Spatial epidemiology of networked metapopulation: An overview

Lin WANG; Xiang Li

Assuming that interactive individuals are mixed homogeneously, the aforementioned epidemic compartment model neglects the significance of population connectivity. Such simplification can hardly solve new puzzles emerged in the present networking society. For example, why is it extremely difficult to eradicate computer viruses from the Internet or the World Wide Web, and why do those viruses have an unusual long lifetime [44] ? Similar matters have been observed in diverse systems, ranging from the web of human sexual relations to vaccination campaigns [4] . One key factor inducing such problems is the scale-free property of the networked systems, which causes a serious trouble that the threshold of disease outbreak vanishes [45] . Within complex networks, the basic reproductive number is R sf 0 = R 0 [1 + (CV ) 2 ], with CV identifying the coefficient of variation of the degree distribution (degree represents the number of edges k per node) [46] . For large networks taking on a scalefree heterogeneous topology, R 0 is always larger than 1 no matter how small the transmission rate may be, due to the infinite variance of the degree distribution.