%0 Journal Article %1 Castellano2010 %A Castellano, Claudio %A Pastor-Satorras, Romualdo %D 2010 %I American Physical Society %J Phys. Rev. Lett. %K epidemics epidemiology graphs networks scale-free %N 21 %P 218701 %R 10.1103/PhysRevLett.105.218701 %T Thresholds for Epidemic Spreading in Networks %V 105 %X We study the threshold of epidemic models in quenched networks with degree distribution given by a power-law. For the susceptible-infected-susceptible model the activity threshold λc vanishes in the large size limit on any network whose maximum degree kmax⁡ diverges with the system size, at odds with heterogeneous mean-field (HMF) theory. The vanishing of the threshold has nothing to do with the scale-free nature of the network but stems instead from the largest hub in the system being active for any spreading rate λ>1/√kmax⁡ and playing the role of a self-sustained source that spreads the infection to the rest of the system. The susceptible-infected-removed model displays instead agreement with HMF theory and a finite threshold for scale-rich networks. We conjecture that on quenched scale-rich networks the threshold of generic epidemic models is vanishing or finite depending on the presence or absence of a steady state.

@article{Castellano2010, abstract = {We study the threshold of epidemic models in quenched networks with degree distribution given by a power-law. For the susceptible-infected-susceptible model the activity threshold λc vanishes in the large size limit on any network whose maximum degree kmax⁡ diverges with the system size, at odds with heterogeneous mean-field (HMF) theory. The vanishing of the threshold has nothing to do with the scale-free nature of the network but stems instead from the largest hub in the system being active for any spreading rate λ>1/√kmax⁡ and playing the role of a self-sustained source that spreads the infection to the rest of the system. The susceptible-infected-removed model displays instead agreement with HMF theory and a finite threshold for scale-rich networks. We conjecture that on quenched scale-rich networks the threshold of generic epidemic models is vanishing or finite depending on the presence or absence of a steady state.}, added-at = {2011-01-13T13:25:37.000+0100}, author = {Castellano, Claudio and Pastor-Satorras, Romualdo}, biburl = {https://www.bibsonomy.org/bibtex/2ff0fc7a0853bfac488b719f21f7b7605/rincedd}, doi = {10.1103/PhysRevLett.105.218701}, file = {Castellano2010 - Thresholds for Epidemic Spreading in Networks.pdf:Contact Processes/Castellano2010 - Thresholds for Epidemic Spreading in Networks.pdf:PDF}, groups = {public}, interhash = {9d46e9ce66b230f90590f9c8f0912052}, intrahash = {ff0fc7a0853bfac488b719f21f7b7605}, journal = {Phys. Rev. Lett.}, keywords = {epidemics epidemiology graphs networks scale-free}, number = 21, pages = 218701, publisher = {American Physical Society}, timestamp = {2011-03-30T16:38:28.000+0200}, title = {Thresholds for Epidemic Spreading in Networks}, username = {rincedd}, volume = 105, year = 2010 }