On the stochastic simulation by optimal control and bifurcation analysis of the computer virus model in Caputo-type

This study investigates a fractional-order computer virus model using the Caputo derivative to capture memory effects in digital networks. The model classifies nodes into four compartments: susceptible (S), latent (L), actively infected (B), and recovered (R). Analytical results establish the well-posedness, positivity, boundedness, and stability of solutions, with the basic reproduction number R0 determining the threshold between virus extinction and persistence. Sensitivity analysis identifies the transmission rate as the most influential parameter, and a transcritical bifurcation at R0=1 separates disease-free and endemic equilibria. An optimal control framework based on Pontryagin’s Maximum Principle is designed to balance infection reduction with intervention costs. Stochastic perturbations are incorporated via the Milstein scheme to validate theoretical predictions and illustrate the impact of randomness. By integrating fractional calculus, stochastic modeling, and optimal control, this work provides a mathematical foundation for adaptive cybersecurity strategies in interconnected networks.