The tumor grows exponentially until a certain detection size, M, is reached, at which point treatment is initiated. The number of point mutations that could in principle confer resistance to monotherapy is n = 50. For dual therapy, the number of point mutations that could confer resistance to drugs 1 and 2 separately is given by n1 = 50 and n2 = 50. The number of point mutations that could confer resistance to both drugs simultaneously is given by n12. The point mutation rate was assumed to be u = 10−9 and the rate of cell division b = 0.14 per day and is unaffected by treatment. The rate of cell death before treatment is d = 0.13 per day; it is increased to d’ for sensitive cells during treatment. (A)–(C) For clinically detectable sizes (M = 1010, 109, 108, depending on the location of the tumors and the detection methods used), monotherapy leads to a temporary shrinkage of the tumor but is always followed by tumor regrowth. (D) Due to stochastic fluctuations the few resistant cells present at the start of treatment go extinct and the lesion is eradicated. (E) Treatment leads to a temporary shrinkage of the tumor followed by regrowth. (F) The tumor decreases slowly in response to dual therapy, but resistant cells eventually evolve and cause treatment failure.