Diseases and other contagion phenomena in nature and society can interact asymmetrically, such that one can benefit from the other, which in turn impairs the first, in analogy with predator-prey systems. Here, we consider two models for interacting diseaselike dynamics with asymmetric interactions and different associated time scales. Using rate equations for homogeneously mixed populations, we show that the stationary prevalences and phase diagrams of each model behave differently with respect to variations of the relative time scales. We also characterize in detail the regime where transient oscillations are observed, a pattern that is inherent to asymmetrical interactions but often ignored in the literature. Our results contribute to a better understanding of disease dynamics in particular, and interacting processes in general, and could provide interesting insights for real-world applications.

中文翻译：

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时间尺度在不对称相互作用疾病传播中的作用

自然界和社会中的疾病和其他传染现象可以不对称地相互作用，从而使一个人可以从另一个中受益，这与掠食者—猎物系统类似，进而损害了第一者。在这里，我们考虑了两个模型，它们以不对称的相互作用和不同的相关时间尺度来相互作用类似疾病的动力学。使用均质混合种群的速率方程，我们表明相对于相对时间尺度的变化，每个模型的平稳流行率和相位图的行为都不同。我们还详细描述了观察到瞬态振荡的状态，这是非对称相互作用所固有的一种模式，但在文献中经常被忽略。我们的结果有助于更好地了解疾病动态，尤其是相互作用的过程，