当代气候研究如何帮助理解流行病动态？--包围方法和快照吸引器
How can contemporary climate research help to understand epidemic dynamics? -- Ensemble approach and snapshot attractors
摘要：
研究了基于房室微分方程的标准流行病模型在连续参数变化的外部强迫下的传播特性。我们发现，季节性调制的接触参数叠加单调衰减需要一个不同的描述比标准的混沌动力学。快照吸引子及其自然概率分布的概念已从最新的气候变化研究领域中被采用，以显示瞬态效应和疾病传播的集合解释的重要性。在给出扩展的麻疹分岔图后，研究了相空间结构的时间变化。通过定义集合上的统计度量，我们可以将流行病的内部变异性解释为复杂动态的开始，即使对于那些预期有规律行为的接触参数值也是如此。我们认为，异常爆发的传染类不能消亡，直到瞬态混沌的各种参数。更重要的是，这一事实变得可见，通过使用合奏的方法，而不是单一的轨迹表示。这些发现是普遍适用于非线性动力系统，如标准的流行病模型，无论参数值。
英文摘要：
Standard epidemic models based on compartmental differential equations are investigated under continuous parameter change as external forcing. We show that seasonal modulation of the contact parameter superimposed a monotonic decay needs a different description than that of the standard chaotic dynamics. The concept of snapshot attractors and their natural probability distribution has been adopted from the field of the latest climate-change-research to show the importance of transient effect and ensemble interpretation of disease spread. After presenting the extended bifurcation diagram of measles, the temporal change of the phase space structure is investigated. By defining statistical measures over the ensemble, we can interpret the internal variability of the epidemic as the onset of complex dynamics even for those values of contact parameter where regular behavior is expected. We argue that anomalous outbreaks of infectious class cannot die out until transient chaos is presented for various parameters. More important, that this fact becomes visible by using of ensemble approach rather than single trajectory representation. These findings are applicable generally in nonlinear dynamical systems such as standard epidemic models regardless of parameter values.
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