{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T17:57:22Z","timestamp":1792000642675,"version":"4.4.0"},"reference-count":29,"publisher":"Public Library of Science (PLoS)","issue":"10","license":[{"start":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T00:00:00Z","timestamp":1791936000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>\n                    A computer virus is a type of malware that, upon execution, can replicate itself by modifying other computer programs and inserting its code into them. This study develops a stochastic fractional-order delay differential equation model (SFDDE) to describe computer-virus dynamics by partitioning the system into uninfected\n                    <jats:italic>S<\/jats:italic>\n                    (\n                    <jats:italic>t<\/jats:italic>\n                    ), latent infected\n                    <jats:italic>L<\/jats:italic>\n                    (\n                    <jats:italic>t<\/jats:italic>\n                    ), and actively seizing\n                    <jats:italic>V<\/jats:italic>\n                    (\n                    <jats:italic>t<\/jats:italic>\n                    ) computer populations. The model establishes the well-posedness of solutions, including existence, uniqueness, positivity, and boundedness, and identifies two equilibria: the computer-virus-free equilibrium (CV-FE) and the computer-virus-present equilibrium (CV-PE). The basic reproduction number is derived using the next-generation matrix method, followed by local and global stability analyses of the equilibrium points. A sensitivity analysis is performed to assess the influence of key parameters on virus transmission. Furthermore, a stochastic Non-Standard Finite Difference (NSFD) scheme is constructed to preserve the essential qualitative properties of the model, and its numerical performance is compared with the fractional Euler\u2013Maruyama method using step-size refinement and quantitative error measures. The numerical experiments illustrate the effects of fractional memory, transmission delay, and stochastic perturbations on computer-virus dynamics. The results provide mathematical insight into computer-virus propagation and indicate the importance of reducing virus transmission and improving detection, removal, and recovery processes for effective cybersecurity management. The study demonstrates the usefulness of stochastic fractional-order delay modeling and structure-preserving numerical methods for analyzing complex computer-virus dynamics.\n                  <\/jats:p>","DOI":"10.1371\/journal.pone.0360254","type":"journal-article","created":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T17:43:05Z","timestamp":1791999785000},"page":"e0360254","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["A stochastic fractional model for computer virus propagation with memory effects and exponential delay"],"prefix":"10.1371","volume":"21","author":[{"given":"Ali","family":"Raza","sequence":"first","affiliation":[{"name":"F\u0131rat University","place":["Elaz\u0131\u011f, T\u00fcrkiye"],"department":["Department of Mathematics"]},{"name":"IT4Innovations, VSB\u2013Technical University of Ostrava","place":["Ostrava, Czech Republic"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marek","family":"Lampart","sequence":"additional","affiliation":[{"name":"IT4Innovations, VSB\u2013Technical University of Ostrava","place":["Ostrava, Czech Republic"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Umar","family":"Shafique","sequence":"additional","affiliation":[{"name":"IT4Innovations, VSB\u2013Technical University of Ostrava","place":["Ostrava, Czech Republic"]},{"name":"VSB\u2013Technical University of Ostrava","place":["Ostrava, Czech Republic"],"department":["Faculty of Electrical Engineering and Computer Science"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Lebanese American University","place":["Beirut, Lebanon"],"department":["Department of Computer Science and Mathematics"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maysaa Elmahi","family":"Abd Elwahab","sequence":"additional","affiliation":[{"name":"College of Science, Princess Nourah bint Abdulrahman University","place":["Riyadh, Saudi Arabia"],"department":["Department of Mathematical Sciences"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,10,14]]},"reference":[{"issue":"3","key":"pone.0360254.ref001","doi-asserted-by":"crossref","first-page":"772","DOI":"10.1007\/s40435-019-00604-y","article-title":"Numerical dynamics of nonstandard finite difference schemes for a computer virus propagation model","volume":"8","author":"Q Dang","year":"2020","journal-title":"Int J Dynam Control"},{"key":"pone.0360254.ref002","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1016\/j.matcom.2024.04.035","article-title":"Analysis and numerical simulation of computer virus propagation model based on limited resources","volume":"223","author":"W Yang","year":"2024","journal-title":"Math Comput Simul"},{"issue":"3","key":"pone.0360254.ref003","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1080\/00207160.2024.2326926","article-title":"Numerical performance-based artificial neural networks to deal with the computer viruses spread on the complex networks","volume":"101","author":"AA Alderremy","year":"2024","journal-title":"Int J Comput Math"},{"issue":"2","key":"pone.0360254.ref004","doi-asserted-by":"crossref","first-page":"3195","DOI":"10.3934\/math.2024155","article-title":"A reliable numerical algorithm based on an operational matrix method for treatment of a fractional order computer virus model","volume":"9","author":"J Singh","year":"2024","journal-title":"MATH"},{"issue":"1","key":"pone.0360254.ref005","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1007\/s41478-023-00663-7","article-title":"Numerical solution of a modified epidemiological model of computer viruses by using Fibonacci wavelets","volume":"32","author":"G Manohara","year":"2023","journal-title":"J Anal"},{"issue":"4","key":"pone.0360254.ref006","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1007\/s12346-024-01041-9","article-title":"Modeling and Qualitative Dynamics of the Effects of Internal and External Storage device in a Discrete Fractional Computer Virus","volume":"23","author":"R Dhineshbabu","year":"2024","journal-title":"Qual Theory Dyn Syst"},{"key":"pone.0360254.ref007","doi-asserted-by":"crossref","unstructured":"Baba BA, Faruk N, Garba S. 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