A stochastic fractional model for computer virus propagation with memory effects and exponential delay
5 affiliations
- 1Department of Mathematics, Fırat University, Elazığ, Türkiye
- 2IT4Innovations, VSB–Technical University of Ostrava, Ostrava, Czech Republic
- 3Faculty of Electrical Engineering and Computer Science, VSB–Technical University of Ostrava, Ostrava, Czech Republic
- 4Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
- 5Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia
Abstract
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 S(t), latent infected L(t), and actively seizing V(t) 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–Maruyama 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.
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BibTeX
@article{raza2026stochastic,
title = {{A stochastic fractional model for computer virus propagation with memory effects and exponential delay}},
author = {Ali Raza and Marek Lampart and Umar Shafique and Dumitru Baleanu and Maysaa Elmahi Abd Elwahab},
journal = {PLOS One},
year = {2026},
month = oct,
doi = {10.1371/journal.pone.0360254},
url = {https://doi.org/10.1371/journal.pone.0360254},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A stochastic fractional model for computer virus propagation with memory effects and exponential delay
AU - Ali Raza
AU - Marek Lampart
AU - Umar Shafique
AU - Dumitru Baleanu
AU - Maysaa Elmahi Abd Elwahab
PY - 2026
DA - 2026/10/14
JO - PLOS One
DO - 10.1371/journal.pone.0360254
UR - https://doi.org/10.1371/journal.pone.0360254
AB - 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 S(t), latent infected L(t), and actively seizing V(t) 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–Maruyama 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.
SN - 1932-6203
ER -