title: Steady-state analysis of necrotic core formation for solid avascular tumors with time delays in regulatory apoptosis.
abstract: A mathematical model for the growth of solid avascular tumor with time delays in regulatory apoptosis is studied. The existence of stationary solutions and the mechanism of formation of necrotic cores in the growth of the tumors are studied. The results show that if the natural death rate of the tumor cell exceeds a fixed positive constant, then the dormant tumor is nonnecrotic; otherwise, the dormant tumor is necrotic.
authors: College of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, China.
authors: Fangwei
authors: 0000-0003-1511-2155
authors: F
authors: Zhang
authors: School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China.
authors: Shihe
authors: 0000-0002-1961-3398
authors: S
authors: Xu
mesh_terms: D000465:Algorithms; D000818:Animals; D017209:Apoptosis; D006801:Humans; D008954:Models, Biological; D009336:Necrosis; D009369:Neoplasms / Q000473:pathology*