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Modelling of Epidemics with a Generalized Nonlinear Incidence on Complex Networks

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Complex Sciences (Complex 2009)

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Abstract

In this paper the spreading of epidemic model on complex networks with a generalized nonlinear incidence rate is presented. Firstly the SIS model on homogeneous networks with nonlinear incidence rate is considered, and the existence conditions about the disease-free equilibrium and the endemic equilibrium are given. And then the model on heterogenous scale-free (SF) networks is considered, where the absence of the threshold on SF networks with nonlinear incidence is demonstrated. At last the stability of the disease-free equilibrium on SF networks is obtained. From this paper, it is shown that, while the number of the equilibria is indeed different from the corresponding model with linear incidence rate, the basic reproductive number, which determinate whether the disease is spreading or not, is independent of the functional form of the nonlinear incidence rate.

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, P.R. China

    Maoxing Liu & Jiong Ruan

  2. Department of Mathematics, North University of China, Taiyuan, Shanxi, 030051, P.R. China

    Maoxing Liu

Authors
  1. Maoxing Liu
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  2. Jiong Ruan
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Editors and Affiliations

  1. Network Technology Research Centre, Research Techno Plaza, Nanyang Technology University, 4th story X‘Frontiers, Block 50 Nanyang Drive, 637553, Singapore

    Jie Zhou

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© 2009 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering

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Liu, M., Ruan, J. (2009). Modelling of Epidemics with a Generalized Nonlinear Incidence on Complex Networks. In: Zhou, J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02469-6_88

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  • DOI: https://doi.org/10.1007/978-3-642-02469-6_88

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02468-9

  • Online ISBN: 978-3-642-02469-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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