Free Access
Issue
Math. Model. Nat. Phenom.
Volume 9, Number 2, 2014
Epidemics models on networks
Page(s) 4 - 42
DOI https://doi.org/10.1051/mmnp/20149202
Published online 24 April 2014
  1. R. M. Anderson, R. M. May. Infectious Diseases of Humans. Oxford University Press, Oxford (1991). [Google Scholar]
  2. F. Ball, P. Neal. Network epidemic models with two levels of mixing. Mathematical Biosciences, 212 (2008), no. 1, 69–87. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  3. M. Boguñá, C. Castellano, R. Pastor-Satorras. Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks. Physical Review Letters, 111 (2013), no. 6, 068701, [Google Scholar]
  4. T. Britton, M. Deijfen, A. Lageras, M. Lindholm. Epidemics on random graphs with tunable clustering. Journal of Applied Probability, 45 (2008), no. 3, 743–756. [CrossRef] [Google Scholar]
  5. S. Chatterjee, R. Durrett. Contact processes on random graphs with power law degree distributions have critical value 0. The Annals of Probability, 37 (2009), no. 6, 2332–2356. [CrossRef] [MathSciNet] [Google Scholar]
  6. O. Diekmann, M. C. M. De Jong, J. A. J. Metz. A deterministic epidemic model taking account of repeated contacts between the same individuals. Journal of Applied Probability, 35 (1998), no. 2, 448–462. [CrossRef] [Google Scholar]
  7. K. Eames, M. Keeling. Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases. Proceedings of the National Academy of Sciences, 99 (2002), no. 20, 13330–13335. [Google Scholar]
  8. K. T. D. Eames. Modelling disease spread through random and regular contacts in clustered populations. Theoretical Population Biology, 73 (2008), no. 1, 104–111. [CrossRef] [PubMed] [Google Scholar]
  9. J. Gleeson, S. Melnik, A. Hackett. How clustering affects the bond percolation threshold in complex networks. Physical Review E, 81 (2010), no. 6, 066114. [CrossRef] [MathSciNet] [Google Scholar]
  10. D. M. Green, I. Z. Kiss. Large-scale properties of clustered networks: Implications for disease dynamics. Journal of Biological Dynamics, 4 (2010), no. 5, 431–445. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  11. L. Hébert-Dufresne, O. Patterson-Lomba, G. M. Goerg, B. M. Althouse. Pathogen mutation modeled by competition between site and bond percolation. Physical Review Letters, 110 (2013), no. 10, 108103. [CrossRef] [PubMed] [Google Scholar]
  12. M. A. van der Hoef, M. van Sint Annaland, N. Deen, J. Kuipers. Numerical simulation of dense gas-solid fluidized beds: A multiscale modeling strategy. Annual Review of Fluid Mechanics, 40 (2008) 47–70. [Google Scholar]
  13. T. House, G. Davies, L. Danon, M. J. Keeling. A motif-based approach to network epidemics. Bulletin of Mathematical Biology, 71 (2009), no. 7, 1693–1706. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  14. T. House, M. Keeling. Insights from unifying modern approximations to infections on networks. Journal of The Royal Society Interface, 8 (2011), no. 54, 67–73, ISSN 1742-5689. [CrossRef] [PubMed] [Google Scholar]
  15. E. T. Jaynes. Information theory and statistical mechanics. Physical review, 106 (1957), no. 4, 620. [CrossRef] [MathSciNet] [Google Scholar]
  16. B. Karrer, M. E. J. Newman. Random graphs containing arbitrary distributions of subgraphs. Physical Review E, 82 (2010), no. 6, 066118. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. J. Keeling. The implications of network structure for epidemic dynamics. Theoretical Population Biolology, 67 (2005), no. 1, 1–8. [CrossRef] [Google Scholar]
  18. E. Kenah, J. M. Robins. Network-based analysis of stochastic SIR epidemic models with random and proportionate mixing. Journal of Theoretical Biology, 249 (2007), no. 4, 706–722. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  19. A. N. Kolmogorov. Dissipation of energy in locally isotropic turbulence. In Dokl. Akad. Nauk SSSR, volume 32, pages 16–18. [Google Scholar]
  20. A. N. Kolmogorov. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. In Dokl. Akad. Nauk SSSR, volume 30, pages 299–303. [Google Scholar]
  21. M. Kretzschmar, R. White, M. Caraël. Concurrency is more complex than it seems. AIDS (London, England), 24 (2010), no. 2, 313. [CrossRef] [PubMed] [Google Scholar]
  22. J. Lindquist, J. Ma, P. van den Driessche, F. Willeboordse. Effective degree network disease models. Journal of Mathematical Biology, 62 (2011), no. 2, 143–164, ISSN 0303-6812. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  23. R. M. May, R. M. Anderson. The transmission dynamics of human immunodeficiency virus (HIV). Philosophical Transactions of the Royal Society London B, 321 (1988), no. 1207, 565–607. [Google Scholar]
  24. R. M. May, A. L. Lloyd. Infection dynamics on scale-free networks. Physical Review E, 64 (2001), no. 6, 066112. [Google Scholar]
