An individual-based model of stochastic branching is proposed and studied, in which point particles drift in \(\bar{\mathbb {R}}_{+}:=[0,+\infty )\) toward the origin (edge) with unit speed, where each of them splits into two particles that instantly appear in \(\bar{\mathbb {R}}_{+}\) at random positions. During their drift, the particles are subject to a random disappearance (death). The model is intended to capture the main features of the proliferation of tumor cells, in which trait \(x\in \bar{\mathbb {R}}_{+}\) of a given cell is time to its division and the death is caused by therapeutic factors. The main result of the paper is proving the existence of an honest evolution of this kind and finding a condition that involves the death rate and cell cycle distribution parameters, under which the mean size of the population remains bounded in time.

提出并研究了基于个体的随机分支模型，其中点粒子在\（\ bar {\ mathbb {R}} _ {+}：= [0，+ \ infty）\）中向原点（边缘）漂移）并以单位速度将它们每个都分成两个粒子，这些粒子立即在随机位置的\（\ bar {\ mathbb {R}} _ {+} \）中出现。在其漂移期间，粒子会随机消失（死亡）。该模型旨在捕获肿瘤细胞增殖的主要特征，其中特征\（x \ in \ bar {\ mathbb {R}} _ {+} \）给定细胞的分裂是分裂的时间，而死亡是由治疗因素引起的。该论文的主要结果是证明了这种诚实的进化过程的存在，并找到了涉及死亡率和细胞周期分布参数的条件，在该条件下种群的平均大小仍在时间范围内。