Chemotherapeutic treatments: A study of the interplay among drug resistance, toxicity and recuperation from side effects.

*(English)*Zbl 0899.92024Summary: A system of differential equations for the control of tumor growth cells in a cycle nonspecific chemotherapy is analyzed. Spontaneously acquired drug resistance is taken into account, and a criterion for the selection of chemotherapeutic treatment is used. This criterion purports to describe the possibility of improvement of the patient’s health when treatment is discontinued. Contrary to our early results [see the authors and R. C. Bassanezi, Math. Biosci. 125, No. 2, 191-209 (1995; Zbl 0821.92015); ibid. 211-228 (1995; Zbl 0821.92016)] which also take drug resistance into account, in this context strategies of continuous chemotherapy in which rest periods take part may be better than maximum drug concentration throughout the treatment (which appears to be in accordance with clinical practice). This bears out our previous conjecture that when drug resistance is accounted for, the imperfections in the usual modelling of treatment criteria, which in general do not allow for patient recuperation, ruled out the possibility of rest periods in optimal continuous chemotherapy.

##### MSC:

92C50 | Medical applications (general) |

49N70 | Differential games and control |

49N75 | Pursuit and evasion games |

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. 2, 205--232 (1997; Zbl 0899.92024)

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