Well-posedness of a coupled PDE–ODE model of stem cell lineage involving homeostatic regulation

We present existence and uniqueness results for a proposed coupled nonlinear PDE–ODE model representing cancer population dynamics. We establish this global result using Banach fixed point theory. The model describes the evolution of two progenies of stem cell lineage consisting of healthy and mutated cells kept in homeostasis via feedback regulation. We also show continuous dependence of the solution on the initial data, concluding the original model’s well-posedness. Finally, we present numerical simulations of the model for illustration.