A note on global stability of the virose equilibrium for network-based computer viruses epidemics

It has been recently conjectured in Yang et al. (2013) [27] that the unique virose equilibrium of a network-based model is globally asymptotically stable in the feasible region. The aim of this paper is to investigate the global stability of the virose equilibrium by using the direct Lyapunov method and appropriate grouping techniques for Lyapunov function derivatives. Some sufficient conditions are established, which improves the relevant results. Moreover, we provide a new brief proof for global stability of the virus-free equilibrium by using comparison method, and discuss quantitatively the effect of various immunization schemes, including uniform immunization, targeted immunization and high-risk immunization, on the viruses spread, which suggests promising strategy to halt viruses spread in computer networks.