Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
Book cover

Mathematical Epidemiology pp 133–146Cite as

  1. Home
  2. Mathematical Epidemiology
  3. Chapter
An Introduction to Networks in Epidemic Modeling

An Introduction to Networks in Epidemic Modeling

  • Fred Brauer7 
  • Chapter
  • 13k Accesses

  • 13 Citations

Part of the Lecture Notes in Mathematics book series (LNMBIOS,volume 1945)

We use a stochastic branching process to describe the beginning of a disease outbreak. Unlike compartmental models, if the basic reproduction number is greater than one there may be a minor outbreak or a major epidemic with a probability depending on the nature of the contact network. We use a network approach to determine the distribution of outbreak and epidemic sizes.

Download chapter PDF

References

  1. R. Albert & A.-L. Barabási: Statistical mechanics of complex networks, Rev. Mod. Phys. 74, 47–97 (2002).

    CrossRef  Google Scholar 

  2. A.-L. Barabási & R. Albert: Emergence of scaling in random networks, Science 286, 509–512 (1999).

    CrossRef  MathSciNet  Google Scholar 

  3. P. Erdös & A. Rényi: On random graphs, Publ. Math. 6, 290–297 (1959).

    MATH  Google Scholar 

  4. P. Erdös & A. Rényi: On the evolution of random graphs, Pub. Math. Inst. Hung. Acad. Sci. 5, 17–61 (1960).

    MATH  Google Scholar 

  5. P. Erdös & A. Rényi: On the strengths of connectedness of a random graph, Acta Math. Sci. Hung. 12, 261–267 (1961).

    CrossRef  MATH  Google Scholar 

  6. D.S. Callaway, M.E.J. Newman, S.H. Strogatz & D.J. Watts: Network robustness and fragility: Percolation on random graphs, Phys. Rev. Lett. 85, 5468–5471 (2000).

    CrossRef  Google Scholar 

  7. O. Diekmann & J.A.P. Heesterbeek: Mathematical Epidemiology of Infectious Diseases, Wiley, Chichester (2000).

    Google Scholar 

  8. N.M. Ferguson, D.A.T. Cummings, S. Cauchemez, C. Fraser, S. Riley, A. Meeyai, S. Iamsirithaworn & D.S. Burke: Strategies for containing an emerging influenza pandemic in Southeast Asia, Nature 437, 209–214 (2005).

    CrossRef  Google Scholar 

  9. I.M. Longini, M.E. Halloran, A. Nizam & Y. Yang: Containing pandemic influenza with antiviral agents, Am. J. Epidem. 159, 623–633 (2004).

    CrossRef  Google Scholar 

  10. I.M. Longini, A. Nizam, S. Xu, K. Ungchusak, W. Hanshaoworakul, D.A.T. Cummings & M.E. Halloran: Containing pandemic influenza at the source, Science 309, 1083–1087 (2005).

    CrossRef  Google Scholar 

  11. M.J. Keeling & K.T.D. Eames: Networks and epidemic models, J. R. Soc. Interface 2, 295–307 (2006).

    CrossRef  Google Scholar 

  12. L.A. Meyers, B. Pourbohloul, M.E.J. Newman, D.M. Skowronski & R.C. Brunham: Network theory and SARS: Predicting outbreak diversity. J. Theor. Biol. 232, 71–81 (2005).

    CrossRef  MathSciNet  Google Scholar 

  13. A.L. Lloyd & R.M. May: Epidemiology: How viruses spread among computers and people, Science 292, 1316–1317 (2001).

    CrossRef  Google Scholar 

  14. M.E.J. Newman: The spread of epidemic disease on networks, Phys. Rev. E 66, 016128 (2002).

    CrossRef  MathSciNet  Google Scholar 

  15. M.E.J. Newman: The structure and function of complex networks. SIAM Rev. 45, 167–256 (2003).

    CrossRef  MATH  MathSciNet  Google Scholar 

  16. M.E.J. Newman, S.H. Strogatz & D.J. Watts: Random graphs with arbitrary degree distributions and their applications, Phys. Rev. E 64, 026118 (2001).

    CrossRef  Google Scholar 

  17. S. Riley, C. Fraser, C.A. Donnelly, A.C. Ghani, L.J. Abu-Raddad, A.J. Hedley, G.M. Leung, L.-M. Ho, T.-H. Lam, T.Q. Thach, P. Chau, K.-P. Chan, S.-V. Lo, P.-Y. Leung, T. Tsang, W. Ho, K.-H. Lee, E.M.C. Lau, N.M. Ferguson & R.M. Anderson: Transmission dynamics of the etiological agent of SARS in Hong Kong: Impact of public health interventions, Science 300, 1961–1966 (2003).

    CrossRef  Google Scholar 

  18. S.H. Strogatz: Exploring complex networks, Nature 410, 268–276 (2001).

    CrossRef  Google Scholar 

  19. D.J. Watts & S.H. Strogatz: Collective dynamics of ‘small world’ networks, Nature 393, 440–442 (1998).

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, 1984, Mathematics Road, Vancouver, BC, V6T 1Z2, Canada

    Fred Brauer

Authors
  1. Fred Brauer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of British Columbia, Vancouver, B.C. V6T 1Z2, Canada

    Fred Brauer

  2. Department of Mathematics and Statistics, University of Victoria, 3060 STN CSC, Victoria, B.C. V8W 3R4, Canada

    Pauline van den Driessche

  3. Center for Disease Modeling Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada

    Jianhong Wu

Rights and permissions

Reprints and Permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Brauer, F. (2008). An Introduction to Networks in Epidemic Modeling. In: Brauer, F., van den Driessche, P., Wu, J. (eds) Mathematical Epidemiology. Lecture Notes in Mathematics, vol 1945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78911-6_4

Download citation

  • .RIS
  • .ENW
  • .BIB
  • DOI: https://doi.org/10.1007/978-3-540-78911-6_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78910-9

  • Online ISBN: 978-3-540-78911-6

  • eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

Share this chapter

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature