Mathematical Biosciences and Engineering, 2013, 10(1): 221-234. doi: 10.3934/mbe.2013.10.221

Primary: 92B05; Secondary: 37N25.

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Mathematical analysis and simulations involving chemotherapy and surgeryon large human tumours under a suitable cell-kill functional response

1. Universidade de São Paulo, Depto de Matemática Aplicada e Estatística, ICMC, USP, 13560-970, São Carlos
2. Universidade Estadual Paulista, Depto de Bioestatística, IBB, UNESP, 18618-970, Botucatu

Dosage and frequency of treatment schedulesare important for successful chemotherapy.However, in this work we argue that cell-kill response and tumoralgrowth should not be seen as separate and therefore are essential in a mathematical cancer model.This paper presents a mathematical model for sequencing of cancer chemotherapy andsurgery. Our purpose is to investigate treatments for large human tumoursconsidering a suitable cell-kill dynamics. Weuse some biological and pharmacological data in a numerical approach,where drug administration occurs in cycles (periodic infusion)and surgery is performed instantaneously. Moreover, we alsopresent an analysis of stabilityfor a chemotherapeutic model with continuous drug administration.According to Norton & Simon [22], our results indicate that chemotherapy is lessefficient in treating tumours that have reached a plateau level of growingand that a combination with surgical treatment can provide better outcomes.
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