blog:2020-03-22:covid-19_spread_part_ii
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blog:2020-03-22:covid-19_spread_part_ii [2020/03/22 10:28] – [COVID-19 Spread (Part II)] va7fi | blog:2020-03-22:covid-19_spread_part_ii [2020/08/07 13:03] (current) – external edit 127.0.0.1 | ||
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- | ====== COVID-19 Spread (Part II) ====== | + | ====== COVID-19 Spread (Part II) Updated |
<WRAP center round important 90%> | <WRAP center round important 90%> | ||
* I'm not an epidemiologist, | * I'm not an epidemiologist, | ||
+ | * This was originally written on Sunday March 22nd. | ||
</ | </ | ||
+ | |||
+ | <WRAP center round tip 90%> | ||
+ | * Jump straight to the [[# | ||
+ | </ | ||
+ | |||
- | In [[blog/ | + | In [[blog/ |
<WRAP half column> | <WRAP half column> | ||
Line 14: | Line 20: | ||
{{: | {{: | ||
</ | </ | ||
- | <hidden Show Formulae> | ||
- | The formulae for the exponential curves are: | ||
- | * $N = 24.5 \times 2^{(\frac{t}{4.1})}$ for the green line (where //t// is the number of days since March 2) | ||
- | * $N = 93.1 \times 2^{(\frac{t}{2.7})}$ for the blue line (where //t// is the number of days since March 10) | ||
- | </ | ||
- | \\ | ||
- | Initially, the number of cases doubled every 2.7 days, predicting almost 1600 cases by the end of Saturday, but in the last two or three days, the rate of infection | + | Initially, the number of cases doubled every 2.7 days, predicting almost 1600 cases by the end of Saturday |
- | ====== Growth | + | ====== Growth |
- | There' | + | There' |
<WRAP half column> | <WRAP half column> | ||
|< 10px >| | |< 10px >| | ||
- | ^Day ^# of Cases ^New Cases ^Growth | + | ^Day ^# of Cases ^New Cases ^Growth |
|Day1 |100 | | |Day1 |100 | | ||
|Day2 |110 |10 | | | |Day2 |110 |10 | | | ||
Line 37: | Line 37: | ||
<WRAP half column> | <WRAP half column> | ||
- | To calculate the growth | + | <WRAP box> |
- | * | + | To calculate the growth |
- | * | + | * |
+ | * | ||
+ | </ | ||
</ | </ | ||
- | * If the growth | + | * If the **growth |
- | * If the growth | + | * If the **growth |
- | * If the growth | + | * If the **growth |
+ | * If the **growth factor = 0**, then the epidemic is over. | ||
+ | Here are the number of cases in Canada with the calculated growth factors: | ||
+ | ===== March ===== | ||
+ | <WRAP half column> | ||
+ | |<100% >| | ||
+ | ^Date ^ # of Cases ^ New Cases^ Growth Factor| | ||
+ | |2020-03-01| | ||
+ | |2020-03-02| | ||
+ | |2020-03-03| | ||
+ | |2020-03-04| | ||
+ | |2020-03-05| | ||
+ | |2020-03-06| | ||
+ | |2020-03-07| | ||
+ | |2020-03-08| | ||
+ | |2020-03-09| | ||
+ | |2020-03-10| | ||
+ | |2020-03-11| | ||
+ | |2020-03-12| | ||
+ | |2020-03-13| | ||
+ | |2020-03-14| | ||
+ | |2020-03-15| | ||
+ | |2020-03-16| | ||
+ | </ | ||
+ | <WRAP half column> | ||
+ | |<100% >| | ||
+ | ^Date ^ # of Cases ^ New Cases^ Growth Factor| | ||
+ | |2020-03-17| | ||
+ | |2020-03-18| | ||
+ | |2020-03-19| | ||
+ | |2020-03-20| | ||
+ | |2020-03-21| | ||
+ | |2020-03-22| | ||
+ | |2020-03-23| | ||
+ | |2020-03-24| | ||
+ | |2020-03-25| | ||
+ | |2020-03-26| | ||
+ | |2020-03-27| | ||
+ | |2020-03-28| | ||
+ | |2020-03-29| | ||
+ | |2020-03-30| | ||
+ | |2020-03-31| | ||
+ | </ | ||
- | ====== COVID-19 Spread (Part I)====== | + | ===== April ===== |
+ | <WRAP half column> | ||
+ | |<100% >| | ||
+ | ^Date ^ # of Cases ^ New Cases^ Growth Factor| | ||
