Adaptive cancer treatment as an eco-evolutionary leader-follower game

Cancer consists of heterogeneous cell populations that repeatedly undergo natural selection. These cell populations contest with each other for space and nutrients and try to generate phenotypes that maximize their ecological fitness. For achieving this, they evolve evolutionarily stable strategies. When an oncologist starts to treat cancer, another game emerges. While affected by the cellular evolution processes, modeling of this game owes to the results of the classical game theory. This thesis investigates the theoretical foundations of adaptive cancer treatment. It draws from two game theoretical approaches, evolutionary game theory and Stackelberg leader-follower game. The underlying hypothesis of adaptive regimen is that the patient's cancer burden can be administered by leveraging the resource competition between treatment-sensitive and treatment-resistant cells. The intercellular competition is mathematically modelled as an evolutionary game using the G function approach. The properties of the evolutionary stability, such as ESS, the ESS maximum principle, and convergence stability, that are relevant to tumorigenesis and intra-tumoral dynamics, are elaborated. To mitigate the patient's cancer burden, it is necessary to find an optimal modulation and frequency of treatment doses. The Stackelberg leader-follower game, adopted from the economic studies of duopoly, provides a promising framework to model the interplay between a rationally playing oncologist as a leader and the evolutionary evolving tumor as a follower. The two game types applied simultaneously to cancer therapy strategisizing can nourish each other and improve the planning of adaptive regimen. Hence, the characteristics of the Stackelberg game are mathematically studied and a preliminary dose-optimization function is presented. The applicability of the combination of the two games in the planning of cancer therapy strategies is tested with a theoretical case. The results are critically discussed from three perspectives: the biological veracity of the eco-evolutionary model, the applicability of the Stackelberg game, and the clinical relevance of the combination. The current limitations of the model are considered to invite further research on the subject