Nonsmooth Modeling of Computer Virus Propagation

Abstract

Most previous computer virus propagation (CVP) models are smooth, meaning that their right-hand sides are continuously differentiable. However, recovery resources for compromised hosts are often limited, and the aggregate recovery rate may decrease once the number of bursting nodes exceeds a defense threshold. To describe this resource-constrained mechanism, this article proposes a nonsmooth susceptible–latent–bursting–susceptible (SLBS) model with a two-level recovery function and a Holling-II saturated infection rate. Well-posedness, positivity, and positive invariance of the feasible region are first proved. The basic reproduction number is derived by the next-generation matrix method, and its normalized sensitivity indices is provided. The virus-endemic equilibria are obtained by reducing the equilibrium equations to a strictly increasing scalar equation, with special attention to the threshold case at the nonsmooth switching surface. Local stability is established by piecewise linearization and explicit Routh–Hurwitz criteria. Finally, vector-graphic numerical simulations, convergence checks, and parameter robustness tests are reported. The results clarify how limited recovery capacity and saturated infection jointly affect hierarchical control of network viruses.