An epidemic spreads through a population at a rate proportional to the product of the number of people already infected and the number of people susceptible, but not yet infected. Therefore, if S denotes the total population of susceptible people and I = I ( t ) denotes the number of infected people at time t , then I ' = r I ( S − I ) , where r is a positive constant. A) Assuming that I ( 0 ) = I 0 , find I ( t ) for t > 0