메뉴 건너뛰기




Volumn 9, Issue 2, 2014, Pages 4-42

Epidemic spread in networks: Existing methods and current challenges

Author keywords

Configuration model networks; Edge based compartmental models; Effective degree; Epidemic; Network; Pairwise; SIR disease

Indexed keywords

MATHEMATICAL MODELS; NETWORKS (CIRCUITS);

EID: 84902210339     PISSN: 09735348     EISSN: 17606101     Source Type: Journal    
DOI: 10.1051/mmnp/20149202     Document Type: Article
Times cited : (75)

References (50)
  • 2
    • 39649125153 scopus 로고    scopus 로고
    • Network epidemic models with two levels of mixing
    • F. Ball, P. Neal. Network epidemic models with two levels of mixing. Mathematical Biosciences, 212 (2008), no. 1, 69-87.
    • (2008) Mathematical Biosciences , vol.212 , Issue.1 , pp. 69-87
    • Ball, F.1    Neal, P.2
  • 3
    • 84881503536 scopus 로고    scopus 로고
    • Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks
    • 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
    • (2013) Physical Review Letters , vol.111 , Issue.6 , pp. 068701
    • Boguñá, M.1    Castellano, C.2    Pastor-Satorras, R.3
  • 5
    • 77049093438 scopus 로고    scopus 로고
    • Contact processes on random graphs with power law degree distributions have critical value 0
    • 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.
    • (2009) The Annals of Probability , vol.37 , Issue.6 , pp. 2332-2356
    • Chatterjee, S.1    Durrett, R.2
  • 6
    • 0032392720 scopus 로고    scopus 로고
    • A deterministic epidemic model taking account of repeated contacts between the same individuals
    • 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.
    • (1998) Journal of Applied Probability , vol.35 , Issue.2 , pp. 448-462
    • Diekmann, O.1    De Jong, M.C.M.2    Metz, J.A.J.3
  • 7
    • 0036790984 scopus 로고    scopus 로고
    • Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases
    • 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.
    • (2002) Proceedings of the National Academy of Sciences , vol.99 , Issue.20 , pp. 13330-13335
    • Eames, K.1    Keeling, M.2
  • 8
    • 37849013474 scopus 로고    scopus 로고
    • Modelling disease spread through random and regular contacts in clustered populations
    • K. T. D. Eames. Modelling disease spread through random and regular contacts in clustered populations. Theoretical Population Biology, 73 (2008), no. 1, 104-111.
    • (2008) Theoretical Population Biology , vol.73 , Issue.1 , pp. 104-111
    • Eames, K.T.D.1
  • 9
    • 77953973695 scopus 로고    scopus 로고
    • How clustering affects the bond percolation threshold in complex networks
    • J. Gleeson, S. Melnik, A. Hackett. How clustering affects the bond percolation threshold in complex networks. Physical Review E, 81 (2010), no. 6, 066114.
    • (2010) Physical Review e , vol.81 , Issue.6 , pp. 066114
    • Gleeson, J.1    Melnik, S.2    Hackett, A.3
  • 10
    • 77950796114 scopus 로고    scopus 로고
    • Large-scale properties of clustered networks: Implications for disease dynamics
    • 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.
    • (2010) Journal of Biological Dynamics , vol.4 , Issue.5 , pp. 431-445
    • Green, D.M.1    Kiss, I.Z.2
  • 12
    • 39049113048 scopus 로고    scopus 로고
    • Numerical simulation of dense gas-solid fluidized beds: A multiscale modeling strategy
    • DOI 10.1146/annurev.fluid.40.111406.102130
    • 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. (Pubitemid 351234692)
    • (2008) Annual Review of Fluid Mechanics , vol.40 , pp. 47-70
    • Van Der Hoef, M.A.1    Van Sint Annaland, M.2    Deen, N.G.3    Kuipers, J.A.M.4
  • 14
    • 78650846890 scopus 로고    scopus 로고
    • Insights from unifying modern approximations to infections on networks
    • ISSN 1742-5689
    • 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.
