAg2011 said:

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updated charts. I had to push the peak date out 3 days and the quantity up a bit to maintain a reasonable looking fit. 2 days at 1900+ deaths threw a wrench in my lower forecast. Also added data labels to each case load estimate showing what the value is at the last number based on real rather than forecast death counts.

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Any chance you can update what this would look like if we really have peaked in deaths/day?

was actually just working on getting all of my plots updated this morning. With the assumption that we have peaked here is what I have

Wonder if you could swag an Rt for each of the CFR hypotheticals based on the exponential rate at the start of the curve.

Then you could use 1-(1/R0) to estimate a final population infected, and a from there a rough total fatality estimate for each.

k2aggie07 said:

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Wonder if you could swag an Rt for each of the CFR hypotheticals based on the exponential rate at the start of the curve.

Then you could use 1-(1/R0) to estimate a final population infected, and a from there a rough total fatality estimate for each.

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So I actually tried that and have a plot of Rt values vs time (just realized I mislabeled it R0). The problem I ran into was that since R0 or Rt is only dependent on doubling time and the length of the infectious period(i), the R for each of the case load curves is the same since they are each just a multiple of the death curve. In the formula for the number infected N(t)=N(0)*R^(t/i), the only thing changing between each of those curves is N(0). Only thing that changes is when we get there. I'll post my Rt curves over here when I get back to my desk, but they are on the daily plots thread already.

k2aggie07 said:

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I think people are misunderstanding what she said, or at least the implication.

I don't think the CDC is wanting doctors to overrule what they feel is the underlying cause of death and put COVID19 instead. I think they're wanting to make sure that IF covid19 is the underlying cause of death, then covid19 is what is recorded. Not "viral infection" not "pneumonia" but also not putting cancer if cancer wasn't what actually lead to death.

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Birx seems to be at the center of a lot of confusion and issues created at these press conferences. She needs to (1) better understand how her comments come across and (2) be more exacting in her responses.

I appreciate her efforts, but the actual CDC guidance and how this is actually working in the real world---based on my understanding---doesn't quite match that really boiled down version she just gave. Actual guidance asks for linking Covid-19 into the causal chain behind a death.

But that can't be quite right, eh? If you have more cases, your transmission rate has to be higher.

I believe if you fit the early portion of each hypothetical case trendline to a Ce^(rt) function, their rate r is related to R0 by:

R0 = 1 + r / gamma

Gamma is the recovery rate, or infectious period - one over how long you're infectious. For this, I've seen a published value of about 12 days.

And from there the percent infected is 1 - 1/R0, so you'd multiply that by your hypothetical CFR to get a range of fatality outcomes.

k2aggie07 said:

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But that can't be quite right, eh? If you have more cases, your transmission rate has to be higher.

I believe if you fit the early portion of each hypothetical case trendline to a Ce^(rt) function, their rate r is related to R0 by:

R0 = 1 + r / gamma

Gamma is the recovery rate, or infectious period - one over how long you're infectious. For this, I've seen a published value of about 12 days.

And from there the percent infected is 1 - 1/R0, so you'd multiply that by your hypothetical CFR to get a range of fatality outcomes.

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we are saying the same thing.

for the total cumulative cases function
N(t)=Ce^(rt)

C determines the y-intercept and r will determine the exponential growth rate (or slope on a semi-log plot). if you look closely at each of those calculated total case curves, they all have identical slopes at any given point in time because they are just multiples of the death curve. from a physical standpoint this would mean the only difference is the number of total cases when the growth turned exponential.

to put it mathematically, on any given day, the CFR implied case curve is just N_CFR=N_deaths/CFR
(obviously with a time shift but this is irrelevant to the discussion. Since the death curve function is
N_death(t)=Ce^(rt)
then the calculated CFR curve at the associated point should be
N_CFR(t)=(C/CFR)*e^(rt)

same slope so same r.

to your statement in bold, not quite. if you have a higher rate of growth your transmission rate has to be higher. if you took 1 person infected with a disease that will double ever 4 days and dropped them in a pool of 1MM at the end of 4 weeks you will have 128 cases. if you drop 100 people into the same pool with the same disease, at the end of that same 4 weeks you will have 12,800 cases. same rate of growth, different initial case load.

Right ok I see your CFR curves are timeshifted left to make it work out. But there's two problems there - one is that we know these all began from the same case load, whatever number you want to assume (1 or 10 or 100). And the other is that they can't go negative in time. Maybe some back from Jan 15 but not likely beyond Jan 1.

k2aggie07 said:

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Right ok I see your CFR curves are timeshifted left to make it work out. But there's two problems there - one is that we know these all began from the same case load, whatever number you want to assume (1 or 10 or 100).

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right, but each starting case load only works for one CFR curve so if we knew that we would know which of the curves was right. and that number doesn't have to be the number of real initial cases. I was reading in one of the CDC papers, than many infectious diseases essentially have a minimum threshold for number of cases before growth becomes exponential.

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And the other is that they can't go negative in time. Maybe some back from Jan 15 but not likely beyond Jan 1.

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i don't follow. why would they need to go negative in time? my time shift is entirely dependent upon the average days from infection to death. I'm using 14 but it could be more or less.

and here's the plot I mentioned earlier where i did a rolling 1 week R calc based on the death and confirmed infection curves for a variety of "infectious days" which I called "ti"

Bleh forums are difficult for this.

Ok, so basically we have an unknown number of cases creating a known number of fatalities, but we don't know the ratio of cases to fatalities. But those fatalities are fixed in time.

Let's say we have 1 and the true CFR is 1/10,000. Clearly means when you hit 10,000 cases you get 1, and 20,000 you get 2, and so on. But for a fixed Rt, that moves the beginning of the case curve to the left - let's say 2, just for simplicity. To get to 10,000 you need 12-13 doublings.

For the same Rt at a CFR of 1/100, you only need 6-7 doublings.

We have a kind of known rhythm or serial interval to this, cases can't go faster than the incubation period. Even if a super spreader infects 30 people, those people likely won't be infecting people for ~4 days. Serial interval has been estimated around 4-7.

Taken together that means for the CFR of 1/100, you need ~36 days or so to see your first death, and for the CFR of 1/10,000 you need ~72 days.

Feb 29 was the first death reported. 72 days from then was December 15. So, we have to do something - either the CFR is not 1/10,000 (i.e., we didn't have 10,000 cases on Feb 29) or Rt is not 2.

Since one part of the picture is fixed in time (deaths), there is a relationship between CFR and transmission rate in order to fit those curves.

Agreed, forums are difficult for this. But I think I follow. I struggle though to use my specific curves this way though since they all show the same slope, they will just each have different start dates. so i put a growth curve to each and plotted it backwards to 1 case. Day -60 is 12/16/2019. using that growth rate I plotted what the required number of cases would be on 1/19/2020 or roughly when we had our first few confirmed cases. i shifted my curves a bit though based on this article :https://wwwnc.cdc.gov/eid/article/26/7/20-0282_article and said deaths lag infected date by 21 days when accounting for incubation period and all other factors. here is my plot:


then i took a different look. Taking the latest death numbers and looked backwards 21 days to 3/24 and took that projected case load by CFR and assumed a starting case load and starting date. using that I calculated what doubling rate would be required to get to each calculated case load, used that to calculate various R0 for different infections periods and then used that and the original assumed CFR to calculate what the death count would be for that CFR if things had been left completely unchecked


maybe something like this is what you envisioned?