Epidemiology Problems - Page 6

Applications of Systems of Differential Equations

Epidemiology: The Spread of Disease

 

 

(continued from last page...)

Exercises for You to Do

OK, you can't claim that I haven't given you enough help! We went through the entire Predator-Prey laboratory doing problems like this, and I've just held your hand through another example in this Epidemiology lab. It's time for you to show a little independence.

Instructions

Repeat the steps that we did in the worked example, namely:

 

  1. Solve the initial value problem:

    System Initial Conditions
    S′ = - 0.001 S I
    I′ = 0.001 S I - 0.3 I    		 S(0) = So
    I(0) = Io

    using NDSolve, assigning the result to the variable disease#, where # represents the number of the problem you are working on.

  2. Create sus# and inf#, variables containing the susceptible and infected components of the previous solution, using the [[1,#,2]] trick.

  3. Make pictures called sus#plot and inf#plot, of the graphs of susceptibles versus time, and the infecteds vs. time, using different colors for each.

  4. Display both sus#plot and inf#plot on the same graph using the Show command.

  5. Make a parametric plot disease#plot, of sus# vs.inf#.

for each of the following five sets of initial conditions:

 

  1. S(0) = 600, I(0) = 100, on the interval 0 ≤ t ≤ 30.
  2. S(0) = 600, I(0) = 150, on the interval 0 ≤ t ≤ 30.
  3. S(0) = 600, I(0) = 200, on the interval 0 ≤ t ≤ 30.
  4. S(0) = 600, I(0) =  1, on the interval 0 ≤ t ≤ 40.
  5. S(0) = 400, I(0) =  1, on the interval 0 ≤ t ≤ 100.

(No, number 1 is not missing—it was the example I worked with you.) Be careful! Not all of the S(0)'s are the same, and not all of the t-intervals are the same.

Go on! You've got a lot of work ahead of you! See you back here in half an hour or so.

Let's go look at the graphs you should have come up with...

Compass If you're lost, impatient, want an overview of this laboratory assignment, or maybe even all three, you can click on the compass button on the left to go to the table of contents for this laboratory assignment.