Stability Analysis Of Two Computer Virus Propagation Models

The compartment modeling is recognized as an effective approach in the study of computer virus propagation model. An SIPS(Susceptible-Infected-Patched)compartment model is studied in literature[30] and offers a new approach to the evaluation of effectiveness of countermeasures. However, the linear assumption of the infection rate in the SIPS model fits well with the real situation only when the number of infected nodes is very small. What’s more, the computer virus propagation models are mostly deterministic models in recent years. In fact the propagation of computer virus is extremely complex and influenced by a large number of factors. In order to characterize the propagation process more accurately to make people better understand the combined action of the virus and anti-virus measures, the SIPS model is improved in this paper.Two kinds of computer virus propagation models are proposed(i.e., SIPS model with nonlinear infection rate and SIPS model with stochastic perturbation), and the stability of the two models are analyzed in this paper. Specifically, the main results of this paper are as follows.1. A computer virus propagation model with nonlinear incidence rate is established on the basis of previous work, and this model is described by a differential dynamical system. Depending on the parameter values, the new system may have one or two equilibria, and the global asymptotic stability of the equilibria is proved. On this basis,some policies to contain the viral prevalence are suggested.2. The global stochastic perturbation is introduced in the deterministic model, and assuming that the white noise stochastic perturbations were around the equilibria, and a more authentic computer virus model with stochastic perturbation is established. Themodel is abstracted into a stochastic differential dynamic system based on a series of reasonable assumptions. This paper proves that the equilibria of stochastic systems are same with the equilibria of the deterministic system and the solution is stable in probability by the direct Lyapunov method.