Epidemic. Consider the following model of how an epidemic spreads through a population. First we will introduce some definitions:
N = number of individuals in population
Mk = the number of susceptible after k weeks
Sk = number of infectious after k weeks
Ik = the number of immune after k weeks
d = disease duration in weeks
k = constant, which describes how easily the disease is infecting
Then we can formulate our mathematical model
Mk +1 = Mk - k * Sk * Mk (1)
Sk + 1 = Sk + k * Sk * Mk - Sk/d (2)
Ik + 1 = Ik + Sk/d (3)
Recognize the first model equations in words! Then examine how Mk, Sk and Ik developed week by week until the epidemic is over. You can use the values N = 1000, S0 = 1, k = 0.002 and d = 1.
The Attempt at a Solution
I have tried to combine all three equations into one, and I know that the problem is solved once the number of immunes Ik, equal the total number of individual in the population. Yet, all I get is a constant equation that repeats itself. I assume that N=Mk+Ik+Sk. Can somebody help me out with this tricky problem????