Different spreading processes in multiplex networks may interact with each other and display intertwined effects. In this paper, we propose a theoretical framework called infection-probability-dependent interlayer interaction propagation processes in multiplex networks with an arbitrary number of layers, to more precisely depict the intertwined effects which bring challenges to the existing state-dependent interlayer interaction models. Specifically, the spreading rate of each node is regulated by the proposed spreading rate function (SRF) which depends on both the intrinsic dynamics in its layer and the infection probabilities of its counterparts. We propose an algorithm to obtain the spreading threshold of each layer of the proposed theoretical framework. We analyze the three-layer tuberculosis-awareness-flu model with the SRF of each node being the expectation of infection-probability-dependent spreading rate. This paper gives a thorough and detailed numerical investigation of the impact and interaction of system settings and the spreading threshold of each layer. We find that for tuberculosis spreading which is in competing relation with awareness and cooperation relation with flu, the epidemic threshold is a constant when other layers’ intrinsic spreading rates are small. The cooperation layer has dramatic influence on the constant while the competing layer has no effect on it.

中文翻译：

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多重网络中感染概率相关的层间交互传播过程

多重网络中的不同传播过程可能会相互影响并表现出相互交织的效果。在本文中，我们提出了一个理论框架，称为具有任意层数的多路复用网络中的感染概率相关层间交互传播过程，以更准确地描述对现有状态相关层间交互模型带来挑战的交织效应。具体来说，每个节点的传播率由提议的传播率函数（SRF）调节，该函数取决于其层中的内在动态及其对应物的感染概率。我们提出了一种算法来获得所提出的理论框架的每一层的传播阈值。我们分析了三层结核病意识流感模型，每个节点的 SRF 是感染概率依赖传播率的期望。本文对系统设置的影响和相互作用以及每一层的传播阈值进行了彻底和详细的数值研究。我们发现，对于与流感的意识和合作关系存在竞争关系的结核病传播，当其他层的内在传播率较小时，流行阈值是恒定的。合作层对常数有显着影响，而竞争层对常数没有影响。本文对系统设置的影响和相互作用以及每一层的传播阈值进行了彻底和详细的数值研究。我们发现，对于与流感的意识和合作关系存在竞争关系的结核病传播，当其他层的内在传播率较小时，流行阈值是恒定的。合作层对常数有显着影响，而竞争层对常数没有影响。本文对系统设置的影响和相互作用以及每一层的传播阈值进行了彻底和详细的数值研究。我们发现，对于与流感的意识和合作关系存在竞争关系的结核病传播，当其他层的内在传播率较小时，流行阈值是恒定的。合作层对常数有显着影响，而竞争层对常数没有影响。