Stability analysis and control strategies for worm attack in mobile networks via a VEIQS propagation model

Mobile devices are considerably pervasive in society, but also increase their vulnerability to worm attacks from mobile networks. In this paper, we propose a new Vulnerable-Exposed-Infectious-Quarantined-Secured worm propagation model with saturated incidence and strategies of both vaccination and quarantine. We obtain that the basic reproduction number R₀ is a sharp threshold parameter such that the worm-free equilibrium is asymptotically stable for R₀ ≤ 1, implying that the worm dies out eventually and its attack remains under control; the worm-existence equilibrium is asymptotically stable when R₀ > 1, namely, the worm is always persistent and spreading within a population. This paper provides some novel insights to cyber security by that (a) the stability of worm-free equilibrium establishes the control strategies to reduce the intensity of worm attacks, and the optimal control strategy is proposed by using Pontryagins Minimum Principle; (b) the stability of worm-existence equilibrium predicts the tendency of worm propagation in a long run and assesses the level of the worm popularity by the final scale of infected devices. Numerical simulations are implemented to illustrate the feasibility of the theoretical results and the effectiveness of the control strategies.