Analysis of a time-delayed free boundary problem for solid tumor growth with angiogenesis and direct influence of inhibitors

Abstract

Abstract In this paper we consider a free boundary problem for tumor growth under direct effect of inhibitors with angiogenesis and time delays in proliferation. The existence and uniqueness of the steady state solution is studied. The asymptotic behavior of steady state solution is proved, and the condition under which the tumor will tend to disappear is given. Finally, we also discuss the effects of the concentration of external inhibitors, the concentration of external nutrients, and the consumption rate of nutrients and inhibitors on the growth of tumors. The results show that under certain conditions the tumor will eventually disappear or will tend to a steady state. The increase of inhibitor concentration (or consumption rate) will lead to the reduction of the radius of the tumor, and the increase of nutrient concentration (or consumption rate) will lead to the increase of the radius of the tumor.

Keywords

• Tumor growth
• Angiogenesis
• Time delay
• Free boundary problem
• Stability