论文标题
死亡的细胞种群中的寄生虫感染
Parasite infection in a cell population with deaths
论文作者
论文摘要
我们引入了一类分支马尔可夫过程，用于在细胞群体中建模寄生虫感染。每个细胞都包含一定数量的寄生虫，这些寄生虫会随着正跳的扩散而演变。该数量的寄生虫的增长率，扩散功能和正跳速取决于其当前价值。细胞的分裂速率还取决于它们所含的寄生虫的数量。在除法中，一个细胞生了两个子细胞，并在它们之间共享其寄生虫。细胞也可能死亡，这可能取决于它们所含的寄生虫的数量。我们研究寄生虫感染的长期行为。特别是，我们对“典型”细胞中的寄生虫数量以及细胞群的存活感兴趣。我们特别关注两个参数对细胞种群生存和/或包含寄生虫感染的概率的影响：分裂的子细胞之间的寄生虫共享的定律与细胞的划分形式和死亡率和死亡率作为所包含的寄生虫数量的功能。
We introduce a general class of branching Markov processes for the modelling of a parasite infection in a cell population. Each cell contains a quantity of parasites which evolves as a diffusion with positive jumps. The growth rate, diffusive function and positive jump rate of this quantity of parasites depend on its current value. The division rate of the cells also depends on the quantity of parasites they contain. At division, a cell gives birth to two daughter cells and shares its parasites between them. Cells may also die, at a rate which may depend on the quantity of parasites they contain. We study the long time behaviour of the parasite infection. In particular, we are interested in the quantity of parasites in a `typical' cell and on the survival of the cell population. We specifically focus on the influence of two parameters on the probability for the cell population to survive and/or contain the parasite infection: the law of the sharing of the parasites between the daughter cells at division and the form of the division and death rates of the cells as functions of the quantity of parasites they contain.
