We analyze the sequence in which the three most commonly prescribed cancer treatments -surgery (S), chemotherapy (C) and radiotherapy (R) -should be administered. A system of ordinary differential equations is formulated that captures the various local and systemic effects of the three modes of treatment, as well as the first-order effects of the interrelationship between the primary tumor and the distant metastatic tumors, including primary tumor shedding and the primary tumor's effect on the rate of angiogenesis in the metastatic tumors.Under a set of stated assumptions on the parameter values, we find the exact cancer cure probability (subject to toxicity constraints) for the six permutation schedules (i.e., SCR, CSR, CRS, SRC, RSC, RCS) and for two novel schedules, SRCR and RSCR, that apply radiotherapy in disjoint, optimally-timed portions. We show analytically that SRCR and RSCR are the two best-performing (i.e., highest cure probability) schedules among the eight considered. Further, SRCR is shown to be optimal among all possible schedules, provided a modest condition is satisfied on the delay of initial angiogenesis experienced by the patient's dormant tumors.

Ve present results from a mathematical analysis that is aimed at finding the best way to sequence the three traditional cancer treatments: surgery (S), chemotherapy (C) and radiotherapy (R). The mathematical model tracks the temporal evolution of the primary tumor and its associated metastases, and incorporates the primary tumor's effect on the dormancy and growth of the metastases. We show that the SCR schedule (i.e., surgery followed by chemotherapy followed by radiotherapy) achieves a higher cure probability than SRC if the primary tumor is sufficiently large or if the metastatic population is sufficiently large relative to the primary tumor. We also show that a novel schedule, SRCR, which splits the radiotherapy regimen into two disjoint portions, is optimal among all schedules, provided that the patient's dormant metastatic tumors do not become vascularized within about 40 days after surgery.

We analyze the sequence in which the three most commonly prescribed cancer treatments -surgery (S), chemotherapy (C) and radiotherapy (R) -should be administered. A system of ordinary differential equations is formulated that captures the various local and systemic effects of the three modes of treatment, as well as the first-order effects of the interrelationship between the primary tumor and the distant metastatic tumors, including primary tumor shedding and the primary tumor's effect on the rate of angiogenesis in the metastatic tumors.Under a set of stated assumptions on the parameter values, we find the exact cancer cure probability (subject to toxicity constraints) for the six permutation schedules (i.e., SCR, CSR, CRS, SRC, RSC, RCS) and for two novel schedules, SRCR and RSCR, that apply radiotherapy in disjoint, optimally-timed portions. We show analytically that SRCR and RSCR are the two best-performing (i.e., highest cure probability) schedules among the eight considered. Further, SRCR is shown to be optimal among all possible schedules, provided a modest condition is satisfied on the delay of initial angiogenesis experienced by the patient's dormant tumors.