Stability analysis of an e-SEIAR model with point-to-group worm propagation

•We propose an e-SEIAR model which takes P2G propagation mode and benign worms.•We prove the global stability of the worm-free equilibrium using Lyapunov function.•We prove the global stability of the endemic equilibrium using Lyapunov function.•The reproduction number determines whether a worm dies out completely.•Number of neighbors of benign worms plays an important role in worm propagation.

Internet worms have drawn significant attention due to their enormous threats to the Internet. The main goal of this paper is to explore the interaction dynamics between a malicious worm and an benign worm, using a mathematical model, namely e-SEIAR. The e-SEIAR model takes two important network environment factors into consideration: point-to-group worm propagation mode and benign worms. Furthermore, some related dynamics properties are studied, along with the analysis of how to combat the worm prevalence based on the stability of equilibria. Simulation results show that the performance of our proposed models is effective in combating such worms, in terms of decreasing the number of hosts infected by the malicious worm and reducing the malicious worm propagation speed. Based on our simulations, we believe there is great potential for an effective method to use benign worms to combat malicious worms in some point-to-group applications.