A mathematical model of integro-differential equations is studied to describe the evolution of a heterogeneous population of cancer stem cells and tumor cells. This model has recently been analyzed by Hillen et al., who reduced the analysis to a system of ordinary differential equations to prove the so-called "tumor growth paradox". In this paper we study the reaction-diffusion systems of integro-differential equations and we have the positivity and global existence of solution by an invariant set. The stability of steady states is investigated after having proven that every spatially inhomogeneous pattern disappears by using "energy estimates"