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**Conflicting objectives in chemotherapy with drug resistance.**
*(English)*
Zbl 0878.92012

Summary: A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. Spontaneously acquired drug resistance is accounted for, as well as the evolution in time of normal cells. In addition, optimization of conflicting objectives forms the aim of the chemotherapeutic treatment. For general cell growth, some results are given, whereas for the special case of Malthusian (exponential) growth of tumor cells and rather general growth rate for normal cells, the optimal strategy is worked out. The latter, from the clinical standpoint, corresponds to maximum drug concentration throughout the treatment.

### MSC:

92C50 | Medical applications (general) |

93C95 | Application models in control theory |

93C15 | Control/observation systems governed by ordinary differential equations |

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\textit{M. I. S. Costa} and \textit{J. L. Boldrini}, Bull. Math. Biol. 59, No. 4, 707--724 (1997; Zbl 0878.92012)

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### References:

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