{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T06:36:19Z","timestamp":1726036579351},"reference-count":43,"publisher":"Elsevier BV","issue":"1","content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Communications in Nonlinear Science and Numerical Simulation"],"published-print":{"date-parts":[[2014,1]]},"DOI":"10.1016\/j.cnsns.2013.06.018","type":"journal-article","created":{"date-parts":[[2013,6,20]],"date-time":"2013-06-20T21:22:17Z","timestamp":1371763337000},"page":"92-100","update-policy":"http:\/\/dx.doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":84,"title":["A propagation model of computer virus with nonlinear vaccination probability"],"prefix":"10.1016","volume":"19","author":[{"given":"Chenquan","family":"Gan","sequence":"first","affiliation":[]},{"given":"Xiaofan","family":"Yang","sequence":"additional","affiliation":[]},{"given":"Wanping","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Qingyi","family":"Zhu","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.cnsns.2013.06.018_b0005","series-title":"The art of computer virus research and defense","author":"Szor","year":"2005"},{"key":"10.1016\/j.cnsns.2013.06.018_b0010","doi-asserted-by":"crossref","unstructured":"Kephart JO, White SR. Directed-graph epidemiological models of computer viruses. In: Proceedings of 1991 IEEE computer society symposium research in security and privacy; 1991, p. 343\u201359.","DOI":"10.1109\/RISP.1991.130801"},{"key":"10.1016\/j.cnsns.2013.06.018_b0015","unstructured":"Tippett PS. The kinetics of computer viruses replication: a theory and preliminary survey. In: Safe Computing: Proceedings of fourth annual computer virus and security conference, New York; March 1991, p. 66\u201387."},{"issue":"1","key":"10.1016\/j.cnsns.2013.06.018_b0020","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/0167-4048(87)90122-2","article-title":"Computer viruses: theory and experiments","volume":"6","author":"Cohen","year":"1987","journal-title":"Comput Secur"},{"issue":"2","key":"10.1016\/j.cnsns.2013.06.018_b0025","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/0167-4048(88)90327-6","article-title":"The application of epidemiology to computer viruses","volume":"7","author":"Murray","year":"1988","journal-title":"Comput Secur"},{"key":"10.1016\/j.cnsns.2013.06.018_b0030","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1109\/6.275061","article-title":"Computers and epidemiology","author":"Kephart","year":"1993","journal-title":"IEEE Spectr"},{"key":"10.1016\/j.cnsns.2013.06.018_b0035","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1016\/j.amc.2007.02.004","article-title":"Fixed period of temporary immunity after run of anti-malicious software on computer nodes","volume":"190","author":"Mishra","year":"2007","journal-title":"Appl Math Comput"},{"key":"10.1016\/j.cnsns.2013.06.018_b0040","doi-asserted-by":"crossref","first-page":"1476","DOI":"10.1016\/j.amc.2006.11.012","article-title":"SEIRS epidemic model with delay for transmission of malicious objects in computer network","volume":"188","author":"Mishra","year":"2007","journal-title":"Appl Math Comput"},{"issue":"7\u20138","key":"10.1016\/j.cnsns.2013.06.018_b0045","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.cose.2008.07.006","article-title":"Dynamic models for computer viruses","volume":"27","author":"Piqueira","year":"2008","journal-title":"Comput Secur"},{"key":"10.1016\/j.cnsns.2013.06.018_b0050","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.amc.2009.03.023","article-title":"A modied epidemiological for computer viruses","volume":"213","author":"Piqueira","year":"2009","journal-title":"Appl Math Comput"},{"key":"10.1016\/j.cnsns.2013.06.018_b0055","doi-asserted-by":"crossref","first-page":"2520","DOI":"10.1016\/j.amc.2010.07.064","article-title":"Dynamical behavior of computer virus on internet","volume":"217","author":"Han","year":"2010","journal-title":"Appl Math Comput"},{"key":"10.1016\/j.cnsns.2013.06.018_b0060","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1016\/j.apm.2009.06.011","article-title":"SEIQRS model for the transmission of malicious objects in computer network","volume":"34","author":"Mishra","year":"2010","journal-title":"Appl Math Model"},{"key":"10.1016\/j.cnsns.2013.06.018_b0065","doi-asserted-by":"crossref","first-page":"4335","DOI":"10.1016\/j.nonrwa.2010.05.018","article-title":"Fuzzy epidemic model for the transmission of worms in computer network","volume":"11","author":"Mishra","year":"2010","journal-title":"Nonlinear Anal