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Inducing catastrophe in malignant growth.

Mathematical catastrophe theory is used to describe cancer growth during any time-dependent program a(t) of therapeutic activity. The program may be actively imposed, e.g. as chemotherapy, or occur passively as an immune response. With constant therapy a(t), the theory predicts that cancer mass p(t) grows in time t as a cosine-modulated power law, with power = 1.618..., the Fibonacci constant. The cosine modulation predicts the familiar relapses and remissions of cancer growth. These fairly well agree with clinical data on breast cancer recurrences following mastectomy. Two such studies of 3183 Italian women consistently show an immune system's average activity level of about a = 2.8596 for the women. Fortunately, an optimum time-varying therapy program a(t) is found that effects a gradual approach to full remission over time, i.e. to a chronic disease. Both activity a(t) and cancer mass p(t) monotonically decrease with time, the activity a(t) as 1/(ln t) and mass remission as t--94{-0.382}. These predicted growth effects have a biological basis in the known presence of multiple alleles during cancer growth.