Meng Lingqi, Masuda Naoki
Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA.
Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA; Computational and Data-Enabled Science and Engineering Program, State University of New York at Buffalo, Buffalo, NY 14260-5030, USA; Faculty of Science and Engineering, Waseda University, Tokyo 169-8555, Japan.
J Theor Biol. 2022 Feb 7;534:110960. doi: 10.1016/j.jtbi.2021.110960. Epub 2021 Nov 11.
Metapopulation models have been a powerful tool for both theorizing and simulating epidemic dynamics. In a metapopulation model, one considers a network composed of subpopulations and their pairwise connections, and individuals are assumed to migrate from one subpopulation to another obeying a given mobility rule. While how different mobility rules affect epidemic dynamics in metapopulation models has been studied, there have been relatively few efforts on comparison of the effects of simple (i.e., unbiased) random walks and more complex mobility rules. Here we study a susceptible-infectious-susceptible (SIS) dynamics in a metapopulation model in which individuals obey a parametric second-order random-walk mobility rule called the node2vec. We map the second-order mobility rule of the node2vec to a first-order random walk in a network whose each node is a directed edge connecting a pair of subpopulations and then derive the epidemic threshold. For various networks, we find that the epidemic threshold is large (therefore, epidemic spreading tends to be suppressed) when the individuals infrequently backtrack or infrequently visit the common neighbors of the currently visited and the last visited subpopulations than when the individuals obey the simple random walk. The amount of change in the epidemic threshold induced by the node2vec mobility is in general not as large as, but is sometimes comparable with, the one induced by the change in the diffusion rate for individuals.
集合种群模型一直是理论化和模拟流行病动态的有力工具。在集合种群模型中，人们考虑一个由亚种群及其两两连接组成的网络，并且假设个体根据给定的迁移规则从一个亚种群迁移到另一个亚种群。虽然已经研究了不同的迁移规则如何影响集合种群模型中的流行病动态，但在比较简单（即无偏差）随机游走和更复杂迁移规则的影响方面所做的工作相对较少。在这里，我们研究了一个集合种群模型中的易感-感染-易感（SIS）动态，其中个体遵循一种称为node2vec的参数化二阶随机游走迁移规则。我们将node2vec的二阶迁移规则映射到一个网络中的一阶随机游走，该网络的每个节点是连接一对亚种群的有向边，然后推导出流行病阈值。对于各种网络，我们发现，与个体遵循简单随机游走相比，当个体很少回溯或很少访问当前访问的亚种群和上次访问的亚种群的共同邻居时，流行病阈值较大（因此，流行病传播往往受到抑制）。由node2vec迁移引起的流行病阈值变化量通常不如个体扩散率变化引起的变化量大，但有时与之相当。
