AI 中文总结
本研究分析肺结核模型，证明无延迟或饱和效应时也可出现霍普夫分岔，聚焦病例发现与维持干预的联合影响，结合萨尔塔省数据的模拟揭示了相关动力学对公共卫生政策的挑战。
AI 中文摘要
已知再感染与复发会在多种传染病模型（尤其是肺结核模型）中诱发后向分岔（亚临界叉形分岔），该现象意味着当基本再生数小于1时，系统会存在多个平衡点共存：一个稳定的无病平衡点和两个地方病平衡点，其中一个稳定、一个不稳定。因此可能出现滞后现象，即若系统仍处于地方病状态的吸引域内，将再生数降至1以下可能仍无法消除疾病。另一种常与干预延迟相关的现象是超临界霍普夫分岔，在此情况下，当再生数大于1时地方病平衡点失去稳定性，导致系统以稳定极限环的形式出现持续振荡。尽管该行为在肺结核研究文献中较少被探讨，但它对疾病控制具有重要意义。本研究分析了一个肺结核模型以探究这些动力学效应，证明即使无延迟或饱和效应，霍普夫分岔也可能出现。分岔分析聚焦于两项关键公共卫生干预措施——病例发现与病例维持，以及它们对疾病动力学的联合影响。基于肺结核负担较高的阿根廷萨尔塔省的流行病学数据开展的数值模拟，阐明了这些动力学特性在公共卫生政策设计与实施中带来的挑战。
英文摘要
Reinfection and relapse are known to induce backward bifurcation (a subcritical pitchfork bifurcation) in many infectious disease models, particularly tuberculosis. This phenomenon implies the coexistence of multiple equilibria when the basic reproduction number is below one: a stable disease-free equilibrium and two endemic equilibria, one stable and one unstable. As a result, hysteresis may arise, meaning that reducing the reproduction number below one may not eliminate the disease given that the system remains in the basin of attraction of the endemic state. Another relevant phenomenon, often associated with intervention delays, is the occurrence of supercritical Hopf bifurcations. In this case, the endemic equilibrium loses stability for reproduction numbers above one, leading to sustained oscillations in the form of stable limit cycles. Although less explored in the tuberculosis literature, this behavior has important implications for disease control. In this work, we analyze a tuberculosis model to investigate these dynamical effects and show that Hopf bifurcation can arise even without delays or saturation effects. The bifurcation analysis focuses on two key public health interventions -case finding and case holding- and their combined effect on disease dynamics. Numerical simulations, based on epidemiological data from Salta, Argentina -a province with high TB burden- illustrate the challenges these dynamics pose for the design and implementation of public health policies.
