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## Homework Statement

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?