Department of Mathematics + Computer Science, Lawrence Technological University, 21000 W 10 Mile Rd, Southfield, MI 48075, USA.
Math Biosci Eng. 2023 Aug 8;20(9):16083-16113. doi: 10.3934/mbe.2023718.
We introduce a two-strain model with asymmetric temporary immunity periods and partial cross-immunity. We derive explicit conditions for competitive exclusion and coexistence of the strains depending on the strain-specific basic reproduction numbers, temporary immunity periods, and degree of cross-immunity. The results of our bifurcation analysis suggest that, even when two strains share similar basic reproduction numbers and other epidemiological parameters, a disparity in temporary immunity periods and partial or complete cross-immunity can provide a significant competitive advantage. To analyze the dynamics, we introduce a quasi-steady state reduced model which assumes the original strain remains at its endemic steady state. We completely analyze the resulting reduced planar hybrid switching system using linear stability analysis, planar phase-plane analysis, and the Bendixson-Dulac criterion. We validate both the full and reduced models with COVID-19 incidence data, focusing on the Delta (B.1.617.2), Omicron (B.1.1.529), and Kraken (XBB.1.5) variants. These numerical studies suggest that, while early novel strains of COVID-19 had a tendency toward dramatic takeovers and extinction of ancestral strains, more recent strains have the capacity for co-existence.
我们提出了一个具有不对称临时免疫期和部分交叉免疫的两菌株模型。我们根据菌株特异性基本繁殖数、临时免疫期和交叉免疫程度，推导出了菌株竞争排斥和共存的显式条件。我们的分支分析结果表明，即使两个菌株具有相似的基本繁殖数和其他流行病学参数，临时免疫期和部分或完全交叉免疫的差异也可以提供显著的竞争优势。为了分析动力学，我们引入了一个准稳态简化模型，该模型假设原始菌株保持在其地方性稳定状态。我们使用线性稳定性分析、平面相平面分析和 Bendixson-Dulac 准则对产生的简化平面混合切换系统进行了全面分析。我们使用 COVID-19 发病率数据验证了完整模型和简化模型，重点关注德尔塔（B.1.617.2）、奥密克戎（B.1.1.529）和卡戎（XBB.1.5）变体。这些数值研究表明，虽然 COVID-19 的早期新型菌株有剧烈接管和祖先菌株灭绝的趋势，但最近的菌株有共存的能力。
