A single infected individual enters a community of n susceptible individuals. Let x be the number of
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A single infected individual enters a community of n susceptible individuals. Let x be the number of newly infected individuals at time t. The common epidemic model assumes that the disease spreads at a rate proportional to the product of the total number infected and the number not yet infected. So, dx/dt = k(x + 1)(n - x) and you obtain
Solve for as a function of t.
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