Analysis of a time-delayed mathematical model for solid avascular tumor growth under the action of external inhibitors

In this paper, a time-delayed mathematical model for tumor growth under the action of external inhibitors is studied. In the model, the delay represents the time taken for cells to undergo mitosis. By an external inhibitor, we mean that the inhibitor is either developed from the immune system of the body, or administered by medical treatment. This is in contrasts with a growth inhibitor secreted by tumor itself. Nonnegativity of solutions is studied. Steady-state analysis is presented with respect to the magnitude of delay. Stability is proved for some parameter values. The analysis of the effect of inhibitor’s parameters on tumor’s growth is presented. The results show that the tumor radius will tend to zero or tend to a stationary version under some conditions. Results are illustrated by computer simulations. © 2015, Korean Society for Computational and Applied Mathematics.