+ | |2020-04-01| | ||
+ | |2020-04-02| | ||
+ | |2020-04-03| | ||
+ | |2020-04-04| | ||
+ | |2020-04-05| | ||
+ | |2020-04-06| | ||
+ | |2020-04-07| | ||
+ | |2020-04-08| | ||
+ | |2020-04-09| | ||
+ | |2020-04-10| | ||
+ | |2020-04-11| | ||
- | So there' | ||
- | But doing the right things can change that future. | + | </ |
- | {{ : | + | <WRAP half column> |
- | The real question is how soon will we reach that middle point, and at what height. | + | |< |
+ | ^Date ^ # of Cases ^ New Cases^ Growth Factor| | ||
+ | </ | ||
- | Here's a good video that explains this sort of math and why being able to think in exponential term is important for non-linear systems such as this one. | + | There's a lot of variation in the growth factor because real life is messy. |
- | {{ youtube> | + | We don't have an accurate picture of the world here so it's hard to make any kind of hard predictions. |
+ | {{ : | ||
- | \\ | + | Overall, the growth factor is mostly above 1 (in the exponential phase), but it looks like we might be on track to reach 1 by the end of the month (end of exponential phase). |
- | And here's another one with different animations that complements it very nicely. | ||
- | {{ youtube> | + | ====== The Logistic Curve ====== |
+ | In [[blog/ | ||
+ | {{ : | ||
+ | {{ : | ||
+ | |||
+ | * <fc # | ||
+ | * <fc # | ||
+ | * <fc # | ||
+ | |||
+ | <hidden Show Formulae> | ||
+ | |<100% >| | ||
+ | | <fc # | ||
+ | | \$$N = \frac{2660}{1 + e^{-0.32(t - 21.1)}}\$$ | ||
+ | </ | ||
\\ | \\ | ||
- | Here's an interesting article from [[https:// | + | Here are a few things to know about the Logistic Curve. |
- | {{ : | + | * The curve is flat like a straight line, which indicates that the growth rate is constant. |
+ | * This means that the growth factor is 1 (by definition) | ||
+ | * It also happens that this is the halfway point in terms of total number of cases. | ||
- | ===== More on the Logistic Function ===== | + | So once we reach that point, we'll be able to get a better estimate of where we'll end up. Until then, things are still very much in the air. |
- | This is an update from March 19th. | ||
- | This section illustrates how eventhough the infection follows a Logistic Function, that fact alone doesn' | + | ====== March 28th Update ====== |
- | {{: | + | A lot happened this week: |
+ | * BC seems to be dropping the ball on testing. | ||
+ | * Quebec went the opposite way, increasing their testing and finding a lot more cases. | ||
+ | |||
+ | Over all, it looks like we are back on the exponential curve with an overall doubling time of 3.1 days: | ||
+ | |||
+ | <WRAP half column> | ||
+ | {{:blog:2020-03-22: | ||
+ | </ | ||
+ | <WRAP half column> | ||
+ | {{: | ||
+ | </ | ||
+ | |||
+ | The Growth Factor also seems to support this as it is barely decreasing. | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | |||
+ | Over a [[blog/2020-03-16/ | ||
+ | |||
+ | The updated model (doubling every 3.1 days) predicts that we are about 12 days behind Italy (with now has over 92,000 cases). | ||
+ | |||
+ | According to the [[https:// | ||
+ | <WRAP indent> | ||
+ | "Dix and provincial health officer Dr. Bonnie Henry both said they are optimistic B.C. isn't following the same path as countries like Italy that have seen their healthcare systems overwhelmed by huge spikes in hospitalizations and deaths." | ||
+ | </ | ||
+ | |||
+ | Country-wide, | ||
+ | |||
