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Dynamical analysis of a fractional SIR model with birth and death on heterogeneous complex networks

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  • Huo, Jingjing
  • Zhao, Hongyong

Abstract

In this paper, a fractional SIR model with birth and death rates on heterogeneous complex networks is proposed. Firstly, we obtain a threshold value R0 based on the existence of endemic equilibrium point E∗, which completely determines the dynamics of the model. Secondly, by using Lyapunov function and Kirchhoff’s matrix tree theorem, the globally asymptotical stability of the disease-free equilibrium point E0 and the endemic equilibrium point E∗ of the model are investigated. That is, when R0<1, the disease-free equilibrium point E0 is globally asymptotically stable and the disease always dies out; when R0>1, the disease-free equilibrium point E0 becomes unstable and in the meantime there exists a unique endemic equilibrium point E∗, which is globally asymptotically stable and the disease is uniformly persistent. Finally, the effects of various immunization schemes are studied and compared. Numerical simulations are given to demonstrate the main results.

Suggested Citation

  • Huo, Jingjing & Zhao, Hongyong, 2016. "Dynamical analysis of a fractional SIR model with birth and death on heterogeneous complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 41-56.
    • Handle: RePEc:eee:phsmap:v:448:y:2016:i:c:p:41-56
    DOI: 10.1016/j.physa.2015.12.078
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    References listed on IDEAS

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    1. Zhang, Jiancheng & Sun, Jitao, 2014. "Stability analysis of an SIS epidemic model with feedback mechanism on networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 24-32.
    2. Sabina Alistar & Elisa Long & Margaret Brandeau & Eduard Beck, 2014. "HIV epidemic control—a model for optimal allocation of prevention and treatment resources," Health Care Management Science, Springer, vol. 17(2), pages 162-181, June.
    3. Yan, Ye & Kou, Chunhai, 2012. "Stability analysis for a fractional differential model of HIV infection of CD4+ T-cells with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(9), pages 1572-1585.
    4. Ahmed, E. & Elgazzar, A.S., 2007. "On fractional order differential equations model for nonlocal epidemics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 607-614.
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    Cited by:

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    3. Mohammad Imam Utoyo & Windarto & Aminatus Sa’adah, 2018. "Analysis of Fractional Order Mathematical Model of Hematopoietic Stem Cell Gene-Based Therapy," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2018, pages 1-11, August.
    4. Zhu, Linhe & Liu, Wenshan & Zhang, Zhengdi, 2020. "Delay differential equations modeling of rumor propagation in both homogeneous and heterogeneous networks with a forced silence function," Applied Mathematics and Computation, Elsevier, vol. 370(C).

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