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Global stability of an SIR model with differential infectivity on complex networks

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  • Yuan, Xinpeng
  • Wang, Fang
  • Xue, Yakui
  • Liu, Maoxing

Abstract

In this paper, an SIR model with birth and death on complex networks is analyzed, where infected individuals are divided into m groups according to their infection and contact between human is treated as a scale-free social network. We obtain the basic reproduction number R0 as well as the effects of various immunization schemes. The results indicate that the disease-free equilibrium is locally and globally asymptotically stable in some conditions, otherwise disease-free equilibrium is unstable and exists an unique endemic equilibrium that is globally asymptotically stable. Our theoretical results are confirmed by numerical simulations and a promising way for infectious diseases control is suggested.

Suggested Citation

  • Yuan, Xinpeng & Wang, Fang & Xue, Yakui & Liu, Maoxing, 2018. "Global stability of an SIR model with differential infectivity on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 443-456.
    • Handle: RePEc:eee:phsmap:v:499:y:2018:i:c:p:443-456
    DOI: 10.1016/j.physa.2018.02.065
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    References listed on IDEAS

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    1. Yuan, Xinpeng & Xue, Yakui & Liu, Maoxing, 2014. "Global stability of an SIR model with two susceptible groups on complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 59(C), pages 42-50.
    2. Wang, Yi & Jin, Zhen, 2013. "Global analysis of multiple routes of disease transmission on heterogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 3869-3880.
    3. Yuan, Xinpeng & Ning, Jianguo & Ma, Tianbao & Wang, Cheng, 2016. "Stability of Newton TVD Runge–Kutta scheme for one-dimensional Euler equations with adaptive mesh," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 1-16.
    4. Yuan, Xinpeng & Xue, Yakui & Liu, Maoxing, 2013. "Analysis of an epidemic model with awareness programs by media on complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 48(C), pages 1-11.
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    Cited by:

    1. Zhang, Weitong & Zhang, Rui & Shang, Ronghua & Li, Juanfei & Jiao, Licheng, 2019. "Application of natural computation inspired method in community detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 130-150.
    2. Zhang, Yuexia & Pan, Dawei, 2021. "Layered SIRS model of information spread in complex networks," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    3. Satoh, Daisuke & Uchida, Masato, 2021. "Riccati equation as topology-based model of computer worms and discrete SIR model with constant infectious period," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    4. Liu, Liya & Jiang, Daqing & Hayat, Tasawar, 2021. "Dynamics of an SIR epidemic model with varying population sizes and regime switching in a two patch setting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).

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