Kogan Oleg, Khasin Michael, Meerson Baruch, Schneider David, Myers Christopher R
Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA.
SGT Inc., NASA Ames Research Center, Moffett Field, Mountain View, California 94035, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Oct;90(4):042149. doi: 10.1103/PhysRevE.90.042149. Epub 2014 Oct 31.
We develop a perturbation method for studying quasineutral competition in a broad class of stochastic competition models and apply it to the analysis of fixation of competing strains in two epidemic models. The first model is a two-strain generalization of the stochastic susceptible-infected-susceptible (SIS) model. Here we extend previous results due to Parsons and Quince [Theor. Popul. Biol. 72, 468 (2007)], Parsons et al. [Theor. Popul. Biol. 74, 302 (2008)], and Lin, Kim, and Doering [J. Stat. Phys. 148, 646 (2012)]. The second model, a two-strain generalization of the stochastic susceptible-infected-recovered (SIR) model with population turnover, has not been studied previously. In each of the two models, when the basic reproduction numbers of the two strains are identical, a system with an infinite population size approaches a point on the deterministic coexistence line (CL): a straight line of fixed points in the phase space of subpopulation sizes. Shot noise drives one of the strain populations to fixation, and the other to extinction, on a time scale proportional to the total population size. Our perturbation method explicitly tracks the dynamics of the probability distribution of the subpopulations in the vicinity of the CL. We argue that, whereas the slow strain has a competitive advantage for mathematically "typical" initial conditions, it is the fast strain that is more likely to win in the important situation when a few infectives of both strains are introduced into a susceptible population.
我们开发了一种微扰方法，用于研究一类广泛的随机竞争模型中的准中性竞争，并将其应用于分析两种流行病模型中竞争菌株的固定情况。第一个模型是随机易感-感染-易感（SIS）模型的两菌株推广。在此，我们扩展了帕森斯和昆斯[《理论种群生物学》72, 468 (2007)]、帕森斯等人[《理论种群生物学》74, 302 (2008)]以及林、金和多林[《统计物理杂志》148, 646 (2012)]之前的结果。第二个模型是具有种群更替的随机易感-感染-康复（SIR）模型的两菌株推广，此前尚未被研究过。在这两个模型中的每一个中，当两种菌株的基本再生数相同时，一个具有无限种群规模的系统会趋近于确定性共存线（CL）上的一个点：在亚种群规模的相空间中由固定点组成的一条直线。散粒噪声在与总种群规模成比例的时间尺度上，驱使其中一个菌株种群固定，而另一个菌株种群灭绝。我们的微扰方法明确地跟踪了共存线附近亚种群概率分布的动态。我们认为，虽然对于数学上“典型”的初始条件，慢菌株具有竞争优势，但在将两种菌株的少量感染者引入易感种群的重要情况下，快菌株更有可能获胜。
