We consider once again the specific rate equations
discussed in the text on pages 
- . We saw that at time t = 1,
S', I', and R' when t
= 1, and then use these values to determine S, I, and R one day
later .
S, I, and R when t = 2.
Using these values, calculate the rates S', I', and R' and then
determine the new values of S, I, and R when t = 3. See the
table on page .
t = 0
and to the initial values
Recalculate the values of S, I, and R at time t = 2 by using a
time step of 
. You should perform only a single round of
calculations, and use the rates S', I', and R' that are current at
time t = 0.
t = 0 and then back again. There are two ways to do this:
with a time step of 
(as in the previous question),
and with a pair of time steps of 
.
). Using the values of S, I, and R at
time t = 2 that you just got in the previous question, calculate the
rates S', I', and R'. Then using a time step of 
,
estimate new values of S, I, and R at time t = 0. How much do
these new values differ from the original values 45,400, 2100, 2500?
). Now make a new start, using the values
that occur when t = 2 if we make estimates with a time step 
. (These values come from the table on page )
Using two rounds of calculations with a time step of 
,
estimate another set of new values for S, I, and R at time t =
0. How much do these new values differ from the original values
45,400, 2100, 2500?
, or two rounds of
calculations with ? Consequently, which process
produces better estimates--in the sense in which we used to measure
estimates on page ?
S. Changing the transmission coefficient, as in part (a),
changes the threshold level for S. What is the new threshold?
S = 45,400. Does quarantine eliminate the
epidemic, in the sense that the number of infected immediately goes down
from 2100, without ever showing an increase in the number of cases?
I never goes up, can you find a smaller value that
does guarantee I never goes up? Continue to assume we start with
S = 45400.
I never goes up? What level of quarantine does
this represent? That is, do you have to reduce the chance that a
susceptible will fall ill to one-third of what it was with no quarantine
at all, to one-fourth, or what?