分支Feller扩散用于寄生虫感染的细胞分裂
Branching Feller diffusion for cell division with parasite infection
摘要：
我们描述了在连续时间分裂的细胞群体中寄生虫数量的演变。细胞中寄生虫的数量遵循Feller扩散，当分裂发生时，Feller扩散在两个子细胞之间随机分裂。细胞分裂速率可能取决于细胞内寄生虫的数量，我们感兴趣的是恒定或单调分裂速率的情况。我们首先确定的渐近行为的寄生虫的数量在一个细胞系中，它遵循Feller扩散与乘法跳跃。然后，我们考虑细胞群感染的演变，并给出标准来确定感染细胞的比例是否为零（恢复），或者是否有阳性比例的细胞被大量感染（细胞内寄生虫的增殖）。
英文摘要：
We describe the evolution of the quantity of parasites in a population of cells which divide in continuous-time. The quantity of parasites in a cell follows a Feller diffusion, which is splitted randomly between the two daughter cells when a division occurs. The cell division rate may depend on the quantity of parasites inside the cell and we are interested in the cases of constant or monotone division rate. We first determine the asymptotic behavior of the quantity of parasites in a cell line, which follows a Feller diffusion with multiplicative jumps. We then consider the evolution of the infection of the cell population and give criteria to determine whether the proportion of infected cells goes to zero (recovery) or if a positive proportion of cells becomes largely infected (proliferation of parasites inside the cells).
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