+ | Here's a different way to look at the exponential curve when the number of cases is presented as a multiple of 10 on the vertical axis (called a [[wp> | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | If we stay on that line, we'll reach 100,000 cases by April 10< | ||
+ | |||
+ | |||
+ | ====== Cleaning Groceries ====== | ||
+ | |||
+ | Here's a video shared by the [[http:// | ||
+ | {{ youtube> | ||
+ | |||
+ | |||
+ | ====== Other Models ====== | ||
+ | |||
+ | Compartmental Models are popular such as the SEIR (Susceptible, | ||
+ | |||
+ | Kaggle has a modelling competition which has some good data sets. You need to use a Google ID to access this (I think since Google brought Kaggle a few years ago). [[https:// | ||
+ | |||
+ | |||
+ | ====== April 3rd Update ====== | ||
+ | |||
+ | Hard to believe that a month ago, there was only 27 reported cases in Canada (compared to 12,549 cases today). | ||
- | The equation for "Model 3" is: | ||
<WRAP centeralign> | <WRAP centeralign> | ||
- | $$N = \frac{2000}{1 + e^{-0.32(t | + | <WRAP half column> |
+ | {{:blog:2020-03-22: | ||
</ | </ | ||
+ | <WRAP half column> | ||
+ | {{: | ||
+ | </ | ||
+ | For the last week, the infection rate seems to be flatter than it has been. | ||
- | It reaches its halfway point around March 21 and peaks at 2000 people infected. | + | {{ :blog: |
+ | The Growth Factor continues to (slowly) decrease. | ||
+ | </ | ||
- | {{: | + | With the same physical distancing measures in place, it looks like we could see between 20,000 and 35,000 cases. But the future is still highly unpredictable precisely because it is up to us. |
- | Its equation | + | {{ : |
+ | {{ : | ||
+ | |||
+ | I've also said a few times that BC is way behind on testing and that the numbers we see are vast underestimates. | ||
+ | |||
+ | On a lighter note, [[https:// | ||
+ | |||
+ | {{ https:// | ||
<WRAP centeralign> | <WRAP centeralign> | ||
- | $$N = \frac{20000}{1 + e^{-0.24(t - 32)}}$$ | + | " |
+ | This model apparently explores time travel." | ||
</ | </ | ||
- | But it reaches its halfway point at on April 1st and peaks at 20,000 people. | ||
- | Reality | + | ====== April 12th Update ====== |
+ | It's been over a week since the last update and according to the numbers, it looks like we are off the Exponential curve... | ||
+ | {{ : | ||
+ | |||
+ | ... and into the linear middle section of the Logistic curve: | ||
+ | {{ : | ||
+ | {{ : | ||
+ | |||
+ | |||
+ | The calculated Growth Factor also seems to have dipped below 1: | ||
+ | {{ : | ||
+ | |||
+ | Again, recall that: | ||
+ | * If the **growth factor > 1**, the number of new cases is itself increasing each day, which means we are still in the exponential phase. | ||
+ | * If the **growth factor = 1**, then the number of cases is growing at a constant rate (same amount each day). This is the middle of the Logistic Curve. | ||
+ | * If the **growth factor < 1**, then the infection rate is levelling off. | ||
+ | * If the **growth factor = 0**, then the epidemic is over. | ||
+ | |||
+ | ===== Evidence and Certainty ===== | ||
+ | |||
+ | I am still very skeptical that these numbers are an accurate description of our current situation so I feel like I have to explain an apparent contradiction here: | ||
+ | |||
+ | <WRAP indent> | ||
+ | |||
+ | The quick answer is no. The way evidence works is not symmetrical. | ||