Real"},{"key":"10.1016\/j.cnsns.2013.06.018_b0070","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1016\/j.cose.2009.10.002","article-title":"Stability analysis of a SEIQV epidemic model for rapid spreading worms","volume":"29","author":"Wang","year":"2010","journal-title":"Comput Secur"},{"issue":"7","key":"10.1016\/j.cnsns.2013.06.018_b0075","doi-asserted-by":"crossref","first-page":"1823","DOI":"10.1016\/j.camwa.2011.02.010","article-title":"Influence of removable devices on computer worms: dynamic analysis and control strategies","volume":"61","author":"Song","year":"2011","journal-title":"Comput Math Appl"},{"key":"10.1016\/j.cnsns.2013.06.018_b0080","doi-asserted-by":"crossref","first-page":"8438","DOI":"10.1016\/j.amc.2011.03.041","article-title":"Dynamic model of worms with vertical transmission in computer network","volume":"217","author":"Mishra","year":"2011","journal-title":"Appl Math Comput"},{"key":"10.1016\/j.cnsns.2013.06.018_b0085","doi-asserted-by":"crossref","DOI":"10.1155\/2012\/841987","article-title":"Stability and Hopf bifurcation in a computer virus model with multistate antivirus","volume":"2012","author":"Dong","year":"2012","journal-title":"Abstr Appl Anal"},{"issue":"7\u20138","key":"10.1016\/j.cnsns.2013.06.018_b0090","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.mcm.2011.12.010","article-title":"Hopf bifurcation analysis of a delayed viral infection model in computer networks","volume":"56","author":"Feng","year":"2012","journal-title":"Math Comput Model"},{"key":"10.1016\/j.cnsns.2013.06.018_b0095","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.chaos.2011.10.003","article-title":"A delayed computer virus propagation model and its dynamics","volume":"45","author":"Ren","year":"2012","journal-title":"Chaos Soliton Fractal"},{"key":"10.1016\/j.cnsns.2013.06.018_b0100","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1016\/j.nonrwa.2011.07.048","article-title":"A novel computer virus model and its dynamics","volume":"13","author":"Ren","year":"2012","journal-title":"Nonlinear Anal Real"},{"key":"10.1016\/j.cnsns.2013.06.018_b0105","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2012\/371792","article-title":"Dynamics of a delay-varying computer virus propagation model","volume":"2012","author":"Ren","year":"2012","journal-title":"Discrete Dyn Nat Soc"},{"key":"10.1016\/j.cnsns.2013.06.018_b0110","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2012\/828246","article-title":"Adaptive human behavior in a two-worm interaction model","volume":"2012","author":"Song","year":"2012","journal-title":"Discrete Dyn Nat Soc"},{"issue":"17","key":"10.1016\/j.cnsns.2013.06.018_b0115","doi-asserted-by":"crossref","first-page":"2307","DOI":"10.1080\/00207160.2012.715388","article-title":"A novel computer virus propagation model and its dynamics","volume":"89","author":"Yang","year":"2012","journal-title":"Int J Comput Math"},{"key":"10.1016\/j.cnsns.2013.06.018_b0120","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2012\/693695","article-title":"Propagation behavior of virus codes in the situation that infected computers are connected to the Internet with positive probability","volume":"2012","author":"Yang","year":"2012","journal-title":"Discrete Dyn Nat Soc"},{"issue":"8","key":"10.1016\/j.cnsns.2013.06.018_b0125","doi-asserted-by":"crossref","first-page":"3914","DOI":"10.1016\/j.amc.2012.10.027","article-title":"The spread of computer viruses under the influence of removable storage devices","volume":"219","author":"Yang","year":"2012","journal-title":"Appl Math Comput"},{"key":"10.1016\/j.cnsns.2013.06.018_b0130","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2012\/925648","article-title":"An SLBRS model with vertical transmission of computer virus over the Internet","volume":"2012","author":"Yang","year":"2012","journal-title":"Discrete Dyn Nat Soc"},{"key":"10.1016\/j.cnsns.2013.06.018_b0135","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2012\/456919","article-title":"Computer virus: Theory, model, and methods","volume":"2012","author":"Yang","year":"2012","journal-title":"Discrete Dyn Nat Soc"},{"key":"10.1016\/j.cnsns.2013.06.018_b0140","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2012\/259671","article-title":"Towards the epidemiological modeling of computer viruses","volume":"2012","author":"Yang","year":"2012","journal-title":"Discrete Dyn Nat Soc"},{"key":"10.1016\/j.cnsns.2013.06.018_b0145","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2012\/304868","article-title":"Hopf bifurcation in an SEIDQV worm propagation model with quarantine