Understanding the Virus with Math
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Started by joj - March 11, 2020, 8:29 a.m.

I've enjoyed all the extra time in my day avoiding posting here.  But I'm making an exception in the name of public service.  It's all about the inflection point.  Not there yet.  Wash your hands.  

https://www.youtube.com/watch?v=Kas0tIxDvrg&fbclid=IwAR05H0FekY6FvAf-I9T0f6ExcG__-ORvgGzVupmhXFBD4mlbX3soYNU1THw&app=desktop

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By metmike - March 11, 2020, 11:56 a.m.
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Very Welcome back joj!

Wonderful video and post. Thanks for sharing it!

Our minds are thinking the exact same thing here.


Early last month I described this in seeing signs of China topping out......which was confirmed by the additional data for the rest of February. 



https://www.marketforum.com/forum/topic/47120/


                Re: Corona  Virus            

            

                         68 responses |                

                By metmike - Feb. 8, 2020, 1:37 p.m.            

            

                                                        

Despite being bombarded with scary Coronavirus news daily, let's use some  unemotional math(calculus) to show you that the new cases and deaths may be DEcelerating and the rate of  spread is being contained/is slowing. 


First, the math lesson for those that like calculus:

Inflection point

https://en.wikipedia.org/wiki/Inflection_point

 For a curve given by parametric equations, a point is an inflection point if its signed curvature changes from plus to minus or from minus to plus, i.e., changes sign.

For a twice differentiable function, an inflection point is a point on the graph at which the second derivative has an isolated zero and changes sign.

 

Plot of f(x) = sin(2x) from −π/4 to 5π/4; the second derivative is f″(x) = –4sin(2x), and its sign is thus the opposite of the sign of f. Tangent is blue where the curve is convex (above its own tangent), green where concave (below its tangent), and red at inflection points: 0, π/2 and π


You may connect better to this explanation.

Inflection Points 

https://www.mathsisfun.com/calculus/inflection-points.html

An Inflection Point is where a curve changes from  Concave upward to Concave downward (or vice versa)

So what is  concave upward / downward ?

Concave upward is when the slope increases: concave upward slope increases
Concave downward is when the slope decreases: concave downward slope decreases



Now the Corona Virus graph

This is updated every day after the Feb. 8 date of this particular post, so comments on Feb 8, are relevant only  to the graph at that point-additional comments are added below with the fresh updates:

https://en.wikipedia.org/wiki/2019%E2%80%9320_Wuhan_coronavirus_outbreak

 

Semi-log plot of daily new confirmed cases and deaths in China.[112]


You will note on the graph above that the slope is DECREASING(rate of increase is slowing down) for daily NEW cases reported and also of daily new deaths.

The flattening out of the slope is a feature of being concave downward(in calculus). If we were to assume that these numbers are accurate and will continue on that path, the concave downward projection is on its way to new daily cases actually going down consistently. 

Going from the initial, extremely steep slope of increasing reports............and unreliable information that maintained for around the first 12 points on the graph  out of 23 points.

The last  11 black dot points on the graph are clearly rising at a much slower rate. 


ps: I should note that the plot of cases and deaths is on a semi-logarithic graph, which is needed because the changes/data going from small to much larger numbers. Using linear values for both axis(y is vertical) would have required massive height to the graph(Y axis) to be more useful or else the lower numbers to the left would not have shown up well.

https://en.wikipedia.org/wiki/Semi-log_plot

In science and engineering, a semi-logarithmic or semi-log graph or plot has one axis on a logarithmic scale, the other on a linear scale. It is useful for data with exponential relationships, or where one variables covers a large range of values

By joj - March 11, 2020, 1:55 p.m.
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I don't trust anything coming from China.  I'm interested in data from S. Korea and Italy.

By metmike - March 11, 2020, 2:51 p.m.
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Regardless of it coming from China(I wouldn't trust them either), as you pointed out the math for predicting using the inflection point is solid and even if China is not being 100% accurate, things have clearly improved in a massive way...........and signs of that first showed up a month ago on the graph...........when the news was still getting much worse in China.


So the inflection point will happen, likely BEFORE the worst news peaks.

It's the point where the bad news is still getting worse but the rate of it getting worse is slowing down. 

It will not be a smooth curve in most cases and a no brainer to track because we could have more than 1 peak and more than 1 inflection point.


By TimNew - March 12, 2020, 3:09 a.m.
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Good Stuff JOJ.  And good to see you.


We need to be concerned.   We should not be (as we are) panicked.  At least not yet...

By metmike - March 12, 2020, 3:26 a.m.
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Yep!

By metmike - March 14, 2020, 7:37 p.m.
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Get all the Coronavirus threads here:


                Crazy Coronavirus Compilation            

            

                Started by metmike - March 13, 2020, 12:13 p.m.            

https://www.marketforum.com/forum/topic/48881/