A Caputo Fractional SLBS Computer Virus Model with Stage-Specific Holling Type-II Incidence

Abstract

Computer virus propagation (CVP) models translate malware movement in a network into analyzable dynamical systems. Two features are especially important for modern networks: infected hosts may remain latent before a damaging burst, and infection efficiency is usually saturated by limited contacts, filtering, isolation, or response resources. This article develops a two-dimensional Caputo fractional susceptible–latent–bursting–susceptible (SLBS) CVP model in which the susceptible–latent and susceptible–bursting channels have different Holling type-II incidence functions. The fractional derivative represents memory effects in the propagation process, while the two incidence functions allow the latent and bursting stages to have separate transmission strengths and saturation levels. Non-negativity, boundedness, and well-posedness are established. The system is then used to derive the basic reproduction number, classify all endemic equilibria, and obtain local asymptotic stability criteria for the virus-free, latency-free burst-endemic, and latency–burst coexistence equilibria. Numerical simulations based on an Adams predictor–corrector scheme illustrate the theoretical thresholds and suggest global convergence in representative parameter regions. The results provide a stage-sensitive modeling tool for analyzing and designing targeted defense policies against computer virus outbreaks.