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.
Funding source: Scientific Research Project of Tianjin Municipal Education Commission
Award Identifier / Grant number: 2021KJ007
Funding source: Fundamental Research Funds for the Central Universities
Award Identifier / Grant number: 2452022016
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: This work was supported by the Scientific Research Project of Tianjin Municipal Education Commission (Grant Number: 2021KJ007) and the Fundamental Research Funds for the Central Universities (Grant Number: 2452022016).
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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