SARS-CoV-2 Omicron 的地方性振荡——一项 SIRS 模型分析
Endemic Oscillations for SARS-CoV-2 Omicron -- A SIRS model analysis
AI总结：
本文将含恒定接种和免疫衰减的 SIRS 模型映射至 Hethcote 经典模型，推导地方性分岔统一公式，并据此指出 Omicron 或难避免阻尼式地方性振荡。
摘要：
众所周知，具有恒定疫苗接种率和免疫力衰减率的 SIRS 模型，在基本再生数 $r_0$ 升高至阈值以上时，会表现出从无病平衡态向地方性平衡态的转变。本文表明，该模型可映射到 Hethcote 最初于 1973 年发表的经典地方性模型。由此，人们可为一整类表现出地方性分岔的模型获得统一公式。特别地，如果疫苗接种率小于恢复率，并且对于某些上下界 $r_\pm$ 有 $r_- < r_0 < r_+$，则轨迹会通过阻尼感染波螺旋进入地方性平衡态。SARS-CoV-2 Omicron 变异株的最新数据表明，根据这一简化模型，持续的疫苗接种计划将无法摆脱振荡性地方性阶段。然而，鉴于模型预测出很强的阻尼因子，在现实中这些振荡无疑会被随时间变化的接触行为所盖过。
英文摘要：
The SIRS model with constant vaccination and immunity waning rates is well known to show a transition from a disease-free to an endemic equilibrium as the basic reproduction number $r_0$ is raised above threshold. It is shown that this model maps to Hethcote's classic endemic model originally published in 1973. In this way one obtains unifying formulas for a whole class of models showing endemic bifurcation. In particular, if the vaccination rate is smaller than the recovery rate and $r_- < r_0 < r_+$ for certain upper and lower bounds $r_\pm$, then trajectories spiral into the endemic equilibrium via damped infection waves. Latest data of the SARS-CoV-2 Omicron variant suggest that according to this simplified model continuous vaccination programs will not be capable to escape the oscillating endemic phase. However, in view of the strong damping factors predicted by the model, in reality these oscillations will certainly be overruled by time-dependent contact behaviors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
