Assignment given 14 April 2009

This assignment was given on 14 April 2009. The work is due 21 April 2009.

Write a program which can model the evolution of a disease in a hospital in which patients are arranged on an array of beds.

Assume that the beds form an array of M rows and N columns, so that there are a total of M * N patients.

Assume that the patients can be classified as Susceptible, Infected or Recovering, with the properties that

• Susceptible: A patient who has never been infected with the disease. A susceptible patient can get the disease.
• Infected: A patient who has never gotten the disease. A patient stays infected for K days. On the K+1 of the disease, the patient "recovers".
• Recovered: A patient who has had the disease, that is, has caught the disease and been sick for a full K days. A recovered patient never gets sick again.

Set up an M by N array P to represent the patients. P(I,J) contains information on the patient in row I, column J. P(I,J) will be

• 0, if the patient is susceptible.
• a value between 1 and K, if the patient is infected. The value is the number of days the patient has been infected.
• -1, if the patient is recovered.

The rules for transmission of the disease essentially update the patient array once a day. If patient P(I,J) was:

• 0, then check the four neighbors P(I-1,J), P(I+1,J), P(I,J-1) and P(I,J+1). For each neighbor that is infected, pick a random number, and if that random number is less than TAU, then patient P(I,J) becomes infected, that is, we set P(I,J) to 1.
• a value between 1 and K, then the value is increased by 1. But if the value was already K, it is now reset to -1, because the patient has recovered.
• -1, nothing happens.

Let's suppose we start with exactly one infected patient, P(M/2,N/2) whose value is 1. All other patients start at 0.

Using the rules for transmission of the disease, update the patient array one day at a time. (You'll probably need an "old" and a "new" copy of the array, so you keep all the old information until all the updated information has been computed.)

On each day, compute the values of S, I, and R, that is, the total number of susceptible, infected, and recovering patients. Store these values in vectors, so that we can plot them.

The actual number of days to simulate will depend on the problem size and other issues. For now, let's just try using 50 days. You should count the initial condition (all patients are "S" except for 1 "I" and no "R"'s) as day #1.)

Question 1: Using M = 10, N = 10, K = 4 and TAU = 0.2, run your program for 50 days.

Turn in: Make one plot on which you display the values of S, I, and R over this time period.