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Modeling and Analysis of Epidemic Diffusion within Small‐World Network

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  • Ming Liu
  • Yihong Xiao

Abstract

To depict the rule of epidemic diffusion, two different models, the Susceptible‐Exposure‐Infected‐Recovered‐Susceptible (SEIRS) model and the Susceptible‐Exposure‐Infected‐Quarantine‐Recovered‐Susceptible (SEIQRS) model, are proposed and analyzed within small‐world network in this paper. Firstly, the epidemic diffusion models are constructed with mean‐filed theory, and condition for the occurrence of disease diffusion is explored. Then, the existence and global stability of the disease‐free equilibrium and the endemic equilibrium for these two complex epidemic systems are proved by differential equations knowledge and Routh‐Hurwiz theory. At last, a numerical example which includes key parameters analysis and critical topic discussion is presented to test how well the proposed two models may be applied in practice. These works may provide some guidelines for decision makers when coping with epidemic diffusion controlling problems.

Suggested Citation

  • Ming Liu & Yihong Xiao, 2012. "Modeling and Analysis of Epidemic Diffusion within Small‐World Network," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:841531
    DOI: 10.1155/2012/841531
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    References listed on IDEAS

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    1. David L. Craft & Lawrence M. Wein & Alexander H. Wilkins, 2005. "Analyzing Bioterror Response Logistics: The Case of Anthrax," Management Science, INFORMS, vol. 51(5), pages 679-694, May.
    2. Peilin Shi & Lingzhen Dong, 2012. "Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-20, January.
    3. Stone, Thomas E. & Jones, Matthew M. & McKay, Susan R., 2010. "Comparative effects of avoidance and vaccination in disease spread on a dynamic small-world network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5515-5520.
    4. M.M. Telo da Gama & A. Nunes, 2006. "Epidemics in small world networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 205-208, March.
    5. Xu, Xin-Jian & Peng, Hai-Ou & Wang, Xiao-Mei & Wang, Ying-Hai, 2006. "Epidemic spreading with time delay in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 525-530.
    6. Peilin Shi & Lingzhen Dong, 2012. "Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    7. Stephen Eubank & Hasan Guclu & V. S. Anil Kumar & Madhav V. Marathe & Aravind Srinivasan & Zoltán Toroczkai & Nan Wang, 2004. "Modelling disease outbreaks in realistic urban social networks," Nature, Nature, vol. 429(6988), pages 180-184, May.
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    Cited by:

    1. Ming Liu & Yihong Xiao, 2013. "Modeling and Analysis of Epidemic Diffusion with Population Migration," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    2. Feng Rao, 2014. "Dynamics Analysis of a Stochastic SIR Epidemic Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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