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Once the dynamic system becomes unstable, the propagation of malware will be out of control, which will seriously threaten the security of the industrial control network. So, it is necessary to model and study the propagation of malware in the industrial control network. In this paper, a SIDQR model with dual delay is proposed by fully considering the characteristics of the industrial control network. By analyzing the nonlinear dynamics of the model, the Hopf bifurcation is discussed in detail when the value of dual delay is greater than zero, and the expression for the threshold is also provided. The results of the experiments indicate that the system may have multiple bifurcation points. By comparing different immune and quarantine rates, it is found that the immune rate can be appropriately increased and the isolation rate can be appropriately reduced in the industrial control network, which can suppress the spread of malware without interrupting the industrial production.<\/jats:p>","DOI":"10.1155\/2023\/8823080","type":"journal-article","created":{"date-parts":[[2023,10,30]],"date-time":"2023-10-30T20:20:58Z","timestamp":1698697258000},"page":"1-12","source":"Crossref","is-referenced-by-count":1,"title":["A Malware Propagation Model with Dual Delay in the Industrial Control Network"],"prefix":"10.1155","volume":"2023","author":[{"given":"Wei","family":"Yang","sequence":"first","affiliation":[{"name":"Software College, Northeastern University, Shenyang 110169, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5490-2419","authenticated-orcid":true,"given":"Qiang","family":"Fu","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Shenyang University of Chemical Technology, Shenyang 110142, China"}]},{"given":"Yu","family":"Yao","sequence":"additional","affiliation":[{"name":"College of Computer Science and Engineering, Northeastern University, Shenyang 110169, China"},{"name":"Engineering Research Center of Security Technology of Complex Network System, Ministry of Education, Shenyang, China"}]}],"member":"311","reference":[{"key":"1","first-page":"767","article-title":"Industrial cyber vulnerabilities: lessons from stuxnet and the internet of things","volume":"72","author":"L. 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