This document is NOT Copyrighted in any way and is meant to be shared.
By: Matt Webb
This is a look at a typical model predicting infectious disease spread sprinkled with some historical perspective in an effort to understand what is going on. It is not meant to downplay the seriousness of what we as a nation are going through. It is mostly a "note to self" in an attempt to understand what are unprecedented actions taken by governments, in what some are claiming is an unprecedented threat scenario, thereby requiring unprecedented sacrifice. Of course even a cursory look back over the last 100 years will put the lie to all those "unprecedented" claims. Never the less, these are and will be considered, for many reasons, as historic times and we should endeavor to understand what is happening to us in as real time as possible. This document may be updated from time to time.
Executive Summary: What is most likely regarding the C19 situation based upon what we know as of about 3/25/20
Infectious peak % likely occurs around April 10 but it is predicted that Governors will extend “shut down” restrictions for perhaps 2 more weeks past that… “in an abundance of caution”… and because they really can’t back off so fast given the dire statements that have been made and the unprecedented actions that have been taken.
On or about April 24, the Infectious % of the population will be declining which together with a lowered population of Susceptibles and the increased population of Recovered, will then reduce the number of new cases.
While none of this may change the ultimate # of cases … it will have stretched the timeline (the famous “flattening of the curve”)… as we steam roll toward herd immunity which is the light at the end of the tunnel.
Expect the timing for things to start easing to be about 4 weeks from now. This will be an easing, not a step wise reversal, of restrictions. My thinking is getting more optimistic based upon the numbers I see from CDC and my study of the Infectious Disease Spread SIR Model.
WHY I THINK WHAT I THINK THE ABOVE REGARDING C19 AS OF 3/25/20
Everyone is handling this “crisis” differently, so as Kipling said: “If you can keep your head when all about you are losing theirs and blaming it you” do so. It seems best to pay dispassionate attention to numbers and ferreting out and then testing facts. That is one of the best ways to perceive reality. This may cause one to appear unconcerned or less than empathetic, but, we can be concerned and not fret. It is best to live with reality as it presents itself and, we have family, friends, associates, partners, staff, clients, customers and vendors all depending on us in one way or another. We truly are in a deeply interconnected community and world.
That said, given that everyone handles things differently and each individual circumstance cannot be known, we allow that each person, will act in their own rational self interest which at times like these can easily include self motivated sacrifice to the greater good.
Considering what is happening right now, there are worse things. There are always choices. And, “there is no crying in baseball”.
As far as being concerned, concerns go well beyond the virus.
What if we are getting our response wrong?
Politicians will err toward caution but what about government over reach leading to partial nationalization of “nationally critical industries” under the guise of bailout, which has already been suggested? What about leaving the bill, once again, for the taxpayer? What about indebting future generations to the point of reducing opportunity and burdening them with todays pork barrel waste du jour rather than emergency imperatives and what does this over reaching spending imply about future inflation, interest rates and GDP? Who will pay that bill when it comes due? Not those voting in today's legislatures across the land, but their children and grand children.
So, what is a rational person to make of these CDC facts and figures?
Do those figures denote a crisis requiring the stopping of the engine of the world or spending Trillions of $? Is the cure worse then the virus?
Certainly a look at the “the numbers” and how they are used, or misused is warranted. Statements like…. “over the last 24 hrs the number of confirmed cases has increased by nearly 100%” are rarely provided with counter balancing context of the increased tests being done. Or…. as of midday 3/25 there were 54K cases in the USA, against maybe100K tests (from the CDC site) or, according to Dr. Birx, of the administration task force, claiming about 450K tests have been done, and saying (paraphrasing) “there is just a lag between actions and posting or delivering of the data”. I have read in various places that testing indicates the between 10% and 50% of the tests are returning positive results… which are big percentages, but it must be off-set by the fact that we are only testing those thought to have the virus and who present with symptoms, so we should expect a high % of positives. We simply are not testing those we don’t have good reason to think are infected. Where is the clarifying statement about that?
God forbid if we ever to share that we probably now have maybe 540K cases in the USA as it has been estimated that less than 1 in 10 people who have, or have had, or will have, C19, will ever be actually confirmed since so many recover and never know if it was a cold, the flu A or B, H1N1 or C19, or if they just had a "blah" few days!
