The above is an Excel spreadsheet of about 18MB. I just did an extension of what wilson did and plotted the graphs. Now
we can get almost exactly what the Earn articles have in terms of figures.
After you open the file, you can mess around with the numbers in the constants box on the upper left corner.
Try messing around with alpha (amplitude of seasonal variation). I set it to 0.045 now, which gets a graph kindda like
figure 2 in the Earn article (Measles in NY City before vaccination from 1930-1960). If you get alpha to 0 (no seasonal variation,
meaning the thing is just a damped oscillator (damped because people are assumed to have immunity after getting the measles)),
then you get exactly the graph in figure 3 of Earn's article.
Also try to mess around with 1/gamma (mean infectious period). It always has to be something divided by 365 (see Wilson's
note in his email). Right now it's get to be 5/365 (5 days, or 0.0137 years). Setting the period longer but fewer gives
longer epidemics; setting the period shorter gives shorter but more outbreaks.
The constants in red are most interesting in my opinion, then comes the constants in blue. The constants in green adjusts
initial conditions. The constants in black depends on some other constant, so don't mess with those.
I also plotted I vs S graph. It also has some very interesting changes if you change the alpha. I suggest trying 0, 0.045,
and 1.
