一种COVID-19的SIR型模型的余维二分岔及其流行病学意义
Codimension-Two Bifurcations of an SIR-Type Model for COVID-19 and Their Epidemiological Implications
AI总结：
本文利用AUTO分析COVID-19的SIR型模型在谨慎程度与床位占用率变化下的余维二分岔，揭示后向分岔中极限环与同宿轨道的复杂转变，并提出防控策略。
摘要：
我们研究了一种近期开发的用于描述COVID-19传播的SIR型数学模型所呈现的余维二分岔，此时其两个主要参数——易感个体的谨慎程度和医院床位占用率——在各自定义域内变化。我们使用AUTO生成该模型在相关分岔点附近的分岔图：两个Bogdanov-Takens点和两个广义Hopf点，以及若干相图，用以描述在每个分岔点附近、不同参数值组合下模型的轨道行为。分析表明，当在基本再生阈值处发生后向分岔时，模型的渐近行为从地方性流行向无病状态的转变，是通过一系列出乎意料复杂的拓扑变化实现的，这些变化不仅涉及平衡点的产生与消失，还涉及极限环和同宿轨道的产生与消失。在流行病学意义上，该分析证实了适当控制上述参数取值对于成功消灭COVID-19的重要性。我们推荐了若干可实现此类控制的策略。
英文摘要：
We study the codimension-two bifurcations exhibited by a recently-developed SIR-type mathematical model for the spread of COVID-19, as its two main parameters -- the susceptible individuals' cautiousness level and the hospitals' bed-occupancy rate -- vary over their domains. We use AUTO to generate the model's bifurcation diagrams near the relevant bifurcation points: two Bogdanov-Takens points and two generalised Hopf points, as well as a number of phase portraits describing the model's orbital behaviours for various pairs of parameter values near each bifurcation point. The analysis shows that, when a backward bifurcation occurs at the basic reproduction threshold, the transition of the model's asymptotic behaviour from endemic to disease-free takes place via an unexpectedly complex sequence of topological changes, involving the births and disappearances of not only equilibria but also limit cycles and homoclinic orbits. Epidemiologically, the analysis confirms the importance of a proper control of the values of the aforementioned parameters for a successful eradication of COVID-19. We recommend a number of strategies by which such a control may be achieved.
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。
