Despite great advances in modeling and cancer therapy using optimal control theory, tumor heterogeneity and drug resistance are major obstacles in cancer treatments. Since recent biological studies demonstrated the evidence of tumor heterogeneity and assessed potential biological and clinical implications, tumor heterogeneity should be taken into account in the optimal control problem to improve treatment strategies. Here, first we study the effects of two different treatment strategies (i.e., symmetric and asymmetric) in a minimal two-population model to examine the long-term effects of these treatment methods on the system. Second, by considering tumor adaptation to treatment as a factor of the cost function, the optimal treatment strategy is derived. Numerical examples show that optimal treatment decreases tumor burden for the long-term by decreasing rate of tumor adaptation over time.
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