Every outbreak of a serious infectious disease has the potential to pose unprecedented challenges to humanity. Understanding how epidemic spreads among populations is a key step in preventing and controlling it to spread. In this paper, for modeling the epidemic spreading and its associated information spreading, we put forward a novel coupled two-layered networking framework. One layer deals with the modeling of an SI${}_1$I${}_2$R process, where each node in the network may be in four states: susceptible, mildly infected, severely infected and recovery. Whereas, for the other layer, the transmission dynamics can be represented by an unaware–aware–refractory (UAT) model, which is significantly different from the classical unaware–aware–unaware (UAU) process since there exist individuals who are unwilling to share information. Moreover, we set a group of discrete time Microscopic Markov equations and derive the epidemic threshold. Finally, some numerical simulations are carried out to validate the analytical results. This work is of great significance to prevent epidemic, and it can be applicable in guiding the input on disease-related information on complex networks.

每次严重传染病的爆发都有可能给人类带来前所未有的挑战。了解流行病如何在人群中传播是预防和控制其传播的关键步骤。在本文中，为了对流行病传播及其相关信息传播进行建模，我们提出了一种新颖的耦合两层网络框架。一层处理SI的建模${}_{\mathrm{1个}}$一世${}_{\mathrm{2个}}$R进程，其中网络中的每个节点可能处于四种状态：易感染，轻度感染，重度感染和恢复。而对于另一层，传输动态可以由不知道-耐心的（UAT）模型表示，该模型与经典的不知道-不知道的（UAU）过程有很大的不同，因为存在不愿意共享的个人信息。此外，我们设置了一组离散时间微观马尔可夫方程，并得出了流行病阈值。最后，进行了一些数值模拟以验证分析结果。这项工作对预防流行病具有重要意义，可用于指导在复杂网络上输入与疾病有关的信息。