+ | * If you catch a mouse, you can, with 100% certainty, say that there was (at least) one mouse in the basement. | ||
+ | * If you don't catch anything, you can't say anything with 100% certainty. | ||
+ | |||
+ | So back in March, the reported cases grew exponentially, | ||
+ | - The infection is actually flattening out (I really hope and wish this is the case), or | ||
+ | - The amount of testing we do is insufficient and we are not recording the actual spread of the virus (this might very well be the case). | ||
+ | |||
+ | It's hard to say exactly which of these it is because the provinces aren't releasing the daily number of tests they perform (or if they do, I haven' | ||
+ | |||
+ | ^Province ^Cases ^Deaths ^Death Rate | | ||
+ | ^BC |1445 |58 |4.0%| | ||
+ | ^AB |1569 |40 |2.5%| | ||
+ | ^ON |6648 |253 |3.8%| | ||
+ | ^QC |12292 |289 |2.4%| | ||
+ | |||
+ | The number of cases and the number of deaths are reported daily. | ||
+ | <WRAP centeralign> | ||
+ | \text{Death Rate} = \frac{\text{\# | ||
+ | </ | ||
+ | |||
+ | Another way to think of this is: for every 100 reported cases, how many people die? | ||
+ | |||
+ | From this, we see that BC has 4 deaths per 100 reported cases, where as Alberta has 2.5 deaths per 100 reported cases. This suggests that there are a lot more unreported cases in BC since the death rates should be relatively similar across the country. | ||
+ | |||
+ | What we hear from the news also supports this: Alberta is being praised for the high number of tests they are performing (and their death rate is low) while Ontario is being criticized for the opposite (and their death rate is high). | ||
+ | |||
+ | Unfortunately, the number of deaths lags about 2 to 3 weeks behind the number of real cases so using it as a metric is not practical. | ||
+ | |||
+ | ===== A Letter to Dr. Henry ===== | ||
+ | |||
+ | Yesterday, I sent the following letter to [[bonnie.henry@gov.bc.ca |Dr. Henry]]: | ||
+ | |||
+ | <WRAP box center 90%> | ||
+ | Dear Dr. Henry, | ||
+ | |||
+ | I live in a small community on the Sunshine Coast. | ||
+ | |||
+ | I was very happy to hear your recommendation for people to stay home over the long weekend. | ||
+ | |||
+ | Unfortunately, | ||
+ | |||
+ | I implore you. Please, add teeth to the excellent recommendations that you have. There will always be people who: | ||
+ | |||
+ | > " | ||
+ | |||
+ | Clearly, there are people who only think of themselves and not the small communities they could be impacting. | ||
+ | |||
+ | I know that you know that it only takes a few people to start a pandemic. | ||
+ | |||
+ | Please stop appealing to the majority of people' | ||
+ | |||
+ | Thank you, \\ | ||
+ | Patrick Truchon | ||
+ | </ | ||
+ | |||
+ | And this morning, a [[https:// | ||
+ | |||
+ | Unfortunately, | ||
+ | |||
+ | ===== April 17th Update ===== | ||
+ | I finally found a key piece of data((The site I have been using just added the number of tests performed recently: [[https:// | ||
+ | |||
+ | Here's a summary of the four most populous provinces | ||
+ | |||
+ | ^Province ^Tests ^Cases ^Deaths ^Population (Millions) ^^Cases / Tests ^Death / Cases ^Tests / Million ^Cases / Million ^Death / Million | | ||
+ | ^BC |59185 |1575 |77 |5.111 ^|2.7% |4.9% |11580 |308 |15 | | ||
+ | ^AB |85502 |2158 |50 |4.413 ^|2.5% |2.3% |19375 |489 |11 | | ||
+ | ^ON |128093 |8961 |423 |14.712 ^|7.0% |4.7% |8707 |609 |29 | | ||
+ | ^QC |151510 |15857 |630 |8.538 ^|10.5% |4.0% |17745 |1857 |74 | | ||
