During the last decades, various chemotherapeutic drugs have been developed to treat cancer, which makes the chemotherapy design more complicated. To determine optimal drug regimens for patients with colorectal cancer, this study extends two multi-drug cell-cycle specific tumor growth models with distinct action mechanisms. To this end, two of the most commonly used drugs in treating colorectal cancer, namely 5-FU and CPT-11, are assumed. In the extended compartmental models, drug resistance and toxicity are taken into account, and two constraints are imposed to limit the drug dosages during the therapy. Two different drug administration strategies are proposed. In the first strategy, drugs are injected sequentially, while in the second, drugs are simultaneously administered. To minimize the tumor size at the end of therapy or equivalently to prolong the patient’s survival time, an optimal control problem is defined and solved using the genetic algorithm (GA). The in silico results for a variety of scenarios based on the patient’s health conditions demonstrate that the simultaneous approach outperforms the sequential strategy and yields superior results. To verify the resultant findings, a robust evaluation with uncertain model parameters is also performed, which again shows the superiority of the simultaneous strategy.
