%0 Journal Article %1 Valdez2013Temporal %A Valdez, L. %A Macri, P. %A Braunstein, L. %D 2013 %J Physica A: Statistical Mechanics and its Applications %K kinetics, percolation epidemic-models %R 10.1016/j.physa.2013.05.003 %T Temporal percolation of a susceptible adaptive network %U http://dx.doi.org/10.1016/j.physa.2013.05.003 %X In the last decades, due to the appearance of many diseases such as SARS and the H1N1 flu strain, many authors studied the impact of the disease spreading in the evolution of the infected individuals using the susceptible-infected-recovered model. However, few authors focused on the temporal behavior of the susceptible individuals. Recently it was found that in an epidemic spreading, the dynamic of the size of the biggest susceptible cluster can be explained by a temporal node void percolation Valdez et al PLoS ONE 7, e44188 (2012). It was shown that the size of the biggest susceptible cluster is the order parameter of this temporal percolation where the control parameter can be related to the number of links between susceptible individuals at a given time. As a consequence, there is a critical time at which the biggest susceptible cluster is destroyed. In this paper, we study the susceptible-infected-recovered model in an adaptive network where an intermittent social distancing strategy is applied. In this adaptive model a susceptible individual breaks his contact with the infected neighbor with probability \$\sigma\$ and after \$t\_b\$ time units the contact is restored. Using an edge-based compartmental model and percolation theory, we obtain the evolution equations of the fraction susceptible individuals in the susceptible biggest component. We show that when this strategy is applied, the spreading of the disease slows down, protecting the biggest susceptible cluster by increasing the critical time. We also study the strategy in a more realistic situation when it is applied after a macroscopic fraction of the population is infected. We find that in this case, the strategy can still halt the epidemic spreading. Our theoretical results are fully supported by intensive simulations.

@article{Valdez2013Temporal, abstract = {{In the last decades, due to the appearance of many diseases such as SARS and the H1N1 flu strain, many authors studied the impact of the disease spreading in the evolution of the infected individuals using the susceptible-infected-recovered model. However, few authors focused on the temporal behavior of the susceptible individuals. Recently it was found that in an epidemic spreading, the dynamic of the size of the biggest susceptible cluster can be explained by a temporal node void percolation [Valdez et al PLoS ONE 7, e44188 (2012)]. It was shown that the size of the biggest susceptible cluster is the order parameter of this temporal percolation where the control parameter can be related to the number of links between susceptible individuals at a given time. As a consequence, there is a critical time at which the biggest susceptible cluster is destroyed. In this paper, we study the susceptible-infected-recovered model in an adaptive network where an intermittent social distancing strategy is applied. In this adaptive model a susceptible individual breaks his contact with the infected neighbor with probability \$\sigma\$ and after \$t\_b\$ time units the contact is restored. Using an edge-based compartmental model and percolation theory, we obtain the evolution equations of the fraction susceptible individuals in the susceptible biggest component. We show that when this strategy is applied, the spreading of the disease slows down, protecting the biggest susceptible cluster by increasing the critical time. We also study the strategy in a more realistic situation when it is applied after a macroscopic fraction of the population is infected. We find that in this case, the strategy can still halt the epidemic spreading. Our theoretical results are fully supported by intensive simulations.}}, added-at = {2019-06-10T14:53:09.000+0200}, archiveprefix = {arXiv}, author = {Valdez, L. and Macri, P. and Braunstein, L.}, biburl = {https://www.bibsonomy.org/bibtex/245cbdfab55bf5b48b907d8073487e0d2/nonancourt}, citeulike-article-id = {11380164}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.physa.2013.05.003}, citeulike-linkout-1 = {http://arxiv.org/abs/1210.0063}, citeulike-linkout-2 = {http://arxiv.org/pdf/1210.0063}, day = 29, doi = {10.1016/j.physa.2013.05.003}, eprint = {1210.0063}, interhash = {3b4812c687115ac34517d5661c53ba9d}, intrahash = {45cbdfab55bf5b48b907d8073487e0d2}, issn = {0378-4371}, journal = {Physica A: Statistical Mechanics and its Applications}, keywords = {kinetics, percolation epidemic-models}, month = may, posted-at = {2012-10-03 15:57:06}, priority = {2}, timestamp = {2019-07-31T12:34:57.000+0200}, title = {{Temporal percolation of a susceptible adaptive network}}, url = {http://dx.doi.org/10.1016/j.physa.2013.05.003}, year = 2013 }