ANALYSIS OF A NEW MODEL FOR TUMOR-IMMUNE SYSTEM COMPETITION INCLUDING LONG-TIME SCALE EFFECTS

Abstract

This paper deals with the competition between the immune system and an agressive host such as tumor. We are particularly interested in the asymptotic behavior of the system when the time goes to infinity: we prove that this competition will absolutely finish either by the suppression of the harmful substances or by the inhibition of the immune system. The model which we introduce is suitable to describe the disease evolution for a long time scale, because it takes the capacity of the body to repair cells damage into account: body cells produce new cells to replace dead ones. We also examine the evolution of the solutions if we assume that the immune system has a normal healthy state that it always tries to reach.