Guo Yifei, Tu Lilan, Shen Han, Chai Lang
Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan, 430065, Hubei, China and College of Science, Wuhan University of Science and Technology, Wuhan, 430065, Hubei, China.
Phys Rev E. 2022 Sep;106(3-1):034307. doi: 10.1103/PhysRevE.106.034307.
On the basis of existing disease spreading research, in this paper we propose a Hesitant-Taken-Unaware-Aware-Susceptible-Asymptomatic-Symptomatic-Recovered (HTUA-SI^{a}I^{s}R) model with mass media in a two-layer network, which consists of a virtual communication layer and a physical contact layer. Based on the UAU-SIR model, we additionally consider three practical factors, including whether individuals will disseminate information or not, the influence of unaware individuals on aware individuals, and the direct recovery of asymptomatic infected individuals. Based on the microscopic Markov chain approach (MMCA), for the proposed HTUA-SI^{a}I^{s}R model, MMCA equations are generated and the analytical expression of the epidemic threshold is obtained. Compared with Monte Carlo techniques, numerical simulations show the feasibility and effectiveness of the MMCA equations, as well as the HTUA-SI^{a}I^{s}R model theoretically. Meanwhile, extensive simulations demonstrate that the acceleration of the awareness dissemination in the virtual communication layer can effectively block the epidemic spreading and raise the epidemic threshold. However, under certain conditions, the increasing of T-state individuals will increase the U-state individuals because the T-state and U-state individuals can influence the A-state individuals losing their awareness of protection, and then promote the epidemic spreading and decrease the epidemic threshold. In addition, reducing asymptomatic infections can hinder the epidemic spreading. But, when the recovery rate of asymptomatic infections is greater than that of symptomatic infections, decreasing the tendency of individuals acquiring asymptomatic infections will lower the epidemic threshold.
基于现有的疾病传播研究，本文提出了一种在两层网络中带有大众媒体的犹豫-被采取行动-未意识到-意识到-易感-无症状-有症状-康复（HTUA-SIaIsR）模型，该网络由虚拟通信层和物理接触层组成。基于UAU-SIR模型，我们额外考虑了三个实际因素，包括个体是否会传播信息、未意识到的个体对意识到的个体的影响以及无症状感染者的直接康复。基于微观马尔可夫链方法（MMCA），针对所提出的HTUA-SIaIsR模型，生成了MMCA方程并得到了流行阈值的解析表达式。与蒙特卡罗技术相比，数值模拟表明了MMCA方程以及HTUA-SIaIsR模型在理论上的可行性和有效性。同时，大量模拟表明虚拟通信层中意识传播的加速可以有效阻止疫情传播并提高流行阈值。然而，在某些条件下，T状态个体的增加会导致U状态个体增加，因为T状态和U状态个体可以影响A状态个体失去保护意识，进而促进疫情传播并降低流行阈值。此外，减少无症状感染可以阻碍疫情传播。但是，当无症状感染的康复率大于有症状感染的康复率时，降低个体感染无症状感染的倾向会降低流行阈值。
