Zhong Li-Xin, Xu Wen-Juan, Chen Rong-Da, Qiu Tian, Shi Yong-Dong, Zhong Chen-Yang
School of Finance and Coordinated Innovation Center of Wealth Management and Quantitative Investment, Zhejiang University of Finance and Economics, Hangzhou, 310018, China.
School of Economics and Management, Tsinghua University, Beijing, 100084, China.
Physica A. 2015 Oct 15;436:482-491. doi: 10.1016/j.physa.2015.05.023. Epub 2015 May 18.
By incorporating segregated spatial domain and individual-based linkage into the SIS (susceptible-infected-susceptible) model, we propose a generalized epidemic model which can change from the territorial epidemic model to the networked epidemic model. The role of the individual-based linkage between different spatial domains is investigated. As we adjust the timescale parameter from 0 to unity, which represents the degree of activation of the individual-based linkage, three regions are found. Within the region of , the epidemic is determined by local movement and is sensitive to the timescale . Within the region of , the epidemic is insensitive to the timescale . Within the region of , the outbreak of the epidemic is determined by the structure of the individual-based linkage. As we keep an eye on the first region, the role of activating the individual-based linkage in the present model is similar to the role of the shortcuts in the two-dimensional small world network. Only activating a small number of the individual-based linkage can prompt the outbreak of the epidemic globally. The role of narrowing segregated spatial domain and reducing mobility in epidemic control is checked. These two measures are found to be conducive to curbing the spread of infectious disease only when the global interaction is suppressed. A log-log relation between the change in the number of infected individuals and the timescale is found. By calculating the epidemic threshold and the mean first encounter time, we heuristically analyze the microscopic characteristics of the propagation of the epidemic in the present model.
通过将隔离的空间域和基于个体的联系纳入SIS（易感-感染-易感）模型，我们提出了一种广义流行病模型，它可以从地域流行病模型转变为网络流行病模型。研究了不同空间域之间基于个体的联系的作用。当我们将时间尺度参数从0调整到1时（该参数表示基于个体的联系的激活程度），发现了三个区域。在 区域内，流行病由局部移动决定，并且对时间尺度 敏感。在 区域内，流行病对时间尺度 不敏感。在 区域内，流行病的爆发由基于个体的联系的结构决定。当我们关注第一个区域时，在当前模型中激活基于个体的联系的作用类似于二维小世界网络中捷径的作用。仅激活少量基于个体的联系就能促使流行病在全球范围内爆发。检验了缩小隔离空间域和降低流动性在疫情控制中的作用。发现只有在抑制全局相互作用时，这两项措施才有利于遏制传染病的传播。发现了感染个体数量变化与时间尺度 之间的对数-对数关系。通过计算流行病阈值和平均首次接触时间，我们试探性地分析了当前模型中流行病传播的微观特征。
