Social distancing can be divided into two categories: spontaneous social distancing adopted by the individuals themselves, and public social distancing promoted by the government. Both types of social distancing have been proved to suppress the spread of infectious disease effectively. While previous studies examined the impact of each social distancing separately, the simultaneous impacts of them are less studied. In this research, we develop a mathematical model to analyze how spontaneous social distancing and public social distancing simultaneously affect the outbreak threshold of an infectious disease with asymptomatic infection. A communication-contact two-layer network is constructed to consider the difference between spontaneous social distancing and public social distancing. Based on link overlap of the two layers, the two-layer network is divided into three subnetworks: communication-only network, contact-only network, and overlapped network. Our results show that public social distancing can significantly increase the outbreak threshold of an infectious disease. To achieve better control effect, the subnetwork of higher infection risk should be more targeted by public social distancing, but the subnetworks of lower infection risk shouldn’t be overlooked. The impact of spontaneous social distancing is relatively weak. On the one hand, spontaneous social distancing in the communication-only network has no impact on the outbreak threshold of the infectious disease. On the other hand, the impact of spontaneous social distancing in the overlapped network is highly dependent on the detection of asymptomatic infection sources. Moreover, public social distancing collaborates with infection detection on controlling an infectious disease, but their impacts can’t add up perfectly. Besides, public social distancing is slightly less effective than infection detection, because infection detection can also promote spontaneous social distancing.

中文翻译：

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社会疏远对无症状感染者传染病传播的影响：数学模型

社会疏远可分为两类：个人自己采取的自发社会疏远，以及政府推动的公共社会疏远。事实证明，这两种社交距离都可以有效抑制传染病的传播。虽然以前的研究分别检查了每个社会疏远的影响，但对它们同时产生的影响的研究较少。在这项研究中，我们开发了一个数学模型来分析自发的社会疏远和公共社会疏远如何同时影响无症状感染的传染病的爆发阈值。构建通信-接触两层网络以考虑自发社交距离和公共社交距离之间的区别。基于两层链路重叠，二层网络分为三个子网：仅通信网络、仅接触网络和重叠网络。我们的结果表明，公共社交距离可以显着增加传染病的爆发阈值。为达到更好的控制效果，公众社交距离应更有针对性地针对感染风险较高的子网络，但不应忽视感染风险较低的子网络。自发的社交距离的影响相对较弱。一方面，纯通信网络中的自发社交距离对传染病的爆发阈值没有影响。另一方面，重叠网络中自发社交距离的影响高度依赖于无症状感染源的检测。而且，公共社交距离与感染检测合作控制传染病，但它们的影响不能完美地叠加。此外，公共社会疏远的效果略低于感染检测，因为感染检测也可以促进自发的社会疏远。