%0 Journal Article %1 Wang2009 %A Wang, Jiazeng %A Liu, Zengrong %D 2009 %J Journal of Physics A: Mathematical and Theoretical %K directed-networks epidemics epidemiology graphs sir-model %N 35 %P 355001 %R 10.1088/1751-8113/42/35/355001 %T Mean-field level analysis of epidemics in directed networks %V 42 %X The susceptible–infected–removed spreading model in a directed graph is studied. The mean-field level rate equations are built with the degree–degree connectivity correlation element and the (in, out)-degree distribution. And the outbreak threshold is obtained analytically—it is determined by the combination of connectivity probability and the degree distribution. Furthermore, the methods of calculating the degree–degree correlations in directed networks are presented. The numerical results of the discrete epidemic processes in networks verify our analyses.

@article{Wang2009, abstract = {The susceptible–infected–removed spreading model in a directed graph is studied. The mean-field level rate equations are built with the degree–degree connectivity correlation element and the (in, out)-degree distribution. And the outbreak threshold is obtained analytically—it is determined by the combination of connectivity probability and the degree distribution. Furthermore, the methods of calculating the degree–degree correlations in directed networks are presented. The numerical results of the discrete epidemic processes in networks verify our analyses.}, added-at = {2011-02-08T13:07:14.000+0100}, author = {Wang, Jiazeng and Liu, Zengrong}, biburl = {https://www.bibsonomy.org/bibtex/2c0bcfb9d19a164eb08ed509abef7a074/rincedd}, doi = {10.1088/1751-8113/42/35/355001}, interhash = {a895e80e31be1317daccb644c94fc6cf}, intrahash = {c0bcfb9d19a164eb08ed509abef7a074}, journal = {Journal of Physics A: Mathematical and Theoretical}, keywords = {directed-networks epidemics epidemiology graphs sir-model}, number = 35, pages = 355001, timestamp = {2011-02-08T13:07:14.000+0100}, title = {Mean-field level analysis of epidemics in directed networks}, volume = 42, year = 2009 }