Free Access
Issue
Math. Model. Nat. Phenom.
Volume 9, Number 2, 2014
Epidemics models on networks
Page(s) 58 - 81
DOI https://doi.org/10.1051/mmnp/20149204
Published online 24 April 2014
  1. D.A. Rand. Correlation equations and pair approximations for spatial ecologies. CWI Quarterly., 12 (1999), 329–368. [Google Scholar]
  2. D.T. Gillespie. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem., 81 (1977), 2340–2361. [CrossRef] [Google Scholar]
  3. F. Ball, P. Neal. Network epidemic models with two levels of mixing. Math. Biosci., 212 (2008), 69–87. [Google Scholar]
  4. J.C. Miller. Epidemics on networks with large initial conditions or changing structure. Available at http://arxiv.org/abs/1208.3438. [Google Scholar]
  5. J.C. Miller. Spread of infectious disease through clustered populations. J. Roy. Soc. Interface., 6 (2009), 1121–1134. [Google Scholar]
  6. J.C. Miller, A.C. Slim, E.M. Volz. Edge-based compartmental modelling for infectious disease spread. J. Roy. Soc. Interface., 9 (2012), 890–906. [Google Scholar]
  7. J.C. Miller, E.M. Volz. Edge-based compartmental modeling with disease and population structure. Available at http://arxiv.org/abs/1106.6344. [Google Scholar]
  8. J. Joo, J.L. Lebowitz. Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation. Phys. Rev. E., 69 (2004), 066105. [CrossRef] [Google Scholar]
  9. J. Lindquist, J. Ma, P. Van den Driessche, F.H. Willeboordse. Effective degree network disease models. J. Math. Biol., 62 (2011), 143–164. [Google Scholar]
  10. K.B. Athreya, P.E. Ney, Branching processes. Dover Publications, Inc., Mineola, New York, 2008. [Google Scholar]
  11. K.J. Sharkey, C. Fernandez, K.L. Morgan, E. Peeler, M. Thrush, J.F. Turnbull, R.G. Bowers. Pair-level approximations to the spatio-temporal dynamics of epidemics on asymmetric contact networks. J. Math. Biol., 53 (2006), 61–85. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  12. K.T.D. Eames. Modelling disease spread through random and regular contacts in clustered populations. Theor. Popul. Biol., 73 (2008), 104–111. [Google Scholar]
  13. K.T.D. Eames, J.M. Read, W.J. Edmunds, Epidemic prediction and control in weighted networks. Epidemics., 1 (2009), 70–76. [CrossRef] [PubMed] [Google Scholar]
  14. K.T.D. Eames, M.J. Keeling. Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases. Proc. Natl. Acad. Sci. USA., 99 (2002), 13330–13335. [CrossRef] [Google Scholar]
  15. M. Deijfen. Epidemics and vaccination on weighted graphs. Math. Biosci., 232 (2011), 57–65. [Google Scholar]
  16. M.E.J. Newman. Spread of epidemic disease on networks. Phys. Rev. E., 66 (2002), 016128. [Google Scholar]
  17. M. Gilbert, A. Mitchell, D. Bourn, J. Mawdsley, R. Clifton-Hadley, W. Wint. Cattle movements and bovine tuberculosis in Great Britain. Nature., 435 (2005), 491–496. [CrossRef] [PubMed] [Google Scholar]
  18. M.J. Keeling. The effects of local spatial structure on epidemiological invasions. Proc. R. Soc. Lond. B., 266 (1999), 859–867. [CrossRef] [Google Scholar]
  19. M. Molloy, B. Reed. A critical point for random graphs with a given degree sequence. Random Struct Alg., 6 (1995), 161–180. [Google Scholar]
  20. P. Rattana, K.B. Blyuss, K.T.D. Eames, I.Z. Kiss. A class of pairwise models for epidemic dynamics on weighted networks. Accepted for publication in Bull. Math. Biol., (2012). [Google Scholar]
  21. R. Olinky, L. Stone. Unexpected epidemic thresholds in heterogeneous networks: The role of disease transmission. Phys. Rev. E., 70 (2004), 030902(R). [CrossRef] [Google Scholar]
  22. T. Britton, M. Deijfen, F. Liljeros. A weighted configuration model and inhomogeneous epidemics. J. Stat. Phys., 145 (2011), 1368-1384. [CrossRef] [MathSciNet] [Google Scholar]
  23. T. House, M.J. Keeling. Insights from unifying modern approximations to infections on networks. J. Roy. Soc. Interface., 8 (2011), 67–73. [Google Scholar]
  24. V. Marceau, P-A. Noël, L. Hébert-Dufresne, A. Allard, L.J. Dubé. Adaptive networks: coevolution of disease and topology. Phys. Rev. E., 82 (2010), 036116. [CrossRef] [MathSciNet] [Google Scholar]
  25. J. C. Miller, I. Z. Kiss. Epidemic Spread in Networks: Existing Methods and Current Challenges, Math. Model. Nat. Phenom. Vol. 9, No. 2, (2014), 4–42. [CrossRef] [EDP Sciences] [MathSciNet] [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.