发表机构
Universidad de las Américas Puebla (UDLAP); King Abdullah University of Science and Technology (KAUST)（美洲大学; 阿卜杜拉国王科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出SIRCm仓室模型，整合免疫力减弱与突变驱动免疫逃逸，证明地方性平衡存在并发现其不稳定性，扩展了SIRC模型。
AI 中文摘要
我们提出并研究了一个仓室流行病学模型，该模型将免疫力减弱和突变驱动的免疫逃逸整合到一个单毒株框架中。该模型称为SIRCm，扩展了SIRC（易感-感染-康复-交叉免疫）模型，在该模型中，康复个体在恢复完全易感性之前会经过一个中间的交叉免疫类别。在SIRCm中，免疫力减弱速率和免疫逃逸速率均通过一个与当前感染水平相关的反馈函数放大。我们研究了该反馈的两种表述：一种为传播驱动模型，其中突变机会在新感染发生时出现；另一种为流行率驱动模型，其中突变机会仅与感染人群成比例出现。对于两种模型及任意反馈强度，我们利用持久性理论证明了地方性平衡点的存在性，并在弱反馈和强反馈极限下解析地表征了其行为，分别将SIRC和SIS模型作为极限情况恢复。与SIRC模型不同，我们表明SIRCm的地方性平衡点在特定参数区域内是不稳定的。这导致了即使在缺乏季节性强迫的情况下也会出现的新颖行为。
英文摘要
We propose and study a compartmental epidemiological model that incorporates both waning immunity and mutation-driven immune escape into a single-strain framework. The model, termed SIRCm, extends the SIRC (Susceptible-Infected-Recovered-Cross-immune) model, in which recovered individuals pass through an intermediate cross-immune class before returning to full susceptibility. In SIRCm, both the rate of immune waning and the rate of immune escape are amplified by a feedback function tied to the current level of infection. We study two formulations of this feedback, a transmission-driven model, in which mutation opportunities arise at the point of new infection, and a prevalence-driven model, in which they arise in proportion to the infected population alone. For both models and any feedback strength, we prove existence of an endemic equilibrium using persistence theory, and characterize its behavior analytically in the weak and strong-feedback limits, recovering the SIRC and SIS models, respectively, as limiting cases. Unlike the SIRC model, we show that the SIRCm endemic equilibrium is unstable in certain parameter regimes. This leads to novel behavior, even in the absence of seasonal forcing.
Comments28 pages, 20 figures. Code available at https://github.com/danielarenee/infection-modeling-with-mutation
