关于抑制物对肿瘤生长直接效果模型的数学分析

本文研究一个用于描述抑制物对肿瘤生长直接作用效果的数学模型,该模型是对Byrne和chaplain相应模型的一个改进.我们分别在c_1=c_2=0和c_1>0,c_2>o但很小两种情况下研究了该模型解的存在性和解在t→∞时的渐近状况,证明了未血管化的肿瘤在某些情况下趋于消失,而在另一些情况下趋于一个休眠态,且抑制物总能减小肿瘤的半径.

ANALYSIS OF A MATHEMATICAL MODEL OF THE DIRECT EFFECT OF INHIBITORS ON THE GROWTH OF TUMORS

In this paper we study a mathematical model of the direct effect of inhibitors on the growth of tumors. The model improves a similar model proposed by H. Byrne and M. Chaplain. We consider seperately the two cases where c1 = c2 = 0 and where c1 > 0, c2 > 0 and they are small. In both cases we establish global existence and uniqueness of a solution, and study the asymptotic behavior of the solution. The result shows that an avscular tumor either gradually disappears or converges to a dormant state, and the inhibitor always reduces the tumor radius.