{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,29]],"date-time":"2024-03-29T01:48:15Z","timestamp":1711676895050},"reference-count":25,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2019,1,16]],"date-time":"2019-01-16T00:00:00Z","timestamp":1547596800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Key R&D Program of China","doi-asserted-by":"publisher","award":["2017YFB0802703","61121061"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Security and Communication Networks"],"published-print":{"date-parts":[[2019,1,16]]},"abstract":"Epidemic models trade the modeling accuracy for complexity reduction. This paper proposes to group vertices in directed graphs based on connectivity and carries out epidemic spread analysis on the group basis, thereby substantially reducing the modeling complexity while preserving the modeling accuracy. A group-based continuous-time Markov SIS model is developed. The adjacency matrix of the network is also collapsed according to the grouping, to evaluate the Jacobian matrix of the group-based continuous-time Markov model. By adopting the mean-field approximation on the groups of nodes and links, the model complexity is significantly reduced as compared with previous topological epidemic models. An epidemic threshold is deduced based on the spectral radius of the collapsed adjacency matrix. The epidemic threshold is proved to be dependent on network structure and interdependent of the network scale. Simulation results validate the analytical epidemic threshold and confirm the asymptotical accuracy of the proposed epidemic model.<\/jats:p>","DOI":"10.1155\/2019\/1657164","type":"journal-article","created":{"date-parts":[[2019,1,16]],"date-time":"2019-01-16T23:30:26Z","timestamp":1547681426000},"page":"1-9","source":"Crossref","is-referenced-by-count":5,"title":["Group-Based Susceptible-Infectious-Susceptible Model in Large-Scale Directed Networks"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"http:\/\/orcid.org\/0000-0001-9439-6437","authenticated-orcid":true,"given":"Xu","family":"Wang","sequence":"first","affiliation":[{"name":"School of Cyberspace Security, Beijing University of Posts and Telecommunications, Beijing 100876, China"},{"name":"Global Big Data Technologies Centre, University of Technology Sydney, 2007, Australia"}]},{"given":"Bo","family":"Song","sequence":"additional","affiliation":[{"name":"Global Big Data Technologies Centre, University of Technology Sydney, 2007, Australia"},{"name":"School of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications, 210003, China"}]},{"given":"Wei","family":"Ni","sequence":"additional","affiliation":[{"name":"Data 61, CSIRO, Sydney, NSW 2122, Australia"}]},{"given":"Ren Ping","family":"Liu","sequence":"additional","affiliation":[{"name":"Global Big Data Technologies Centre, University of Technology Sydney, 2007, Australia"}]},{"given":"Y. Jay","family":"Guo","sequence":"additional","affiliation":[{"name":"Global Big Data Technologies Centre, University of Technology Sydney, 2007, Australia"}]},{"given":"Xinxin","family":"Niu","sequence":"additional","affiliation":[{"name":"School of Cyberspace Security, Beijing University of Posts and Telecommunications, Beijing 100876, China"},{"name":"State Key Laboratory of Public Big Data, Guizhou 550025, China"}]},{"given":"Kangfeng","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Cyberspace Security, Beijing University of Posts and Telecommunications, Beijing 100876, China"}]}],"member":"98","reference":[{"key":"4","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2068910"},{"key":"5","volume":"28","year":"1992"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1109\/TIFS.2016.2581305"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1109\/tnet.2008.925623"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-009-9814-1"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.110.108701"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1038\/scientificamerican0503-60"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1103\/revmodphys.87.925"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.86.3200"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2015.02.018"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2016.01.045"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1109\/TNET.2007.909678"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/9756982"},{"key":"21","doi-asserted-by":"publisher","volume":"2017","year":"2017","journal-title":"Security and Communication Networks","DOI":"10.1155\/2017\/2910310"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1109\/tdsc.2007.1001"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.86.039901"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1109\/TNET.2016.2594382"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijinfomgt.2017.08.003"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2005.10.004"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.88.062802"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2016.07.037"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1080\/00207179208934253"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1098\/rspb.1999.0716"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-006-0377-3"},{"key":"33","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-2388-4"}],"container-title":["Security and Communication Networks"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2019\/1657164.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2019\/1657164.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2019\/1657164.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,1,16]],"date-time":"2019-01-16T23:30:30Z","timestamp":1547681430000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/scn\/2019\/1657164\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,16]]},"references-count":25,"alternative-id":["1657164","1657164"],"URL":"http:\/\/dx.doi.org\/10.1155\/2019\/1657164","relation":{},"ISSN":["1939-0114","1939-0122"],"issn-type":[{"value":"1939-0114","type":"print"},{"value":"1939-0122","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,16]]}}}
