EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 9 / No 2 (2014) Math. Model. Nat. Phenom., 9 2 (2014) 153-160 References
Free Access
Issue
Math. Model. Nat. Phenom.
Volume 9, Number 2, 2014
Epidemics models on networks
Page(s) 153 - 160
DOI https://doi.org/10.1051/mmnp/20149210
Published online 24 April 2014
  1. R. M. Anderson, R. M. May. Infectious Diseases of Humans. Oxford University Press, Oxford, 1991. [Google Scholar]
  2. H. Andersson, T. Britton. Stochastic Epidemic Models and Their Statistical Analysis, volume 151 of Springer Lectures Notes in Statistics. Springer, Berlin, 2000. [Google Scholar]
  3. S. Bansal, B. T. Grenfell, L. A. Meyers. When individual behaviour matters: homogeneous and network models in epidemiology. Journal of the Royal Society Interface, 4 (2007), no. 16, 879–91. [CrossRef] [PubMed] [Google Scholar]
  4. A. L. Barabási, R. Albert. Emergence of scaling in random networks. Science, 286 (1999), no. 5439, 509–512. [NASA ADS] [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  5. N. Berger, C. Borgs, J. T. Chayes, A. Saberi. On the spread of viruses on the internet. In Proceedings of the 16th Symposium on Discrete Algorithms, 2005. [Google Scholar]
  6. C. Castellano,R. Pastor-Satorras. Thresholds for epidemic spreading in networks. Physical Review Letters, 105 (2010), no. 21, 218701. [Google Scholar]
  7. A. Clauset, C. R. Shalizi, M. E. J. Newman. Power-law distributions in empirical data. SIAM Review, 51 (2009), no. 4, 661–703. [Google Scholar]
  8. L. Danon, A. P. Ford, T. House, C. P. Jewell, M. J. Keeling, G. O. Roberts, J. V. Ross, and M. C. Vernon. Networks and the epidemiology of infectious disease. Interdisciplinary Perspectives on Infectious Diseases, (2011), 1–28. [Google Scholar]
  9. L. Danon, T. House, M. J. Keeling, J. M. Read. Social encounter networks: collective properties and disease transmission. Journal of the Royal Society Interface, 9 (2012), no. 76, 2826–2833. [CrossRef] [Google Scholar]
  10. O. Diekmann, J. A. P. Heesterbeek. Mathematical epidemiology of infectious diseases: Model building, analysis and interpretation. John Wiley & Sons Ltd., 2000. [Google Scholar]
  11. O. Diekmann, J. A. P. Heesterbeek, J. A. J. Metz. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology, 28 (1990), no. 4, 365–382. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  12. R. Durrett. Random Graph Dynamics. Cambridge University Press, 2007. [Google Scholar]
  13. S. Eubank, H. Guclu, V. S. A. Kumar, M. V. Marathe, A. Srinivasan, Z. Toroczkai, N. Wang. Modelling disease outbreaks in realistic urban social networks. Nature, 429 (2004), no. 6988, 180–184. [CrossRef] [PubMed] [Google Scholar]
  14. G. R. Grimmett, D. R. Stirzaker. Probability and Random Processes. Oxford University Press, 3rd edition, 2001. [Google Scholar]
  15. T. House, J. V. Ross, D. Sirl. How big is an outbreak likely to be? Methods for epidemic final-size calculation. Proceedings of the Royal Society A, 469 (2013), no. 2150, 20120436. [CrossRef] [Google Scholar]
  16. M. J. Keeling, P. Rohani. Modeling Infectious Diseases in Humans and Animals. Princeton University Press, New Jersey, 2007. [Google Scholar]
  17. I. Z. Kiss, D. M. Green, R. R. Kao. The effect of contact heterogeneity and multiple routes of transmission on final epidemic size. Mathematical Biosciences, 203 (2006), no. 1, 124–36. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  18. T. G. Kurtz. Solutions of ordinary differential equations as limits of pure jump Markov processes. Journal of Applied Probability, 7 (1970), no. 1, 49–58. [CrossRef] [MathSciNet] [Google Scholar]
  19. T. G. Kurtz. Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. Journal of Applied Probability, 8 (1971), no. 2, 344–356. [CrossRef] [MathSciNet] [Google Scholar]
  20. R. M. May, R. M. Anderson. The transmission dynamics of human immunodeficiency virus (HIV). Philosophical Transactions of the Royal Society of London Series B, 321 (1988), no. 1207, 565–607. [CrossRef] [Google Scholar]
  21. R. M. May, A. L. Lloyd. Infection dynamics on scale-free networks. Physical Review E, 64 (2001), 066112. [Google Scholar]
  22. R. Pastor-Satorras, A. Vespignani. Epidemic dynamics and endemic states in complex networks. Physical Review E, 63 (2001), 066117. [Google Scholar]
  23. R. Pastor-Satorras, A. Vespignani. Epidemic dynamics in finite size scale-free networks. Physical Review E, 65 (2002), no. 3, 035108. [CrossRef] [Google Scholar]
  24. A. Schneeberger, C. H. Mercer, S. A. J. Gregson, N. M. Ferguson, C. A. Nyamukapa, R. M. Anderson, A. M. Johnson, G. P. Garnett. Scale-free networks and sexually transmitted diseases: a description of observed patterns of sexual contacts in Britain and Zimbabwe. Sexually Transmitted Diseases, 31 (2004), no. 6, 380–7. [CrossRef] [PubMed] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.