Stationary patterns and stability in a tumor-immune interaction model with immunotherapy

This paper examines a diffusive tumor-immune system with immunotherapy under homogeneous Neumann boundary conditions. We first investigate the large-time behavior of nonnegative equilibria and then explore the persistence of solutions to the time-dependent system. In particular, we present the sufficient conditions for tumor-free states. We also determine whether nonconstant positive steady-state solutions (i.e., a stationary pattern) exist for this coupled reaction–diffusion system when the parameter of the immunotherapy effect is small. The results indicate that this stationary pattern is driven by diffusion effects. For this study, we employ the comparison principle for parabolic systems and the Leray–Schauder degree.