### Mathematical Biosciences and Engineering

2011, Issue 2: 289-306. doi: 10.3934/mbe.2011.8.289

# Mathematical modeling of cyclic treatments of chronic myeloid leukemia

• Received: 01 April 2010 Accepted: 29 June 2018 Published: 01 April 2011
• MSC : Primary: 92C50; Secondary: 92D25, 60G35.

• Cyclic treatment strategies in Chronic Myeloid Leukemia (CML) are characterized by alternating applications of two (or more) different drugs, given one at a time. One of the main causes for treatment failure in CML is the generation of drug resistance by mutations of cancerous cells. We use mathematical methods to develop general guidelines on optimal cyclic treatment scheduling, with the aim of minimizing the resistance generation. We define a condition on the drugs' potencies which allows for a relatively successful application of cyclic therapies. We find that the best strategy is to start with the stronger drug, but use longer cycle durations for the weaker drug. We further investigate the situation where a degree of cross-resistance is present, such that certain mutations cause cells to become resistant to both drugs simultaneously.

Citation: Natalia L. Komarova. Mathematical modeling of cyclic treatments of chronic myeloid leukemia[J]. Mathematical Biosciences and Engineering, 2011, 8(2): 289-306. doi: 10.3934/mbe.2011.8.289

### Related Papers:

• Cyclic treatment strategies in Chronic Myeloid Leukemia (CML) are characterized by alternating applications of two (or more) different drugs, given one at a time. One of the main causes for treatment failure in CML is the generation of drug resistance by mutations of cancerous cells. We use mathematical methods to develop general guidelines on optimal cyclic treatment scheduling, with the aim of minimizing the resistance generation. We define a condition on the drugs' potencies which allows for a relatively successful application of cyclic therapies. We find that the best strategy is to start with the stronger drug, but use longer cycle durations for the weaker drug. We further investigate the situation where a degree of cross-resistance is present, such that certain mutations cause cells to become resistant to both drugs simultaneously.

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