Modeling Computer Virus Spread Using ABC Fractional Derivatives with Mittag-Leffler Kernels: Symmetry, Invariance, and Memory Effects in a Four-Compartment Network Model

The spread of computer viruses poses a critical threat to networked systems and requires accurate modeling tools. Classical integer-order approaches had failed to capture memory effects inherent in real digital environments. To address this, we developed a four-compartment fractional-order model using the Atangana–Baleanu–Caputo (ABC) derivative with Mittag-Leffler kernels. We established fundamental properties such as positivity, boundedness, existence, uniqueness, and Hyers–Ulam stability. Analytical solutions were derived via Laplace transform and homotopy series, while the Variation-of-Parameters Method and a dedicated numerical scheme provided approximations. Simulation results showed that the fractional order strongly influenced infection dynamics: smaller orders delayed peaks, prolonged latency, and slowed recovery. Compared to classical models, the ABC framework captured realistic memory-dependent behavior, offering valuable insights for designing timely and effective cybersecurity interventions. The model exhibits structural symmetries: the infection flux depends on the symmetric combination L+I and the feasible region (probability simplex) is invariant under the flow. Under the parameter constraint δ=θ (and equal linear loss terms), the system is equivariant under the involution (L,I)↦(I,L), which is reflected in identical Hyers–Ulam stability bounds for the latent and infectious components.