    • (2011) Journal of the Royal Society Interface , vol.8 , Issue.54 , pp. 67-73
    • House, T.1    Keeling, M.2
  • 15
    • 11944266539 scopus 로고
    • Information theory and statistical mechanics
    • E. T. Jaynes. Information theory and statistical mechanics. Physical review, 106 (1957), no. 4, 620.
    • (1957) Physical Review , vol.106 , Issue.4 , pp. 620
    • Jaynes, E.T.1
  • 16
    • 78651444167 scopus 로고    scopus 로고
    • Random graphs containing arbitrary distributions of subgraphs
    • B. Karrer, M. E. J. Newman. Random graphs containing arbitrary distributions of subgraphs. Physical Review E, 82 (2010), no. 6, 066118.
    • (2010) Physical Review e , vol.82 , Issue.6 , pp. 066118
    • Karrer, B.1    Newman, M.E.J.2
  • 17
    • 11844262657 scopus 로고    scopus 로고
    • The implications of network structure for epidemic dynamics
    • M. J. Keeling. The implications of network structure for epidemic dynamics. Theoretical Population Biolology, 67 (2005), no. 1, 1-8.
    • (2005) Theoretical Population Biolology , vol.67 , Issue.1 , pp. 1-8
    • Keeling, M.J.1
  • 18
    • 36249028724 scopus 로고    scopus 로고
    • Network-based analysis of stochastic SIR epidemic models with random and proportionate mixing
    • DOI 10.1016/j.jtbi.2007.09.011, PII S0022519307004304
    • 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. (Pubitemid 350122606)
    • (2007) Journal of Theoretical Biology , vol.249 , Issue.4 , pp. 706-722
    • Kenah, E.1    Robins, J.M.2
  • 19
    • 0002385458 scopus 로고    scopus 로고
    • Dissipation of energy in locally isotropic turbulence
    • A. N. Kolmogorov. Dissipation of energy in locally isotropic turbulence. In Dokl. Akad. Nauk SSSR, volume 32, pages 16-18.
    • Dokl. Akad. Nauk SSSR , vol.32 , pp. 16-18
    • Kolmogorov, A.N.1
  • 20
    • 0002346018 scopus 로고    scopus 로고
    • The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers
    • 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.
    • Dokl. Akad. Nauk SSSR , vol.30 , pp. 299-303
    • Kolmogorov, A.N.1
  • 21
    • 74249096639 scopus 로고    scopus 로고
    • Concurrency is more complex than it seems
    • London, England
    • M. Kretzschmar, R. White, M. Caraël. Concurrency is more complex than it seems. AIDS (London, England), 24 (2010), no. 2, 313.
    • (2010) AIDS , vol.24 , Issue.2 , pp. 313
    • Kretzschmar, M.1    White, R.2    Caraël, M.3
  • 24
    • 0035689341 scopus 로고    scopus 로고
    • Infection dynamics on scale-free networks
    • R. M. May, A. L. Lloyd. Infection dynamics on scale-free networks. Physical Review E, 64 (2001), no. 6, 066112.
    • (2001) Physical Review e , vol.64 , Issue.6 , pp. 066112
    • May, R.M.1    Lloyd, A.L.2
  • 25
    • 60549102355 scopus 로고    scopus 로고
    • Network structure can play a role in vaccination thresholds and herd immunity: A simulation using a network mathematical model
    • 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.
    • (2009) Clinical Infectious Diseases , vol.48 , Issue.5 , pp. 685-686
    • McBryde, E.S.1
  • 26
    • 79961057855 scopus 로고    scopus 로고
    • The unreasonable effectiveness of tree-based theory for networks with clustering
    • 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.
    • (2011) Physical Review e , vol.83 , Issue.3 , pp. 036112
    • Melnik, S.1    Hackett, A.2    Porter, M.3    Mucha, P.4    Gleeson, J.5
  • 27
    • 84902212689 scopus 로고    scopus 로고
    • Dynamics on modular networks with heterogeneous correlations
    • In Press, available at
    • 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.
    • Chaos
    • Melnick, S.1    Porter, M.A.2    Mucha, P.J.3    Gleeson, J.P.4
  • 28
    • 34547299719 scopus 로고    scopus 로고
    • Contact network epidemiology: Bond percolation applied to infectious disease prediction and control
    • 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.
