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Evolution of cancer cell populations under cytotoxic therapy and treatment optimisation: insight from a phenotype-structured model. (English) Zbl 1442.35193

Summary: We consider a phenotype-structured model of evolutionary dynamics in a population of cancer cells exposed to the action of a cytotoxic drug. The model consists of a nonlocal parabolic equation governing the evolution of the cell population density function. We develop a novel method for constructing exact solutions to the model equation, which allows for a systematic investigation of the way in which the size and the phenotypic composition of the cell population change in response to variations of the drug dose and other evolutionary parameters. Moreover, we address numerical optimal control for a calibrated version of the model based on biological data from the existing literature, in order to identify the drug delivery schedule that makes it possible to minimise either the population size at the end of the treatment or the average population size during the course of treatment. The results obtained challenge the notion that traditional high-dose therapy represents a “one-fits-all solution” in anticancer therapy by showing that the continuous administration of a relatively low dose of the cytotoxic drug performs more closely to i.e. the optimal dosing regimen to minimise the average size of the cancer cell population during the course of treatment.

MSC:

35K55 Nonlinear parabolic equations
92C50 Medical applications (general)
35B09 Positive solutions to PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
49J20 Existence theories for optimal control problems involving partial differential equations
49K20 Optimality conditions for problems involving partial differential equations
49N90 Applications of optimal control and differential games
92D25 Population dynamics (general)
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