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Global Dynamics of Infectious Disease with Arbitrary Distributed Infectious Period on Complex Networks

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  • Xiaoguang Zhang
  • Rui Song
  • Gui-Quan Sun
  • Zhen Jin

Abstract

Most of the current epidemic models assume that the infectious period follows an exponential distribution. However, due to individual heterogeneity and epidemic diversity, these models fail to describe the distribution of infectious periods precisely. We establish a SIS epidemic model with multistaged progression of infectious periods on complex networks, which can be used to characterize arbitrary distributions of infectious periods of the individuals. By using mathematical analysis, the basic reproduction number for the model is derived. We verify that the depends on the average distributions of infection periods for different types of infective individuals, which extend the general theory obtained from the single infectious period epidemic models. It is proved that if , then the disease-free equilibrium is globally asymptotically stable; otherwise the unique endemic equilibrium exists such that it is globally asymptotically attractive. Finally numerical simulations hold for the validity of our theoretical results is given.

Suggested Citation

  • Xiaoguang Zhang & Rui Song & Gui-Quan Sun & Zhen Jin, 2014. "Global Dynamics of Infectious Disease with Arbitrary Distributed Infectious Period on Complex Networks," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-9, September.
    • Handle: RePEc:hin:jnddns:161509
    DOI: 10.1155/2014/161509
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    References listed on IDEAS

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    1. Helen J Wearing & Pejman Rohani & Matt J Keeling, 2005. "Appropriate Models for the Management of Infectious Diseases," PLOS Medicine, Public Library of Science, vol. 2(7), pages 1-1, July.
    2. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    3. Carol Y. Lin, 2008. "Modeling Infectious Diseases in Humans and Animals by KEELING, M. J. and ROHANI, P," Biometrics, The International Biometric Society, vol. 64(3), pages 993-993, September.
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