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摘要
In this study, the population growth of the brain tumor GBM, is constructed such as
{dx/dt=px(t) + r(1)x(t) (R-1-alpha(1)x(t)-alpha(2)x([[t]])-gamma(1)x(t)y([[t]])-d(1)x(t)x([[t]]) (A)
dy/dt=r(2)y(t)(R-2-beta(1)y(t)-beta(2)y([[t]])+gamma(1)x([[t]])y(t)-d(2)y(t)y([[t]])
where t=0, the parameters alpha(1), alpha(2), beta(1), beta(2), gamma(1), p, d(1),d(2), R-1, R-2, r(1) and r(2) are positive real numbers and [[t]] denotes the integer part of t is an element of[0,8). System (A) explains a tumor growth, that produces after a specific time another tumor population with different growth rate and different treatment susceptibilities. The local and global stability of this model is analyzed by using the theory of differential and difference equations. Simulations and data of GBM give a detailed description of system (A) at the end of the paper.
- 出版日期2015-5
