Suppose that you have a closed system containing 1000individuals. A flu epidemic starts. Let N(t) represent the number of infected individuals in the closed system at time t. Assume that the rate at which the number of infected individuals is changing is jointly proportional to the number of infected individuals and to the number of uninfected individuals. Furthermore, suppose that when100 individuals are infected, the rate at which individuals are becoming infected is 90 individuals per day. If 20 individuals are infected at time t = 0, when will 90% of the population be infected? Hint: The assumption here is that there are only healthy individuals and sick individuals. Furthermore, the resulting model can be solved using the technique introduced in Exercise 22.
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