Feng Shanshan, Jin Zhen
School of Data Science and Technology, North University of China, Taiyuan 030051, Shanxi, People's Republic of China.
Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, People's Republic of China.
Appl Math Comput. 2019 Nov 15;361:87-97. doi: 10.1016/j.amc.2019.05.005. Epub 2019 Jun 19.
Traditional infectious diseases models on metapopulation networks focus on direct transportations (e.g., direct flights), ignoring the effect of indirect transportations. Based on global aviation network, we turn the problem of indirect flights into a question of second neighbors, and propose a susceptible-infectious-susceptible model to study disease transmission on a connected metapopulation network coupled with its second-neighbor network (SNN). We calculate the basic reproduction number, which is independent of human mobility, and we prove the global stability of disease-free and endemic equilibria of the model. Furthermore, the study shows that the behavior that all travelers travel along the SNN may hinder the spread of disease if the SNN is not connected. However, the behavior that individuals travel along the metapopulation network coupled with its SNN contributes to the spread of disease. Thus for an emerging infectious disease, if the real network and its SNN keep the same connectivity, indirect transportations may be a potential threat and need to be controlled. Our work can be generalized to high-speed train and rail networks, which may further promote other research on metapopulation networks.
传统的异质种群网络传染病模型侧重于直接传播（如直飞航班），而忽略了间接传播的影响。基于全球航空网络，我们将间接航班问题转化为第二邻域问题，并提出了一个易感-感染-易感模型，以研究在与其第二邻域网络（SNN）耦合的连通异质种群网络上的疾病传播。我们计算了与人类流动性无关的基本再生数，并证明了该模型无病平衡点和地方病平衡点的全局稳定性。此外，研究表明，如果SNN不连通，所有旅行者沿着SNN出行的行为可能会阻碍疾病传播。然而，个体沿着与其SNN耦合的异质种群网络出行的行为则有助于疾病传播。因此，对于一种新出现的传染病，如果实际网络及其SNN保持相同的连通性，间接传播可能是一个潜在威胁，需要加以控制。我们的工作可以推广到高速铁路和铁路网络，这可能会进一步推动关于异质种群网络的其他研究。
