With the hit of new pandemic threats, scientific frameworks are needed to understand the unfolding of the epidemic. At the mitigation stage of the epidemics in which several countries are now, the use of mobile apps that are able to trace contacts is of utmost importance in order to control new infected cases and contain further propagation. Here we present a theoretical approach using both percolation and message--passing techniques, to the role of contact tracing, in mitigating an epidemic wave. We show how the increase of the app adoption level raises the value of the epidemic threshold, which is eventually maximized when high-degree nodes are preferentially targeted. Analytical results are compared with extensive Monte Carlo simulations showing good agreement for both homogeneous and heterogeneous networks. These results are important to quantify the level of adoption needed for contact-tracing apps to be effective in mitigating an epidemic.

中文翻译：

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使用应用程序进行流行病追踪和缓解的消息传递方法

随着新的流行病威胁的出现，需要科学框架来了解流行病的发展。在目前多个国家的疫情缓解阶段，使用能够追踪接触者的移动应用程序对于控制新的感染病例并遏制进一步传播至关重要。在这里，我们提出了一种同时使用渗透和消息传递技术的理论方法，以了解接触者追踪在缓解流行病浪潮中的作用。我们展示了应用程序采用水平的增加如何提高流行阈值的值，当优先针对高度节点时，该值最终最大化。分析结果与广泛的蒙特卡罗模拟进行了比较，显示了同构和异构网络的良好一致性。