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--- blog:2020-03-16:covid-19_spread [2020/03/22 09:23] – va7fi
+++ blog:2020-03-16:covid-19_spread [2020/10/13 17:48] (current) – va7fi
@@ 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 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>
 \\
@@ Line 47: / Line 47: @@
 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 74: / Line 74: @@
 The equation for "Model 3" is:
 <WRAP centeralign>
-$$N = \frac{2000}{1 + e^{-0.32(t - 21.1)}}$$
+\$$N = \frac{2000}{1 + e^{-0.32(t - 21.1)}}\$$
 </WRAP>
@@ Line 83: / Line 83: @@
 Its equation is:
 <WRAP centeralign>
-$$N = \frac{20000}{1 + e^{-0.24(t - 32)}}$$
+\$$N = \frac{20000}{1 + e^{-0.24(t - 32)}}\$$
 </WRAP>
@@ Line 89: / Line 89: @@
 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.
+===== 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]].