## Mathematics & Science
Learning Center |
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## Applications of Systems of Differential Equations## Epidemiology: The Spread of Disease
## Making the Problem "Computer Friendly"We're working with the system:
However, in it's current form, the problem doesn't lend itself to computer
solution since it contains the unknown constants An additional difficulty for us is the fact that we're working with three
differential equations instead of just two. While there is nothing theoretically
wrong with three, (or even fifty-three,) equation systems, graphing becomes more
difficult since we would have to deal with Notice that the first two equations are Implementing these changes, we arrive at the following system:
which is a little reminiscent of the predator-prey system we worked with
earlier. In fact, what you will be doing for the rest of this laboratory is
mimicking the steps you took in the Predator-Prey
Laboratory in order to create plots of ## Creating Susceptibles vs. Time and Infecteds vs. Time GraphsIn order to start we need some specific initial conditions. Let's say that at the beginning of our experiment there are 600 susceptible people, and 50 infected people, or symbolically: *S*(0) = 600*I*(0) = 50
If we put these into our initial value problem, it becomes:
which is in just the right form to feed into
(Notice that we're capturing the solution to the system into the variable
t ≤ 30
for the plot. Also, I've used lower case i instead of
I, since I is a reserved Mathematica
constant.)Now jump into You can switch to Mathematica by clicking on the button at left. This will
open up a fresh notebook for you. Remember that it will take it a while to start
up! Don't forget to come back here when you're done! See you in a few
minutes.Now let's go see what you should have gotten... |
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ODE Laboratories: A Sabbatical Project by Christopher A. Barker©2017 San Joaquin Delta College, 5151 Pacific Ave., Stockton, CA 95207, USA e-mail: cbarker@deltacollege.edu |