| Abstract: |
| First, we formulate a mathematical model for tumor growth based on clinical observations of melanoma progression, and then we study how the tumor can be managed by a single drug agent, an inhibitor of a particular mutated pathway. In the model, a state of each cell is described by activities of two distinctive genetic programs. The main program affected by a drug conforms a higher proliferative ability to a cell, whereas the alternative program leads to slower division rate, but protects a cell from the action of a drug. Activation of either program and transition between them are of stochastic nature. Our main result is in finding an optimal control strategy that minimizes a tumor size at the end of a given treatment period. The obtained optimal pattern contains a singularity, where a drug is applied at intermediate dosage. In our work we describe the methodology on how to construct such optimal strategy by using the method of singular characteristics. |
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