+ | |||
+ | That's a lot of numbers so let's unpack this table a bit: | ||
+ | |||
+ | * The " | ||
+ | * The other columns are calculations: | ||
+ | * "Cases / Tests" is the percentage of tests that come back positive. | ||
+ | * "Death / Cases" is the number of death for every 100 **reported** cases. | ||
+ | * "Tests / Million" | ||
+ | * "Cases / Million" | ||
+ | * " | ||
+ | |||
+ | So let's compare these four provinces. | ||
+ | |||
+ | ==== Number of Reported Cases ==== | ||
+ | If we look at the total number of reported cases, it looks like BC is doing the best and Quebec is the worst: | ||
+ | * BC: 1575 cases | ||
+ | * AB: 2158 cases | ||
+ | * ON: 128093 cases | ||
+ | * QC: 151510 cases | ||
+ | |||
+ | If we take these numbers and scale them to take account of each provinces' | ||
+ | * BC: 308 cases / million | ||
+ | * AB: 489 cases / million | ||
+ | * ON: 609 cases / million | ||
+ | * QC: 1857 cases / million | ||
+ | |||
+ | It would be tempting to stop there, but the problem is that not every province is testing the same. This means that some provinces might have a more realistic view of the infection rate than others. | ||
+ | |||
+ | ==== Death Rate ==== | ||
+ | The first clue to this is to look at the number of deaths per hundred cases: | ||
+ | |||
+ | * AB: 2.3 deaths per 100 reported cases. | ||
+ | * QC: 4.0 deaths per 100 reported cases. | ||
+ | * ON: 4.7 deaths per 100 reported cases. | ||
+ | * BC: 4.9 deaths per 100 reported cases. | ||
+ | |||
+ | This time, the ranking is very different as BC went from being first to being last. There are a few different things that could explain this: | ||
+ | * Maybe in Quebec, Ontario, and BC, it's the most vulnerable population that contracted the virus, leading to more deaths. | ||
+ | * Maybe Alberta has unusually successful treatments for people infected. | ||
+ | * Maybe different provinces are not reporting their infected cases in the same way. | ||
+ | |||
+ | We would expect some variation, of course, but for BC to be #1 when it comes to having the fewer number of cases, and then the worst when it comes to the number of deaths / reported cases suggests that we are under-reporting. | ||
+ | |||
+ | ==== Number of Tests ==== | ||
+ | After over a month of looking at these numbers, we finally got access to the number of tests being performed. | ||
+ | |||
+ | * AB 19375 tests / million | ||
+ | * QC 17745 tests / million | ||
+ | * BC 11580 tests / million | ||
+ | * ON 8707 tests / million | ||
+ | |||
+ | Unsurprisingly, | ||
+ | |||
+ | Per capita, Alberta has tested 1.7 times more than we have so far. | ||
+ | |||
+ | |||
+ | ==== Positive Result Rate ==== | ||
+ | Another number that is very interesting to look at is the number of positive cases per 100 tests performed. | ||
+ | * A low number could mean that we are testing uninfected people | ||
+ | * A high number could mean that we are testing people that are more obviously infected. | ||
+ | |||
+ | At any rate, There's a clear divide between the west and the east here and I'm not sure what to make of it. | ||
+ | * AB: 2.5% | ||
+ | * BC: 2.7% | ||
+ | * ON: 7.0% | ||
+ | * QC: 10.5% | ||
+ | |||
+ | ==== Conclusion ==== | ||
+ | One of the main conclusions from this is that, as suspected, BC is behind |
blog/2020-03-22/covid-19_spread_part_ii.1584898105.txt.gz · Last modified: 2020/03/22 10:28 by va7fi