Open quasispecies models: Stability, optimization, and distributed extension

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:481

Article

Yegorov, Ivan¹  Novozhilov, Artem S.¹  Bratus, Alexander S.^2,3 

[1] North Dakota State Univ, 1210 Albrecht Blvd, Fargo, ND 58102 USA

[2] Lomonosov Moscow State Univ, MSU, 2nd Educ Bldg, Moscow 119991, Russia

[3] Russian Univ Transport, Obraztsova 15, Moscow 127994, Russia

关键词: Open quasispecies models;    Population extinction;    Error threshold;    Stability;    Fitness maximization;    Distributed models;   

DOI  :  10.1016/j.jmaa.2019.123477

来源: Elsevier

【 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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free