strategy","volume":"2012","author":"Yao","year":"2012","journal-title":"Discrete Dyn Nat Soc"},{"key":"10.1016\/j.cnsns.2013.06.018_b0150","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.1016\/j.compeleceng.2011.07.009","article-title":"Pulse quarantine strategy of internet worm propagation: Modeling and analysis","volume":"38","author":"Yao","year":"2012","journal-title":"Comput Electr Eng"},{"key":"10.1016\/j.cnsns.2013.06.018_b0155","first-page":"1","article-title":"An impulse model for computer viruses","volume":"2012","author":"Zhang","year":"2012","journal-title":"Discrete Dyn Nat Soc"},{"key":"10.1016\/j.cnsns.2013.06.018_b0160","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2012\/860598","article-title":"A sochastic dynamic model of computer viruses","volume":"2012","author":"Zhang","year":"2012","journal-title":"Discrete Dyn Nat Soc"},{"issue":"23","key":"10.1016\/j.cnsns.2013.06.018_b0165","doi-asserted-by":"crossref","first-page":"11613","DOI":"10.1016\/j.amc.2012.04.092","article-title":"Optimal control of computer virus under a delayed model","volume":"218","author":"Zhu","year":"2012","journal-title":"Appl Math Comput"},{"issue":"12","key":"10.1016\/j.cnsns.2013.06.018_b0170","doi-asserted-by":"crossref","first-page":"5117","DOI":"10.1016\/j.cnsns.2012.05.030","article-title":"Modeling and analysis of the spread of computer virus","volume":"17","author":"Zhu","year":"2012","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"1","key":"10.1016\/j.cnsns.2013.06.018_b0175","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1016\/j.nonrwa.2012.07.005","article-title":"A computer virus model with graded cure rates","volume":"14","author":"Yang","year":"2013","journal-title":"Nonlinear Anal Real"},{"issue":"16","key":"10.1016\/j.cnsns.2013.06.018_b0180","doi-asserted-by":"crossref","first-page":"8705","DOI":"10.1016\/j.amc.2013.02.031","article-title":"Epidemics of computer viruses: a complex-network approach","volume":"219","author":"Yang","year":"2013","journal-title":"Appl Math Comput"},{"key":"10.1016\/j.cnsns.2013.06.018_b0185","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2012\/106950","article-title":"Propagation of computer virus under human intervention: a dynamical model","volume":"2012","author":"Gan","year":"2012","journal-title":"Discrete Dyn Nat Soc"},{"key":"10.1016\/j.cnsns.2013.06.018_b0190","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1098\/rsif.2005.0042","article-title":"Perspectives on the basic reproductive ratio","volume":"2","author":"Heffernan","year":"2005","journal-title":"JR Soc Interface"},{"key":"10.1016\/j.cnsns.2013.06.018_b0195","series-title":"An introduction to dynamical systems: continuous and discrete","author":"Robinson","year":"2004"},{"key":"10.1016\/j.cnsns.2013.06.018_b0200","unstructured":""},{"key":"10.1016\/j.cnsns.2013.06.018_b0205","unstructured":""},{"key":"10.1016\/j.cnsns.2013.06.018_b0210","unstructured":"Arriola L, Hyman J. Forward and adjoint sensitivity analysis with applications in dynamical systems, Lecture notes in linear algebra and optimizatin; 2005."},{"issue":"4","key":"10.1016\/j.cnsns.2013.06.018_b0215","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1145\/316194.316229","article-title":"On power-law relationships of the Internet topology","volume":"29","author":"Faloutsos","year":"1999","journal-title":"ACM SIGCOMM Comput Commun Rev"}],"container-title":["Communications in Nonlinear Science and Numerical Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570413002712?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570413002712?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,7,16]],"date-time":"2019-07-16T00:07:34Z","timestamp":1563235654000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1007570413002712"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1]]},"references-count":43,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,1]]}},"alternative-id":["S1007570413002712"],"URL":"https:\/\/doi.org\/10.1016\/j.cnsns.2013.06.018","relation":{},"ISSN":["1007-5704"],"issn-type":[{"value":"1007-5704","type":"print"}],"subject":[],"published":{"date-parts":[[2014,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A propagation model of computer virus with nonlinear vaccination probability","name":"articletitle","label":"Article Title"},{"value":"Communications in Nonlinear Science and Numerical Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cnsns.2013.06.018","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2013 Elsevier B.V. All rights reserved.","name":"copyright","label":"Copyright"}]}}