  25. E. S. McBryde. Network structure can play a role in vaccination thresholds and herd immunity: a simulation using a network mathematical model. Clinical infectious diseases, 48 (2009), no. 5, 685–686. [CrossRef] [Google Scholar]
  26. S. Melnik, A. Hackett, M. Porter, P. Mucha, J. Gleeson. The unreasonable effectiveness of tree-based theory for networks with clustering. Physical Review E, 83 (2011), no. 3, 036112. [CrossRef] [MathSciNet] [Google Scholar]
  27. S. Melnick, M. A. Porter, P. J. Mucha, J. P. Gleeson. Dynamics on modular networks with heterogeneous correlations. Chaos, (In Press), available at http://arxiv.org/abs/1207.1809. [Google Scholar]
  28. L. A. Meyers. Contact network epidemiology: Bond percolation applied to infectious disease prediction and control. Bulletin of the American Mathematical Society, 44 (2007), no. 1, 63–86. [Google Scholar]
  29. L. A. Meyers, B. Pourbohloul, M. E. J. Newman, D. M. Skowronski, R. C. Brunham, Network theory and SARS: predicting outbreak diversity. Journal of Theoretical Biology, 232 (2005), no. 1, 71–81. [Google Scholar]
  30. J. C. Miller. Percolation and epidemics in random clustered networks. Physical Review E, 80 (2009), no. 2, 020901(R). [CrossRef] [MathSciNet] [Google Scholar]
  31. J. C. Miller. Spread of infectious disease through clustered populations. Journal of The Royal Society Interface, 6 (2009), no. 41, 1121. [CrossRef] [Google Scholar]
  32. J. C. Miller. A note on a paper by Erik Volz: SIR dynamics in random networks. Journal of Mathematical Biology, 62 (2011), no. 3, 349–358, ISSN 0303-6812. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  33. J. C. Miller. A note on the derivation of epidemic final sizes. Bulletin of Mathematical Biology, 74 (2012), no. 9, 2125–2141. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  34. J. C. Miller, A. C. Slim, E. M. Volz. Edge-based compartmental modelling for infectious disease spread. Journal of the Royal Society Interface, 9 (2012), no. 70, 890–906. [Google Scholar]
  35. J. C. Miller, E. M. Volz. Incorporating disease and population structure into models of SIR disease in contact networks. PloS One, 8 (2013), no. 8, e69162. [CrossRef] [PubMed] [Google Scholar]
  36. J. C. Miller, E. M. Volz. Model hierarchies in edge-based compartmental modeling for infectious disease spread. Journal of Mathematical Biology, 67 (2013), no. 4, 869–899. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  37. M. Molloy, B. Reed. A critical point for random graphs with a given degree sequence. Random Structures & Algorithms, 6 (1995), no. 2, 161–179. [Google Scholar]
  38. Y. Moreno, R. Pastor-Satorras, A. Vespignani. Epidemic outbreaks in complex heterogeneous networks. The European Physical Journal B-Condensed Matter and Complex Systems, 26 (2002), no. 4, 521–529. [Google Scholar]
  39. M. E. J. Newman. Spread of epidemic disease on networks. Physical Review E, 66 (2002), no. 1, 016128. [Google Scholar]
  40. M. E. J. Newman. The structure and function of complex networks. SIAM Review, 45 (2003), no. 2, 167–256. [CrossRef] [MathSciNet] [Google Scholar]
  41. M. E. J. Newman. Random graphs with clustering. Physical Review Letters, 103 (2009), no. 5, 58701. [Google Scholar]
  42. P.-A. Noël, B. Davoudi, R. C. Brunham, L. J. Dubé, B. Pourbohloul, Time evolution of disease spread on finite and infinite networks. Physical Review E, 79 (2009), no. 2, 026101. [CrossRef] [MathSciNet] [Google Scholar]
  43. R. Pastor-Satorras, A. Vespignani. Epidemic spreading in scale-free networks. Physical Review Letters, 86 (2001), no. 14, 3200–3203. [Google Scholar]
  44. L. F. Richardson, S. Chapman. Weather prediction by numerical process. Dover publications New York (1965). [Google Scholar]
  45. T. Rogers. Maximum-entropy moment-closure for stochastic systems on networks. Journal of Statistical Mechanics: Theory and Experiment, 2011 (2011), no. 05, P05007. [Google Scholar]
  46. P. Sagaut. Large eddy simulation for incompressible flows, volume 3. Springer Berlin (2000). [Google Scholar]
  47. M. Serrano, M. Boguñá. Percolation and epidemic thresholds in clustered networks. Physical Review Letters, 97 (2006), no. 8, 088701. [CrossRef] [PubMed] [Google Scholar]
  48. T. J. Taylor, I. Z. Kiss. Interdependency and hierarchy of exact and approximate epidemic models on networks. Journal of Mathematical Biology, (In Press), available at http://arxiv.org/abs/1212.3124. [Google Scholar]
  49. E. M. Volz. SIR dynamics in random networks with heterogeneous connectivity. Journal of Mathematical Biology, 56 (2008), no. 3, 293–310. [Google Scholar]
  50. E. M. Volz, J. C. Miller, A. Galvani, L. A. Meyers. Effects of heterogeneous and clustered contact patterns on infectious disease dynamics. PLoS Comput Biol, 7 (2011), no. 6, e1002042. [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.