发表机构
Institute for the Dynamics of Complex Systems, University of Göttingen; School of Technology and Architecture, SRH University of Applied Sciences Heidelberg, Leipzig Campus; Hangzhou International Innovation Institute, Beihang University; Interdisciplinary Center for the Mathematical Modeling of Infectious Disease Dynamics (IMMIDD), University of Münster（哥廷根大学复杂系统动力学研究所; SRH海德堡应用技术大学莱比锡校区技术与建筑学院; 北京航空航天大学杭州国际创新研究院; 明斯特大学传染病动力学数学建模跨学科中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出三阶段建模框架，揭示季节性与行为反馈协同作用可产生混沌，并证明病原体间合作扩展了流行模式谱系，对多病原体建模与控制有重要意义。
AI 中文摘要
传染病可能通过竞争同一宿主或促进后续感染而相互作用。理解此类多病原体系统的动态，特别是那些受地方性季节性和缓解措施影响的系统，对于设计稳健的公共卫生干预措施至关重要。我们提出了一个三阶段建模框架，以厘清季节性与作为缓解方式的行为反馈之间的相互作用。首先，我们分析了一个无外部强迫的耦合易感-感染-恢复-易感（SIRS）系统，并表明无病平衡点与地方性平衡点之间的突变源于后向分岔引起的一阶相变。其次，我们独立考察季节性和行为反馈，刻画了在临界临界点附近振荡行为被诱导的位置和时机。第三，我们证明两者的结合会产生复杂的多年波浪模式，其中高发病率周期由季节性驱动，低发病率间隔由行为反馈驱动。通过将稳定性映射为季节性强迫、缓解强度和合作性的函数，我们识别出由不同机制产生的具有混沌特征的不同倍周期级联：季节性与行为之间的相互作用，以及病原体间合作性及其诱导的后向分岔。随后，我们分析了这些机制如何在参数范围内相互作用。总之，我们表明合作从根本上扩展了可能的流行病模式谱系，强调了在多病原体建模和控制策略中考虑多病原体相互作用的重要性。
英文摘要
Infectious diseases may interact by competing for the same hosts or by facilitating subsequent infections. Understanding the dynamics of such multi-pathogen systems, particularly those subject to endemic seasonality and mitigation, is essential for designing robust public health interventions. We propose a three-stage modeling framework to disentangle the interplay between seasonality and behavioral feedback as a way of mitigation. First, we analyze a coupled susceptible-infectious-recovered-susceptible (SIRS) system without external forcing and show that the abrupt transition between the disease-free and endemic equilibria arises from a backward bifurcation-induced first-order phase transition. Second, we independently examine seasonality and behavioral feedback, characterizing where and when oscillatory behavior is induced near critical tipping points. Third, we demonstrate that their combination generates complex multi-annual wave patterns, with high-incidence cycles driven by seasonality and low-incidence intervals driven by behavioral feedback. By mapping stability as a function of seasonal forcing, mitigation strength, and cooperativity, we identify distinct period-doubling cascades with chaotic signatures arising from different mechanisms: the interplay between seasonality and behavior, and inter-pathogen cooperativity with the backward bifurcation it induces. We then analyze how these mechanisms interact across parameter ranges. Altogether, we show that cooperation fundamentally expands the spectrum of possible epidemic patterns, highlighting the importance of considering multi-pathogen interactions in epidemic modeling and control strategies.
