Nurtay Anel, Hennessy Matthew G, Sardanyés Josep, Alsedà Lluís, Elena Santiago F
Centre de Recerca Matemàtica, Universitat Autònoma de Barcelona, Campus de Bellaterra, Edifici C, 08193 Bellaterra, Spain.
Barcelona Graduate School of Mathematics (BGSMath), Universitat Autònoma de Barcelona, Campus de Bellaterra, Edifici C, 08193 Bellaterra, Spain.
R Soc Open Sci. 2019 Jan 9;6(1):181179. doi: 10.1098/rsos.181179. eCollection 2019 Jan.
We investigate the dynamics of a wild-type viral strain which generates mutant strains differing in phenotypic properties for infectivity, virulence and mutation rates. We study, by means of a mathematical model and bifurcation analysis, conditions under which the wild-type and mutant viruses, which compete for the same host cells, can coexist. The coexistence conditions are formulated in terms of the basic reproductive numbers of the strains, a maximum value of the mutation rate and the virulence of the pathogens. The analysis reveals that parameter space can be divided into five regions, each with distinct dynamics, that are organized around degenerate Bogdanov-Takens and zero-Hopf bifurcations, the latter of which gives rise to a curve of transcritical bifurcations of periodic orbits. These results provide new insights into the conditions by which viral populations may contain multiple coexisting strains in a stable manner.
我们研究了一种野生型病毒株的动力学，该病毒株会产生在感染性、毒力和突变率等表型特性上有所不同的突变株。我们通过数学模型和分岔分析，研究了争夺相同宿主细胞的野生型和突变型病毒能够共存的条件。共存条件是根据菌株的基本繁殖数、突变率的最大值和病原体的毒力来制定的。分析表明，参数空间可分为五个区域，每个区域都有不同的动力学，这些区域围绕退化的博格达诺夫 - 塔肯斯分岔和零霍普夫分岔组织，后者产生了周期轨道的跨临界分岔曲线。这些结果为病毒种群可能以稳定方式包含多种共存菌株的条件提供了新的见解。
