Nonsmooth Modeling of Computer Virus Propagation
TL;DR
A nonsmooth susceptible–latent–bursting–susceptible (SLBS) model with a two-level recovery function and a Holling-II saturated infection rate is proposed, and how limited recovery capacity and saturated infection jointly affect hierarchical control of network viruses is clarified.
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.