Why Is Evolution Important in Cancer and What Mathematics Should Be Used to Treat Cancer? Focus on Drug Resistance

The clinical question of drug resistance in cancer, our initial motivation to study continuous models of adaptive cell population dynamics, leads naturally and more generally to consider the cancer disease itself from an evolutionary biology viewpoint, a consideration without which even the best targeted therapies will likely most often eventually fail. Among the challenging questions to mathematicians who tackle the task of understanding this disease and optimising its treatment are the representation of phenotypic heterogeneity of cancer cell populations and of their plasticity in response to anticancer drug insults. Such representation can be obtained using phenotype-structured models of healthy and cancer cell populations, and optimal control methods to optimise drug effects, with the perspective to implement them in the therapeutics of cancer, aiming at both avoiding the emergence of drug resistance in tumours and taking into account a constraint of limiting unwanted adverse effects to healthy tissues.