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Epidemic threshold and immunization on generalized networks

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  • Peng, Chengbin
  • Jin, Xiaogang
  • Shi, Meixia

Abstract

The susceptible–infected–susceptible (SIS) model is widely adopted in the studies of epidemic dynamics. When it is applied on contact networks, these networks mostly consist of nodes connected by undirected and unweighted edges following certain statistical properties, whereas in this article we consider the threshold and immunization problem for the SIS model on generalized networks that may contain different kinds of nodes and edges which are very possible in the real situation. We proved that an epidemic will become extinct if and only if the spectral radius of the corresponding parameterized adjacent matrix (PAM) is smaller than 1. Based on this result, we can evaluate the efficiency of immune strategies and take several prevailing ones as examples. In addition, we also develop methods that can precisely find the optimal immune strategies for networks with the given PAM.

Suggested Citation

  • Peng, Chengbin & Jin, Xiaogang & Shi, Meixia, 2010. "Epidemic threshold and immunization on generalized networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 549-560.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:3:p:549-560
    DOI: 10.1016/j.physa.2009.09.047
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    References listed on IDEAS

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    1. Wang, Yubo & Xiao, Gaoxi & Hu, Jie & Cheng, Tee Hiang & Wang, Limsoon, 2009. "Imperfect targeted immunization in scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(12), pages 2535-2546.
    2. Zanette, Damián H. & Kuperman, Marcelo, 2002. "Effects of immunization in small-world epidemics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(3), pages 445-452.
    3. Draief, Moez, 2006. "Epidemic processes on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(1), pages 120-131.
    4. Bai, Wen-Jie & Zhou, Tao & Wang, Bing-Hong, 2007. "Immunization of susceptible–infected model on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 656-662.
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    Cited by:

    1. Elias S. Helou & Sandra A. Santos & Lucas E. A. Simões, 2018. "A fast gradient and function sampling method for finite-max functions," Computational Optimization and Applications, Springer, vol. 71(3), pages 673-717, December.
    2. Shams, Bita & Khansari, Mohammad, 2015. "On the impact of epidemic severity on network immunization algorithms," Theoretical Population Biology, Elsevier, vol. 106(C), pages 83-93.
    3. Arbore, Andrea & Fioriti, Vincenzo & Chinnici, Marta, 2016. "The topological defense in SIS epidemic models," Chaos, Solitons & Fractals, Elsevier, vol. 86(C), pages 16-22.
    4. González-Parra, Gilberto & Acedo, L. & Villanueva Micó, Rafael-J. & Arenas, Abraham J., 2010. "Modeling the social obesity epidemic with stochastic networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3692-3701.

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