We know as of 3/25, we had 737 deaths from C19, so the 737/54000 ratio gives a 1.4% mortality rate…. higher than flu but it continues to fall and we should expect it to fall further but where is the headline?
And, since we probably have 540K cases, the real # is probably 400/540000 and the fatality rate is probably 0.14% and again, more in line with what we are finding with other like kind viruses.
And of course, while you can easily find heart wrenching individual deaths being highlighted in the News, the reality of the changing mortality rate won’t fit the disaster narrative, so we should not expect to hear much about it.
It is important to have basis for these thoughts. And the basis are manifold including the CDC facts and figures, News Feeds vetted for common sense, history and of course the typical model being used which is typically the SIR (Susceptible, Infectious, Recovered) model which produces graphs like the one at the top of the page, which was representative for the Hong Kong flu, when it came through in the 1960s, and is thought to be representative.
The equations for these variables are differential equations, but don't be worried. That just means they are equations that show how fast or slow, and in what direction (increasing or decreasing) each variable is changing at any given time.
Looking at the graph, you can see for example where the Susceptible population percent (the fraction of the population who can still get the disease) is the same as (crosses over) the Recovered population percent (the fraction of the population who has recovered from the disease), is right where the infected population percent (the fraction of the population actively infected but not recovered) is highest.
Interestingly that is the point some have called the "inflection point" which mean a turning point, and it just means that the fraction of the people infected is neither increasing or decreasing. And we look for inflection points because they are necessary for things to "turn around"!
So, differential equations merely show the rates of change for each of the Variable an din this case we want to know how fast the population of people who could get the disease (the Susceptible) is changing? And likewise, we want to know how fast the populations of Recovered people and Infected people are changing?
I am going to write the differential equations here, but please don't be put off. I know somewhere someone told most of you or convinced you, or allowed you to convince yourself, that math is hard. Its not!. Its just a language. Learn the vocabulary, a few rule like grammatical rules, and one or two basic process steps and you too can do math, even differential equations (OK maybe its a little harder than that but you can understand what the equations are trying to tell you).
So, here are the equations:
ds/dt = -b X s(t)
And all the means is that the change in the fraction of the population that is susceptible to getting the virus at any time (ds/dt) is equal to a number representing the number of contacts each day that an infected person has (which we call "b"), but only those contacts that are sufficiently close to spread the disease (hence social distancing), multiplied by the fraction of the population that is still susceptible [s(t)]. So, bXs(t) would be the new infected people per day. And since we are taking the newly infected people out the susceptible population, we need a minus sign.
Not so hard and even makes sense, right? Welcome to the world of differential equations!
What is next? Well we want to understand how fast the population of Recovered people is changing at any time. And again, dealing with the percent, or fraction of the population that has been infected and recovered we write a new equation:
dr/dt = k X i(t)
Which means that the change in the fraction of the population that has recovered at any time (dr/dt) is equal to a number we call "k" (which is an estimate of the fixed fraction of the infected population that recovers each day also known as a guess... based on other like kind viruses) multiplied by the fraction of the population that is actively infected at any given time. So the recovered population is increasing at any given time or it flatlines (for a virus where immunity occurs and doesn't reinfect).
Recognize that the number b and the fraction k are initially guessed at by scientists with knowledge of viruses and how they spread and then those numbers are refined as time goes by and more is is learned. Meaning you have to live through it before you can really know what the values of b and k really should be and it is that initial uncertainty that causes fear and may produce what in retrospect might be viewed as a over reaction.
The other thing we might want to know is how fast the fraction of the population that is infected is changing. And this one is really easy because since you canonly reduce the susceptible population by becoming infected and you can only increase the recovered population by having been infected it seems logical that the rate of change of fraction of the population that is infected is just the difference of the other changes so:
di/dt = b X s(t) - k X i(t)
Which is cool because it means that at some point this all comes to an end as if you add the change rates together at any time you get zero:
ds/dt + dr/dt + di/dt = 0
One more commentt about the graph above and the use of fractions or percentages of the population rather than actual numbers.
fractions are cool because then it doesn't matter how big or small the amounts of people in the populations might be and you can look at a county or a city or a State or a country. Its all just pieces of the entire number of people or, the population, we are considering.
