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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.

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  • 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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    References listed on IDEAS

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    Cited by:

    1. Liu, Qiming & Li, Hua, 2019. "Global dynamics analysis of an SEIR epidemic model with discrete delay on complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 289-296.
    2. Manickam Iswarya & Ramachandran Raja & Grienggrai Rajchakit & Jinde Cao & Jehad Alzabut & Chuangxia Huang, 2019. "Existence, Uniqueness and Exponential Stability of Periodic Solution for Discrete-Time Delayed BAM Neural Networks Based on Coincidence Degree Theory and Graph Theoretic Method," Mathematics, MDPI, vol. 7(11), pages 1-18, November.
    3. 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.
    4. Min Zhou & Xiaoqun Liu & Guoan Tang, 2018. "Effect of urban tourist satisfaction on urban macroeconomics in China: A spatial panel econometric analysis with a spatial Durbin model," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-24, October.
    5. 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.
    6. 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).
    7. Wang, Chao & Huang, Xia & Hu, Xiaoqian & Zhao, Longfeng & Liu, Chao & Ghadimi, Pezhman, 2021. "Trade characteristics, competition patterns and COVID-19 related shock propagation in the global solar photovoltaic cell trade," Applied Energy, Elsevier, vol. 290(C).
    8. Jia, Yunfeng, 2020. "Bifurcation and pattern formation of a tumor–immune model with time-delay and diffusion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 92-108.
    9. Jihong Xiao & Xuehong Zhu & Chuangxia Huang & Xiaoguang Yang & Fenghua Wen & Meirui Zhong, 2019. "A New Approach for Stock Price Analysis and Prediction Based on SSA and SVM," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 287-310, January.
    10. Miaadi, Foued & Li, Xiaodi, 2021. "Impulse-dependent settling-time for finite time stabilization of uncertain impulsive static neural networks with leakage delay and distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 259-276.
    11. 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.
    12. Xin Yang & Shigang Wen & Zhifeng Liu & Cai Li & Chuangxia Huang, 2019. "Dynamic Properties of Foreign Exchange Complex Network," Mathematics, MDPI, vol. 7(9), pages 1-19, September.

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