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arXiv 2209.07563q-bio.PEmath.DSphysics.soc-ph
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一种病毒变异体的出现:通过COVID-19废水监测数据验证的交叉免疫时滞竞争模型的动力学

The emergence of a virus variant: dynamics of a competition model with cross-immunity time-delay validated by wastewater surveillance data for COVID-19

Bruce Pell, Samantha Brozak, Tin Phan, Fuqing Wu, Yang Kuang

摘要:

我们考虑一种病毒在人群中传播的动力学,这种病毒产生一种突变株,这种突变株能够感染被已建立株感染的个体。临时交叉免疫包括使用时间延迟,但发现这是一种无害的延迟。当两个菌株相互竞争时,我们给出了保证无病平衡点和两个边界平衡点局部和全局渐近稳定的充分条件。结果表明,由于新生菌株的免疫逃避,新生菌株的繁殖数必须显著低于已建立菌株的繁殖数,才能保证仅建立菌株边界平衡的局部稳定性.为了分析唯一的共存平衡,我们应用一个准稳态参数,以减少完整的模型到一个二维的表现出全局渐近稳定的建立应变唯一的平衡或全局渐近稳定的共存平衡。我们的研究结果表明,这两种菌株的基本繁殖数支配的整体动态,但在非平凡的方式,由于包括交叉免疫。该模型被应用于研究SARS-CoV-2 Delta变体的出现,在阿尔法变体的存在下,使用来自美国马萨诸塞州鹿岛处理厂的废水监测数据。

英文摘要:

We consider the dynamics of a virus spreading through a population that produces a mutant strain with the ability to infect individuals that were infected with the established strain. Temporary cross-immunity is included using a time delay, but is found to be a harmless delay. We provide some sufficient conditions that guarantee local and global asymptotic stability of the disease-free equilibrium and the two boundary equilibria when the two strains outcompete one another. It is shown that, due to the immune evasion of the emerging strain, the reproduction number of the emerging strain must be significantly lower than that of the established strain for the local stability of the established-strain-only boundary equilibrium. To analyze the unique coexistence equilibrium we apply a quasi steady-state argument to reduce the full model to a two-dimensional one that exhibits a global asymptotically stable established-strain-only equilibrium or global asymptotically stable coexistence equilibrium. Our results indicate that the basic reproduction numbers of both strains govern the overall dynamics, but in nontrivial ways due to the inclusion of cross-immunity. The model is applied to study the emergence of the SARS-CoV-2 Delta variant in the presence of the Alpha variant using wastewater surveillance data from the Deer Island Treatment Plant in Massachusetts, USA.

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