A Multi-Compartment Tumor–Immune Model Under Uncertain Differential Dynamics and Therapeutic Forcing

A four-compartment tumor–immune interaction model is studied in a belief-based uncertain framework. The deterministic dynamics for tumor cells, natural killer cells, dendritic cells, and cytotoxic CD8+ T lymphocytes are extended to an uncertain differential system driven by a canonical Liu process, with therapeutic effects represented through treatment-related parameters acting on the respective populations. The analysis establishes well-posedness in the biologically relevant positive orthant under structural conditions compatible with the model nonlinearities, and it characterizes stability properties in the sense appropriate to uncertain dynamical systems. Sufficient conditions are derived for the existence of a global attracting set describing the long-time behavior of trajectories. The analytical results are complemented by numerical experiments based on α-path dynamics to illustrate uncertainty-aware therapeutic scenarios and to connect the qualitative theory with observable system behavior.