论文标题
随机入侵过程的急剧近似和打击时间
Sharp approximation and hitting times for stochastic invasion processes
论文作者
论文摘要
当一个具有正适应性的单个突变体到达平衡处的居民人群时，我们对与相互作用的随机过程的入侵阶段感兴趣。通过现在的经典方法，入侵的第一阶段通过分支过程近似。宏观阶段是通过限制动力学系统描述的，当突变群体处于相同的居民人群的相同顺序时。我们获得了更清晰的估计，并捕获了侵入性人群的中间介质阶段。它使我们能够表征阈值的打击时间，从第一阶段继承了很大的差异。这些问题尤其是通过量化时间来达到癌症人群或流行病的关键价值的动机。
We are interested in the invasion phase for stochastic processes with interactions when a single mutant with positive fitness arrives in a resident population at equilibrium. By a now classic approach, the first stage of the invasion is well approximated by a branching process. The macroscopic phase, when the mutant population is of the same order of the resident population, is described by the limiting dynamical system. We obtain sharper estimates and capture the intermediate mesoscopic phase for the invasive population. It allows us to characterize the hitting times of thresholds, which inherit a large variance from the first stages. These issues are motivated in particular by quantifying times to reach critical values for cancer population or epidemics.
