A stochastic fractional model for computer virus propagation with memory effects and exponential delay.

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.