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Stability Analysis of SIR Model with Distributed Delay on Complex Networks

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  • Chuangxia Huang
  • Jie Cao
  • Fenghua Wen
  • Xiaoguang Yang

Abstract

In this paper, by taking full consideration of distributed delay, demographics and contact heterogeneity of the individuals, we present a detailed analytical study of the Susceptible-Infected-Removed (SIR) epidemic model on complex population networks. The basic reproduction number R 0 of the model is dominated by the topology of the underlying network, the properties of individuals which include birth rate, death rate, removed rate and infected rate, and continuously distributed time delay. By constructing suitable Lyapunov functional and employing Kirchhoff’s matrix tree theorem, we investigate the globally asymptotical stability of the disease-free and endemic equilibrium points. Specifically, the system shows threshold behaviors: if R 0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable, otherwise the endemic equilibrium is globally asymptotically stable. Furthermore, the obtained results show that SIR models with different types of delays have different converge time in the process of contagion: if R 0 > 1, then the system with distributed time delay stabilizes fastest; while R 0 ≤ 1, the system with distributed time delay converges most slowly. The validness and effectiveness of these results are demonstrated through numerical simulations.

Suggested Citation

  • Chuangxia Huang & Jie Cao & Fenghua Wen & Xiaoguang Yang, 2016. "Stability Analysis of SIR Model with Distributed Delay on Complex Networks," PLOS ONE, Public Library of Science, vol. 11(8), pages 1-22, August.
    • Handle: RePEc:plo:pone00:0158813
    DOI: 10.1371/journal.pone.0158813
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    Cited by:

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    7. Zhujia Yin & Yantuan Yu & Jianhuan Huang, 2018. "Evaluation and evolution of bank efficiency considering heterogeneity technology: An empirical study from China," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-19, October.
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    9. Grienggrai Rajchakit & Anbalagan Pratap & Ramachandran Raja & Jinde Cao & Jehad Alzabut & Chuangxia Huang, 2019. "Hybrid Control Scheme for Projective Lag Synchronization of Riemann–Liouville Sense Fractional Order Memristive BAM NeuralNetworks with Mixed Delays," Mathematics, MDPI, vol. 7(8), pages 1-23, August.
    10. Yang, Xin & Wen, Shigang & Zhao, Xian & Huang, Chuangxia, 2020. "Systemic importance of financial institutions: A complex network perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
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    12. Syed Ali, M. & Narayanan, G. & Saroha, Sumit & Priya, Bandana & Thakur, Ganesh Kumar, 2021. "Finite-time stability analysis of fractional-order memristive fuzzy cellular neural networks with time delay and leakage term," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 468-485.

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