Global stability for a SEIQR worm propagation model in mobile internet

Abstract

Abstract Recently, propagation models of worms in the mobile environment are drawing extensive attention, particularly in the Wi-Fi scenario. Considering that worm-free equilibrium is exponential convergent means that the propagation time and control time of worms are much shorter than for other asymptotic convergence. Besides, the global asymptotic stability of the endemic equilibrium is more important than the local asymptotic stability, which reflects the more global qualitative behavior of the worm propagation. In this paper, we discuss the global dynamics of SEIQR worm propagation model in mobile internet proposed by Xiao et al. [X. Xiao, P. Fu, C. Dou, Q. Li, G. Hu, and S. Xia, “Design and analysis of SEIQR worm propagation model in mobile internet,” Commun. Nonlinear Sci. Numer. Simulat., vol. 43, pp. 341–350, 2017] to improve and complement the related results. Through a series of mathematical derivations, sufficient conditions are derived to ensure the global exponentially stability of worm-free equilibrium, and the exponential convergent rate can be unveiled. Then, by using the classical geometric approach, it is shown that the endemic equilibrium is globally asymptotically stable and the system is persistent when R 0 > 1. Moreover, numerical simulations are given to demonstrate our theoretical results.