Bifurcation Analysis for Cancer Resistance Containing Persister Cells: Exploring the Potential Mechanisms of Cancer Recurrence

Drug-tolerant persister cells, which are a subpopulation in a transient pseudo-dormant state following cancer therapy, play a crucial role in disease recurrence. This paper primarily focuses on the bifurcations of a model that describes the relationships among sensitive cells, persister cells, and resistant cells in cancer, such as Hopf bifurcation, Bautin bifurcation, and Bogdanov–Takens bifurcations of codimension-2 and codimension-3. The transformation rates among these three types of cells are regarded as the bifurcation parameters. The research discovers that the dynamics on the center manifold are locally topologically equivalent to specific models, and the local representations of the bifurcation curves are presented. Numerical simulations also confirm the theoretical results. This study offers insights into the influence of transformation rates on cancer therapy and treatment strategies for different bifurcations. Additionally, different types of bistable states are revealed, specifically the bistable states of two equilibria or one limit cycle and one equilibrium, along with different paths to bistability. This paper may offer new perspectives on the role of persister cells in cancer recurrence and provide a scientific basis for cancer treatment and prevention strategies.