A compartmental model for global spread dynamics of malware under mutation

Abstract

Malware mutation is pervasive among networks. Modeling and understanding its propagation characteristics have been of great importance. In this study, a new compartmental model that extends the present model by incorporating mutated malware into the modeling process as a separate dynamic variable is proposed and theoretically analyzed to deepen the understanding of the spreading mechanisms of mutated malware. The model involves two equilibria, namely, malware‐free equilibrium and malware equilibrium, wherein both have proven to be locally and globally asymptotically stable through the Routh‐Hurwitz criterion and Lyapunov functional approach, respectively. An epidemic threshold is obtained that clearly forms the boundary among the comprehensive dynamics of the model between two distinct ramifications: one with mutation infection prevalence and the other without any mutation infection. Both are incarnated via the existence and stability of the equilibria admitted by the model. Further analyses show that the mutation is related not only to the epidemic threshold, but also to the malware prevalence level. The numerical simulations based on the analytic results demonstrate that the diffusion of mutated malware can fall away or can be maintained at a suitable level.