Measles pathogenesis curve by function #f# (see details for questions)?

This question is relevant to Area Between Curves.

I don't know what that constitutes under Socratic guidelines, so it is mentioned here.

A patient infected with the measles virus who has some immunity to the virus has a pathogenesis curve that can be modeled by, for instance, #g(t)=0.9f(t).#

  1. If the threshold concentration of the virus required for infectiousness to begin is #"1210 cells/mL"#, on what day does this occur?
  2. Let #P_3# be the point on the graph of #g# where infectiousness begins. It has been shown that infectiousness ends at a point #P_4# on the graph of #g# where the line through #P_3#, #P_4# has the slope #-23#. On what day does infectiousness end?
  3. Compute the level of infectiousness for this patient.

1 Answer
Gió
Mar 27, 2017

Hi...this is only an attempt, completely without any (probable) connection with your question....because I didn't know the function #f(t)# so I tried with something I found on the internet!!!

Explanation:

I found on the internet this:
http://www.ms.uky.edu/~ma138/oldexams/Answer_Key_Ex1_S13.pdf
enter image source here
Where #f(t)#is measured in number of infected cells per mL of blood plasma.
In your case should be:

#g(t)=0.9[-t(t-21)(t+1)]#

I tried to plot this function:
enter image source here

Solving for #g(t)=1210# I got three solutions:
#t_1=11# days
#t_2=-7# days
#t_3=16# days
I think it should be #t_1=11# days that should be the answer to question 1).

To answer question 2) we need a line passing through the above initial point:
#(11, 1210)# and slope #m-23#.
We can use the general relationship from maths:
#y-y_0=m(x-x_0)#
where for us:
#g(t)-1210=-23(t-11)#
#g(t)=-23t+1463#

we can use this line to find the intercepts with:
#g(t)=0.9[-t(t-21)(t+1)]# and get, substituting:
#-23t+1463=0.9[-t(t-21)(t+1)]#
with again three solutions:
#t_1=11# days
#t_2=-8# days
#t_3=17# days
I would choose #t_3=17# days as answer for the end of infectiousness.

for question 3) I do not have any idea at all....sorry!

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