开放拟种模型：稳定性、最优化和分布扩展
Open Quasispecies Models: Stability, Optimization, and Distributed Extension
摘要：
我们提出了一个自然的方法，导致经典的准种模型的修改，并纳入人口灭绝的可能性，除了增长。由此产生的修改后的模型称为开放模型。他们的基本属性，特别是平衡行为，分析和数值研究。准种动力学的特点，即异质准种分布本身和误差阈值现象，可以观察到在我们的模型中，随着灭绝。为了证明引入的框架的灵活性，我们研究了生物学激励的稳态适应度最大化的标准下的适应度分配的逆问题。考虑到高维准种问题的数值研究的复杂性，以及研究过程中涉及的基因型或等位基因的实际数量可能非常大的事实，我们还建立了连续时间分布的开放准种模型。所获得的结果可以作为开发涉及针对各种病原体的定向治疗的数学模型的初始步骤。
英文摘要：
We suggest a natural approach that leads to a modification of classical quasispecies models and incorporates the possibility of population extinction in addition to growth. The resulting modified models are called open. Their essential properties, regarding in particular equilibrium behavior, are investigated both analytically and numerically. The hallmarks of the quasispecies dynamics, viz. the heterogeneous quasispecies distribution itself and the error threshold phenomenon, can be observed in our models, along with extinction. In order to demonstrate the flexibility of the introduced framework, we study the inverse problem of fitness allocation under the biologically motivated criterion of steady-state fitness maximization. Having in mind the complexity of numerical investigation of high-dimensional quasispecies problems and the fact that the actual number of genotypes or alleles involved in a studied process can be extremely large, we also build continuous-time distributed open quasispecies models. The obtained results may serve as an initial step to developing mathematical models that involve directed therapy against various pathogens.
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