Free Access
Issue |
Math. Model. Nat. Phenom.
Volume 9, Number 2, 2014
Epidemics models on networks
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Page(s) | 4 - 42 | |
DOI | https://doi.org/10.1051/mmnp/20149202 | |
Published online | 24 April 2014 |
- R. M. Anderson, R. M. May. Infectious Diseases of Humans. Oxford University Press, Oxford (1991). [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- E. T. Jaynes. Information theory and statistical mechanics. Physical review, 106 (1957), no. 4, 620. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- M. J. Keeling. The implications of network structure for epidemic dynamics. Theoretical Population Biolology, 67 (2005), no. 1, 1–8. [CrossRef] [Google Scholar]
- 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]
- A. N. Kolmogorov. Dissipation of energy in locally isotropic turbulence. In Dokl. Akad. Nauk SSSR, volume 32, pages 16–18. [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- R. M. May, A. L. Lloyd. Infection dynamics on scale-free networks. Physical Review E, 64 (2001), no. 6, 066112. [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- 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]
- J. C. Miller. Percolation and epidemics in random clustered networks. Physical Review E, 80 (2009), no. 2, 020901(R). [CrossRef] [MathSciNet] [Google Scholar]
- J. C. Miller. Spread of infectious disease through clustered populations. Journal of The Royal Society Interface, 6 (2009), no. 41, 1121. [CrossRef] [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- M. E. J. Newman. Spread of epidemic disease on networks. Physical Review E, 66 (2002), no. 1, 016128. [Google Scholar]
- M. E. J. Newman. The structure and function of complex networks. SIAM Review, 45 (2003), no. 2, 167–256. [CrossRef] [MathSciNet] [Google Scholar]
- M. E. J. Newman. Random graphs with clustering. Physical Review Letters, 103 (2009), no. 5, 58701. [Google Scholar]
- 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]
- R. Pastor-Satorras, A. Vespignani. Epidemic spreading in scale-free networks. Physical Review Letters, 86 (2001), no. 14, 3200–3203. [Google Scholar]
- L. F. Richardson, S. Chapman. Weather prediction by numerical process. Dover publications New York (1965). [Google Scholar]
- 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]
- P. Sagaut. Large eddy simulation for incompressible flows, volume 3. Springer Berlin (2000). [Google Scholar]
- M. Serrano, M. Boguñá. Percolation and epidemic thresholds in clustered networks. Physical Review Letters, 97 (2006), no. 8, 088701. [CrossRef] [PubMed] [Google Scholar]
- 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]
- E. M. Volz. SIR dynamics in random networks with heterogeneous connectivity. Journal of Mathematical Biology, 56 (2008), no. 3, 293–310. [Google Scholar]
- 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]
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