{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:13:00Z","timestamp":1758823980620,"version":"3.41.2"},"reference-count":35,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,1,18]],"date-time":"2021-01-18T00:00:00Z","timestamp":1610928000000},"content-version":"vor","delay-in-days":17,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11975071","61673086"],"award-info":[{"award-number":["11975071","61673086"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004829","name":"Science and Technology Department of Sichuan Province","doi-asserted-by":"publisher","award":["2020YFS0007","2020-YF05-00073-SN"],"award-info":[{"award-number":["2020YFS0007","2020-YF05-00073-SN"]}],"id":[{"id":"10.13039\/501100004829","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>Cooperative spreading dynamics on complex networks is a hot topic in the field of network science. In this paper, we propose a strategy to immunize some nodes based on their degrees. The immunized nodes disable the synergistic effect of cooperative spreading dynamics. We also develop a generalized percolation theory to study the final state of the spreading dynamics. By using the Monte Carlo method, numerical simulations reveal that immunizing nodes with a large degree cannot always be beneficial for containing cooperative spreading. For small values of transmission probability, immunizing hubs can suppress the spreading, while the opposite situation happens for large values of transmission probability. Furthermore, numerical simulations show that immunizing hubs increase the cost of the system. Finally, all numerical simulations can be well predicted by the generalized percolation theory.<\/jats:p>","DOI":"10.1155\/2021\/6645113","type":"journal-article","created":{"date-parts":[[2021,1,19]],"date-time":"2021-01-19T03:35:23Z","timestamp":1611027323000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Immunization of Cooperative Spreading Dynamics on Complex Networks"],"prefix":"10.1155","volume":"2021","author":[{"given":"Jun","family":"Wang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2089-5150","authenticated-orcid":false,"given":"Shi-Min","family":"Cai","sequence":"additional","affiliation":[]},{"given":"Tao","family":"Zhou","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,1,18]]},"reference":[{"key":"e_1_2_9_1_2","article-title":"Statistical physics of social dynamics","volume":"81","author":"Claudio C.","year":"2009","journal-title":"Reviews of Modern Physics"},{"key":"e_1_2_9_2_2","article-title":"Epidemic processes in complex networks","volume":"87","author":"Romualdo P.-S.","year":"2015","journal-title":"Reviews of Modern Physics"},{"key":"e_1_2_9_3_2","article-title":"Epidemic dynamics and endemic states in complex networks","volume":"63","author":"Romualdo P.-S.","year":"2001","journal-title":"Physical Review E"},{"key":"e_1_2_9_4_2","article-title":"Epidemic dynamics in finite size scale-free networks","volume":"65","author":"Romualdo P.-S.","year":"2002","journal-title":"Physical Review E"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2019.07.001"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1103\/physrevresearch.2.023233"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.95.108701"},{"key":"e_1_2_9_8_2","article-title":"Competing epidemics on complex networks","volume":"84","author":"Brian K.","year":"2011","journal-title":"Physical Review E"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.81.036118"},{"key":"e_1_2_9_10_2","doi-asserted-by":"crossref","unstructured":"Watkins NicholasJ. CameronN. Preciado VictorM. andPappas GeorgeJ. Optimal resource allocation for competing epidemics over arbitrary networks Proceedings of the 2015 American Control Conference (ACC) 2015 Chicago IL USA IEEE 1381\u20131386.","DOI":"10.1109\/ACC.2015.7170926"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2016.10.013"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.111.128701"},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.90.012808"},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1038\/srep05097"},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.1038\/srep29259"},{"key":"e_1_2_9_16_2","doi-asserted-by":"publisher","DOI":"10.1038\/nphys3457"},{"key":"e_1_2_9_17_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.99.022308"},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/aa8bd2"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/104\/50001"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2016.10.006"},{"key":"e_1_2_9_21_2","article-title":"Immunization of complex networks","volume":"65","author":"Romualdo P.-S.","year":"2002","journal-title":"Physical Review E"},{"key":"e_1_2_9_22_2","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.91.247901"},{"key":"e_1_2_9_23_2","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.101.058701"},{"key":"e_1_2_9_24_2","doi-asserted-by":"publisher","DOI":"10.1140\/epjb\/e2006-00041-1"},{"key":"e_1_2_9_25_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.67.031911"},{"key":"e_1_2_9_26_2","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/109\/26001"},{"key":"e_1_2_9_27_2","article-title":"Generation of uncorrelated random scale-free networks","volume":"71","author":"Michele C.","year":"2005","journal-title":"Physical Review E"},{"key":"e_1_2_9_28_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.66.016128"},{"key":"e_1_2_9_29_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.61.5678"},{"key":"e_1_2_9_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2005.10.004"},{"key":"e_1_2_9_31_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.98.052312"},{"key":"e_1_2_9_32_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.5063960"},{"key":"e_1_2_9_33_2","article-title":"Structure of shells in complex networks","volume":"80","author":"Jia S.","year":"2009","journal-title":"Physical Review E"},{"key":"e_1_2_9_34_2","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/aa9fc8"},{"key":"e_1_2_9_35_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0129183120501326"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/6645113.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/6645113.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/6645113","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T23:13:00Z","timestamp":1723245180000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/6645113"}},"subtitle":[],"editor":[{"given":"Chenquan","family":"Gan","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/6645113"],"URL":"https:\/\/doi.org\/10.1155\/2021\/6645113","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2020-11-03","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-01-06","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-01-18","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"6645113"}}