Cooperate epidemic spreading dynamics has attracted much attention from the field of network science. In this paper, we study the cooperate epidemic spreading dynamics on multiplex networks with heterogeneous populations, which induces the heterogeneous coinfection susceptibility. We propose a spreading model to describe the evolution mechanisms. To predict the final state of the epidemic outbreak size, a generalized bond percolation theory is suggested. Through numerical simulations and theoretical analyses, we find that the system exhibits a discontinuous phase transition for large average and small variance of the distribution of coinfection susceptibility on ER–ER multiplex networks, while the phase transition is continuous on SF–SF networks. In addition, the final outbreak size increases with the average coinfection susceptibility and decreases with the variance of the coinfection susceptibility. Our suggested bond percolation theory can well predict the numerical simulations.

中文翻译：

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在具有异质人口的多路网络上合作流行病传播

合作流行病传播动力学引起了网络科学领域的广泛关注。在本文中，我们研究了具有异质人群的多重网络上的合作流行病传播动力学，这导致了异质共感染易感性。我们提出了一个传播模型来描述进化机制。为了预测流行病爆发规模的最终状态，提出了广义的债券渗透理论。通过数值模拟和理论分析，我们发现该系统表现出不连续的相变，ER-ER多路复用网络上的共感染易感性分布的平均分布较大且方差较小，而SF-SF网络上的相变是连续的。此外，最终爆发规模随着平均共感染易感性的增加而增加，并随着共感染易感性的方差而减小。我们提出的键渗流理论可以很好地预测数值模拟。