Diffusive tumor-immune interaction systems under immunotherapy

This paper addresses a diffusive tumor-immune system under immunotherapy. First, we examine the global attractor that indicates the large time behavior of the time-dependent system. The results indicate that extinction of the tumor cells could be eradicated as a result of the treatment effects. Second, we investigate the existence of positive periodic solutions for the time-dependent system by using topological degree theory. Finally, we determine the sufficient and necessary conditions for positive coexistence states. (C) 2011 Elsevier Ltd. All rights reserved.