Of course if we are dealing with pieces of the whole population, you can also see that the number of people that are Susceptible and the number of people that have Recovered and the number of people that are infected must equal the entire population. Or, if working in fractions or percent, the fractions must add to 1 or the percentages to 100%.
Mathematically we write:
S + I + R = N (or the total number of people in the population if counting people or,
s(t) + i(t) + r(t) = 1 (if using fractions)
One qualifying comment here as both of the last two equation are of course wrong.
They are wrong because some people die.
Which means the model could include a fourth equation probably looking like this:
dd/dt = q X i(t). … which would be rate of death at any given time, and where q might be a fixed fraction of the number of people who once infected required ventilators.
Therefor, to be more accurate, at any time:
s(t) + i(t) + r(t) + d(t) = 1 (if using fractions and where d(t) is the fraction of the population that were infected and didn't recover.
There is a mathematical reason for leaving out the dead…. and that is that it is typically found to be and is estimated to be in these cases as too small to consider, comparatively (typically less than 1% or even less than 1/10th of 1%, and in fact, it appears to many who live with these models and have started gathering data on this particular disease, that the expectation of the % of dead (mortality rate) will end up less than 1%.
When? Well, once the numbers resolve to a equilibrium state aka when the derivatives with respect to time are zero (zero slope or not changing)… which might happen is as short a time as 4 months from when this started in the USA, typical taken as January 21, so May 21.
But that will not be true because we have been so aggressive in trying to slow down the spread, that the timing for equilibrium, aka "herd immunity" will take longer but the numbers will be changing slower, which will do three things:
1. We will have self inoculated the population by sufficient numbers of people becoming infected and then recovered thereby becoming immune and having permanently removed themselves from the susceptible population that the remaining susceptible population is too small for many to still become infected (too few close contacts with susceptible will be possible or, a shrinking "b").
2. We will have slowed the rate of new infection and thereby reduced the numbers requiring healthcare infrastructure, and specifically hospitalization, ICU or ventilators and such, below the anticipated maximum, but fixed estimate of the supply of such infrastructure (resources).
3. We buy time to develop therapies, if not vaccines, that will be more effective to try to save lives.
So that is the model and the "why" of what has been happening with lock downs and shut downs and social distancing. Without a vaccine we really can't stop the spread and it will progress to herd immunity. It is only a question of how fast?
Which is why there may be logic to quarantining/isolating, in the case of this disease, people over 65, the very young and those with known risk factors, meaning those most likely to have severe complications or die, which really means we temporarily remove them from the herd so the rest of the herd can reach the immunity level sufficient to present low to no significant risk to those most at risk.
This has the benefit of not having to shut down the entire economy.
But has ANYONE in power said any of that out loud? No! Why? They are afraid to say it and be wrong, and because there is still uncertainty in the constants (the k and the b), so even though the potentials for disaster are small, they will wait until they can shout “look how all my infringement of your rights and the destruction of the best economy in the history of mankind, was necessary as I nearly single handedly saved the world”. OK… they won’t say that exactly.
But don’t expect to hear the truth or at least the most likely scenario until they are near certain of the outcome and they can lay claim for the victory.
What about timing and expectations?
It must be understood that the graph above, which again as related to the Hong Kong Flu in the1960's, proceeded with passing time to a peak Infection % at about 76 days, and corresponded to about 8% of the total population infected at one time (in America that would be about 27 million people today). It in interesting to think about that and if that can't be stopped really (just slowed) what is the correct policy for a nation facing that? Does it shut down for ever? And how and when is is turned back on?
This is new ground because we have never done anything like this before.
One might ask how and why is China "turning back on"? Because what they really care about is their economy! A few 100 million people sick (in China), may be on their worry curve given 4-6% mortality rate, but a few % points of lost GDP… that could topple the regime. But it is in China where we may be now seeing the most likely outcomes with regard to timing and the effects of mass quarantine.
It is also interesting to see that it is America, not Communist China, that was so willing to shut down an entire country. Why are we letting them do this? It may be for good reason, as I have tried to define here, but we have not be advised, only frightened.
