Complex Networks and Systems Lagrange Laboratory, Institute for Scientific Interchange, Torino 10133, Italy.
J Theor Biol. 2012 Jan 21;293:87-100. doi: 10.1016/j.jtbi.2011.10.010. Epub 2011 Oct 19.
In this paper we develop a framework to analyze the behavior of contagion and spreading processes in complex subpopulation networks where individuals have memory of their subpopulation of origin. We introduce a metapopulation model in which subpopulations are connected through heterogeneous fluxes of individuals. The mobility process among communities takes into account the memory of residence of individuals and is incorporated with the classical susceptible-infectious-recovered epidemic model within each subpopulation. In order to gain analytical insight into the behavior of the system we use degree-block variables describing the heterogeneity of the subpopulation network and a time-scale separation technique for the dynamics of individuals. By considering the stochastic nature of the epidemic process we obtain the explicit expression of the global epidemic invasion threshold, below which the disease dies out before reaching a macroscopic fraction of the subpopulations. This threshold is not present in continuous deterministic diffusion models and explicitly depends on the disease parameters, the mobility rates, and the properties of the coupling matrices describing the mobility across subpopulations. The results presented here take a step further in offering insight into the fundamental mechanisms controlling the spreading of infectious diseases and other contagion processes across spatially structured communities.
在本文中，我们开发了一个框架来分析复杂亚群网络中传染病和传播过程的行为，其中个体具有其起源亚群的记忆。我们引入了一个元种群模型，其中亚群通过个体的异质通量连接。社区之间的流动过程考虑了个体的居住记忆，并与每个亚群内的经典易感-感染-恢复流行模型相结合。为了深入了解系统的行为，我们使用描述亚群网络异质性的度块变量和个体动态的时间尺度分离技术。通过考虑传染病过程的随机性，我们得到了全局传染病入侵阈值的显式表达式，低于该阈值，疾病在到达亚群的宏观部分之前就会消失。这个阈值在连续的确定性扩散模型中不存在，并且明确取决于疾病参数、迁移率以及描述亚群间迁移的耦合矩阵的特性。这里提出的结果更进一步，深入了解了控制传染病和其他传染病在空间结构社区中传播的基本机制。
