Persister cells and their effects on cancer stabilization therapy

Some cancers have the ability to persist under treatment. Persister cancer cells can be a small subpopulation of cancer cells that enter a dormant or quiescent state, thereby evading the effects of chemotherapy, targeted therapy, or immunotherapy. Motivated by these observations, we develop and investigate an evolutionary game theory model that captures the interactions between three types of cancer cells: treatment-sensitive, drug-tolerant persister, and treatment-resistant cells. In our model, persister cells transition into resistant cells at a rate that can depend on the treatment intensity. We analyze the model's equilibria and derive conditions for their existence and stability. In particular, we show that an equilibrium in which sensitive and resistant cells coexist is stable when intra-type competition is stronger than inter-type competition. We also show that equilibria in which only one cell type persists require the transition rate to exceed an explicit threshold determined by the treatment dose and competition parameters. Our findings reveal that persister cells can both stabilize and destabilize tumor dynamics, depending on treatment and cell type-transition rates, highlighting the importance of accounting for persister behavior in designing effective evolutionary therapies.