We gave the government extraordinary power under declarations of emergency acts, and are apparently willing to trade liberty for safety. Or… are we just losing liberty while they redistribute the wealth of the nation. But either way, it should all be explained in plain language. But they treat us like children as we have apparently decided that a benevolent hierarchy is desirable, or at least, permitted.
As parameters start to reveal themselves with more certainty, the actual shapes of the graph can then be determined for C19. The graphs and equations and parameters being used are guides only. And the forecasts being made are worst case whereas, it is much much much more likely to be far less grave, but as stated, the pols have now cornered themselves and they are invested in certain degree of disaster before they can unwind it it, or they will be shown to be fools.
During the 2017-18 flu season CDC says about 38% of the adult population were vaccinated, which was a drop of 6.2% from the previous season (yes… fewer people are getting vaccinated)… and while 38% is a good number it could/should easily have been higher. one might note that 38% innoculated plus those that caught flu is amazingly close to the estimate of herd immunity! And that means that if everyone were REQUIRED to get the flu vaccine each year, we might have saved between 12K-30K (THOUSAND) lives! Just asking… why don’t we seem to care about that? The latest flu data from CDC is here:
Back to C19…. the governor of NY is actually saying to the population of NY State who he has sworn to protect, that out of about 20 million people in NY State, 12 million (60% of the total which happens to be a commonly used figure to achieve herd immunity in a no vaccine situation) will likely become infected, but then he comes unglued and says that 1.8 million will need to go into a hospital and 72K will require ICU services.
Based upon all this…. how likely are those numbers?
Sites you might interesting are:
And note that the pandemic of the Spanish Flu (an H1N1 virus) of 1918, in unvaccinated environment where flattening the curve was not a consideration, produced a 0.65% mortality rate in the USA and that was given the state of medical arts and accessibility 100 years ago (no ventilators approaching anything modern until the1950s)! One might wonder how anyone survived?
So, does Governor Cuomo really think that on a National level we are going to suffer 200 million infected (herd immunity again)? Maybe. But he can’t possibly really think that 30 million people are going to require hospitalization (far less than 1 million in this past flu season and corrected to remove the vaccinated population would have been less than 5 Million) and 1.2 Million may require an ICU bed.
We’ve never seen anything like that in modern times.
So why say it?
Our leaders are trying to scare or threaten people to stay at home, to slow the spread… slow the spread, not stop saturation to herd immunity. He is after elongation of the time period required to reach herd immunity, he is not promising fewer infections overall. And, he probably just doesn’t think explaining it in full will be enough to drive people into their homes for long enough, or, to justify the extraordinary abuse of basic rights of being a Citizen in America, which he has engaged in, as have others.
Don't mean to be picking on Governor Cuomo, but he is visible very day.
So, those are the % figures that most of the governors have been convinced are “possible” and what we are going to have to deal with even though nothing like it has ever happened before and even though the actual numbers (and rates) that are developing are below the “the sky is falling” estimates.
Said a different way, the estimates being used are extreme worst case guesses or gross overestimates of the most likely scenarios. So the scare stories are improbable given what we now know.
But when a reporter corners a scientist he or she is forced to say something like… “according to the model it is possible” and then everyone starts screaming and drowns out the “but improbable” finish.
The headlines then say “Virus could infect more than half of _______” fill in the blank for the population being considered, and the headline is technically correct. Fear mongering but technically correct… as “could” is taken as “will” because most folks are just a bit scared to think this through, or have been cowed into thinking that everything requires an expert because those of us out here in the great unwashed masses couldn't possibly understand anything marginally complex. Well we can. And we do.
And the pols who taking away our rights are only worried about being accused of not having done everything they could.
Think H1N1 when it cycled through again 10 years ago… no vaccine, but no statewide shut downs. There were a small % of schools that closed for a while (not the rest of the year, which just happened in VA) and some isolated “hot” locations that limited services and business operations, briefly, so….. one might see all that as relatively unabated spread to herd immunity. What happened?
In the 2009-2010 season of H1N1: 60 million were infected, 275K required hospitalization, and 13K died (about 4X fewer than we kill on our highways every single year). And somehow… this did not overwhelm our healthcare system, and many can’t even remember it!!