AI 中文总结
该研究针对多毒株流行病系统的代数复杂性，提出一类可解析处理的两毒株模型，揭示继发感染的相对传播优势决定极限环振荡起始，解释了多毒株流行周期的机制。
AI 中文摘要
多毒株流行病学系统常表现出自持振荡，但严重的代数复杂性长期阻碍了对这些动力学的完整解析表征。为绕过这些障碍，我们确定了一类广泛的、可解析处理的两毒株模型，其特征是不对称交叉免疫，可阻止单一毒株的继发感染。这种针对性的结构简化使我们能够推导共存平衡点的显式表达式并映射其稳定性。我们表明，继发感染的相对传播优势从根本上决定了稳健极限环振荡的起始，扩展了之前狭窄边界的结果。关键的是，数值模拟揭示了丰富的宏观图景，其中小振幅的局部振荡与大振幅的复发性暴发周期共存。通过纳入免疫衰减和隔离等效应，并将框架扩展到可解析处理类之外，证实了这些现象的结构稳健性。这些发现为多毒株流行周期提供了清晰的机制解释，并为未来的理论发展提供了一个高度可处理的基线。
英文摘要
Multi-strain epidemiological systems frequently exhibit self-sustained oscillations, yet severe algebraic complexity has long obstructed a complete analytical characterization of these dynamics. Seeking to bypass these barriers, we have identified a broad, analytically tractable class of two-strain models featuring asymmetric cross-immunity that precludes secondary infections for a single strain. This targeted structural simplification allows us to derive explicit expressions for coexistence equilibria and map their stability. We show that the relative transmission advantage of secondary infections fundamentally governs the onset of robust limit-cycle oscillations, extending previous narrow-borderline results. Crucially, numerical simulations reveal a rich macroscopic landscape where small-amplitude local oscillations coexist with large-amplitude, recurrent outbreak cycles. The structural robustness of these phenomena is confirmed by incorporating effects such as waning immunity and isolation and extending the framework beyond the analytically tractable class. These findings provide a clear mechanistic explanation for multi-strain epidemic cycles and offer a highly tractable baseline for future theoretical developments.
