{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T14:45:53Z","timestamp":1773931553625,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T00:00:00Z","timestamp":1773878400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007684","name":"Ministry of Education and Science of Ukraine","doi-asserted-by":"publisher","award":["24BF038-01"],"award-info":[{"award-number":["24BF038-01"]}],"id":[{"id":"10.13039\/501100007684","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper proposes an impulsive SIRQ model for the analysis of computer network resilience against malware propagation and distributed denial-of-service (DDoS) attacks. The model extends classical epidemic frameworks by combining the continuous-time dynamics of malicious object spreading with discrete control actions corresponding to mass updates, node isolation, and access control policies. A qualitative analysis of the resulting system of impulsive differential equations is performed. The basic reproduction number\u00a0R0, identified as a threshold parameter characterizing the intensity of attack propagation, and sufficient conditions for the global asymptotic stability of the infection-free state are established. It is shown that, under periodic impulsive control, the infection-free state can be stabilized with respect to the target population coordinates even when\u00a0R0&gt;1. An exponential decay estimate for the total active threat is derived, guaranteeing the asymptotic extinction of the infected and quarantined node populations. The proposed approach provides quantitative criteria for the effectiveness of impulsive cyber defense strategies and offers a theoretical foundation for the design of adaptive multi-layer protection systems for critical information infrastructures. Practical interpretation of the results illustrates the dependence of the critical impulsive control period on the model parameters and demonstrates the applicability of the approach to cybersecurity strategy design.<\/jats:p>","DOI":"10.3390\/axioms15030229","type":"journal-article","created":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T11:50:36Z","timestamp":1773921036000},"page":"229","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Application of Impulsive SIRQ Models for the Development of Forecasting and Cyberattack Mitigation Scenarios"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4002-8206","authenticated-orcid":false,"given":"Valentyn","family":"Sobchuk","sequence":"first","affiliation":[{"name":"Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska Street 64, 01601 Kyiv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vitalii","family":"Savchenko","sequence":"additional","affiliation":[{"name":"Educational and Scientific Institute of Cybersecurity and Information Protection, State University of Information and Communication Technologies, Solomyanska Street 7, 03110 Kyiv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-9776-4727","authenticated-orcid":false,"given":"Bohdan","family":"Stepanchenko","sequence":"additional","affiliation":[{"name":"Educational and Scientific Institute of Cybersecurity and Information Protection, State University of Information and Communication Technologies, Solomyanska Street 7, 03110 Kyiv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0591-3290","authenticated-orcid":false,"given":"Halyna","family":"Haidur","sequence":"additional","affiliation":[{"name":"Educational and Scientific Institute of Cybersecurity and Information Protection, State University of Information and Communication Technologies, Solomyanska Street 7, 03110 Kyiv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1515\/nleng-2017-0094","article-title":"A mathematical model on DDoS attack in IoT network","volume":"8","author":"Mishra","year":"2019","journal-title":"Nonlinear Eng."},{"key":"ref_2","first-page":"92","article-title":"Sequential Intrusion Detection System for Zero-Trust Cyber Defence of IoT\/IIoT Networks","volume":"8","author":"Sobchuk","year":"2024","journal-title":"Adv. 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