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--- blog:2020-03-16:covid-19_spread [2020/03/20 07:36] – va7fi
+++ blog:2020-03-16:covid-19_spread [2020/10/13 17:48] (current) – va7fi
@@ Line 1: / Line 1: @@
-====== COVID-19 Spread ======
+====== COVID-19 Spread (Part I)======
 <WRAP center round important 90%>
@@ Line 6: / Line 6: @@
 </WRAP>
-One of the key messages from today's PM announcement is that things will get worse before they get better.  I wanted to have a sense of the rate at which COVID-19 is spreading in Canada, so I made a graph, and did some math.((If you like this sort of thing, I did something similar [[http://ptruchon.pagekite.me/wiki/blog/20111127co2_levels_a_depressing_story |in 2011]] about the atmospheric CO<sub>2</sub> levels, and then updated the data [[http://ptruchon.pagekite.me/wiki/blog/20180806co2levels |seven years]] later to see how my model stacked up.  It might be time for a new update soon...))
+One of the key messages from today's PM announcement is that things will get worse before they get better.  I wanted to have a sense of the rate at which COVID-19 is spreading in Canada, so I made a graph, and did some math.((If you like this sort of thing, I did something similar [[https://ptruchon.pagekite.me/wiki/blog/20111127co2_levels_a_depressing_story |in 2011]] about the atmospheric CO<sub>2</sub> levels, and then updated the data [[http://ptruchon.pagekite.me/wiki/blog/20180806co2levels |seven years]] later to see how my model stacked up.  It might be time for a new update soon...))
@@ Line 17: / Line 17: @@
 |2020-03-04|  33^ |2020-03-11|  117^ |2020-03-18|  727<sup>†</sup>|
 |2020-03-05|  37^ |2020-03-12|  157^ |2020-03-19|  873<sup>†</sup>|
-|2020-03-06|  48^ |2020-03-13|  201^ |2020-03-20|  |
+|2020-03-06|  48^ |2020-03-13|  201^ |2020-03-20|  1087<sup>†</sup>|
-|2020-03-07|  60^ |2020-03-14|  254^ |2020-03-21|  |
+|2020-03-07|  60^ |2020-03-14|  254^ |2020-03-21|  1331<sup>†</sup>|
 {{:blog:2020-03-16:covid19.png}}
@@ Line 32: / Line 32: @@
 <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 = 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)
+  * \$N = 93.1 \times 2^{(\frac{t}{2.7})}\$ for the blue line (where //t// is the number of days since March 10)
 </hidden>
 \\
-**If** the blue exponential pattern continues:
+//If// the blue exponential pattern continues:
   * We should have close to 1600 cases by the end of Saturday (from 342 on Sunday)
   * A week after that: over 9000 cases
@@ Line 43: / Line 43: @@
 {{:blog:2020-03-16:covid19b.png}}
-So there's a very real sense in which, if we don't do anything different, we could simply be about 15 days behind Italy...
+So there's a very real sense in which, //if we don't do anything different//, we could simply be about 15 days behind Italy...
 But doing the right things can change that future.  In reality, the spread of the infection follows more of a [[wp>Logistic_function |Logistic Function]].  At the beginning, it looks like an exponential, but then it flattens out.  This is what the news keeps referring to when they say that social distancing and proper hand washing can help "flattening the curve" more quickly.
 {{ :blog:2020-03-16:480px-logistic-curve.svg.png }}
-The real question is how soon will we reach that middle point, and at what height.
+The real question is how soon we will reach that middle point, and at what height.
 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.
@@ Line 64: / Line 64: @@
 {{ :blog:2020-03-16:sig-gif.gif |}}
-===== More on the Logistics Function =====
+===== More on the Logistic Function =====
 This is an update from March 19th.
-Here, I want to illustrate that even though the infection follows a Logistic Function, that fact alone doesn't help us predict the future in any way.  Here are two very different examples that fit the current data pretty well:
+This section illustrates how eventhough the infection follows a Logistic Function, that fact alone doesn't necessarily help us predict the future. For example, here are two very different models that fit the current data pretty well:
 {{:blog:2020-03-16:covid19c.png}}
-The equation "Model 3" is:
+The equation for "Model 3" is:
+<WRAP centeralign>
+\$$N = \frac{2000}{1 + e^{-0.32(t - 21.1)}}\$$
+</WRAP>
-$$N = \frac{2000}{1 + e^{-0.32(t - 17.6)}}$$
+It reaches its halfway point around March 21 and peaks at 2000 people infected.  Unfortunately, "Model 4" also fits the data just as well:
-It reaches its halfway point around March 18 and peaks at 2000 people infected.  Unfortunately, "Model 4" fits the data just as well:
 {{:blog:2020-03-16:covid19d.png}}
 Its equation is:
+<WRAP centeralign>
+\$$N = \frac{20000}{1 + e^{-0.24(t - 32)}}\$$
+</WRAP>
-$$N = \frac{20000}{1 + e^{-0.25(t - 29)}}$$
+But it reaches its halfway point at on April 1st and peaks at 20,000 people.
-It reaches its halfway point at the end of the month and peaks at 20,000 people.
+Reality could be anywhere in between, or even higher -- I could have easily created a curve that fits the current data just as well and peaks at 2 million people.  The point is that we just don't know because it all depends on how we act now.
-Reality could be anywhere in between, lower, or even higher.  I could have created a curve that fits the data just as well and peaks at  2 million people.  The point is that right now, we just don't know.  But more importantly, which of these we end up on depends on what we do.
+===== Part II =====
+This page is no longer being updated.  Have a look at [[blog/2020-03-22/covid-19_spread_part_ii |Part II for more updates]].