    • (2007) Bulletin of the American Mathematical Society , vol.44 , Issue.1 , pp. 63-86
    • Meyers, L.A.1
  • 30
    • 77549087023 scopus 로고    scopus 로고
    • Percolation and epidemics in random clustered networks
    • J. C. Miller. Percolation and epidemics in random clustered networks. Physical Review E, 80 (2009), no. 2, 020901R.
    • (2009) Physical Review e , vol.80 , Issue.2
    • Miller, J.C.1
  • 31
    • 69249147221 scopus 로고    scopus 로고
    • Spread of infectious disease through clustered populations
    • J. C. Miller. Spread of infectious disease through clustered populations. Journal of The Royal Society Interface, 6 (2009), no. 41, 1121.
    • (2009) Journal of the Royal Society Interface , vol.6 , Issue.41 , pp. 1121
    • Miller, J.C.1
  • 32
    • 79951515510 scopus 로고    scopus 로고
    • A note on a paper by Erik Volz: SIR dynamics in random networks
    • ISSN 0303-6812
    • 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.
    • (2011) Journal of Mathematical Biology , vol.62 , Issue.3 , pp. 349-358
    • Miller, J.C.1
  • 33
    • 84864775325 scopus 로고    scopus 로고
    • A note on the derivation of epidemic final sizes
    • J. C. Miller. A note on the derivation of epidemic final sizes. Bulletin of Mathematical Biology, 74 (2012), no. 9, 2125-2141.
    • (2012) Bulletin of Mathematical Biology , vol.74 , Issue.9 , pp. 2125-2141
    • Miller, J.C.1
  • 34
    • 84859089658 scopus 로고    scopus 로고
    • Edge-based compartmental modelling for infectious disease spread
    • 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.
    • (2012) Journal of the Royal Society Interface , vol.9 , Issue.70 , pp. 890-906
    • Miller, J.C.1    Slim, A.C.2    Volz, E.M.3
  • 35
    • 84899041710 scopus 로고    scopus 로고
    • Incorporating disease and population structure into models of SIR disease in contact networks
    • 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.
    • (2013) PloS One , vol.8 , Issue.8
    • Miller, J.C.1    Volz, E.M.2
  • 36
    • 84883758821 scopus 로고    scopus 로고
    • Model hierarchies in edge-based compartmental modeling for infectious disease spread
    • 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.
    • (2013) Journal of Mathematical Biology , vol.67 , Issue.4 , pp. 869-899
    • Miller, J.C.1    Volz, E.M.2
  • 37
    • 84990671447 scopus 로고
    • A critical point for random graphs with a given degree sequence
    • M. Molloy, B. Reed. A critical point for random graphs with a given degree sequence. Random Structures & Algorithms, 6 (1995), no. 2, 161-179.
    • (1995) Random Structures & Algorithms , vol.6 , Issue.2 , pp. 161-179
    • Molloy, M.1    Reed, B.2
  • 38
    • 0000494582 scopus 로고    scopus 로고
    • Epidemic outbreaks in complex heterogeneous networks
    • DOI 10.1007/s10051-002-8996-y
    • 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. (Pubitemid 135698247)
    • (2002) European Physical Journal B , vol.26 , Issue.4 , pp. 521-529
    • Moreno, Y.1    Pastor-Satorras, R.2    Vespignani, A.3
  • 39
    • 41349106348 scopus 로고    scopus 로고
    • Spread of epidemic disease on networks
    • M. E. J. Newman. Spread of epidemic disease on networks. Physical Review E, 66 (2002), no. 1, 016128.
    • (2002) Physical Review e , vol.66 , Issue.1 , pp. 016128
    • Newman, M.E.J.1
  • 40
    • 0038718854 scopus 로고    scopus 로고
    • The structure and function of complex networks
    • M. E. J. Newman. The structure and function of complex networks. SIAM Review, 45 (2003), no. 2, 167-256.
    • (2003) SIAM Review , vol.45 , Issue.2 , pp. 167-256
    • Newman, M.E.J.1
  • 41
    • 68649124583 scopus 로고    scopus 로고
    • Random graphs with clustering
    • M. E. J. Newman. Random graphs with clustering. Physical Review Letters, 103 (2009), no. 5, 58701.
    • (2009) Physical Review Letters , vol.103 , Issue.5 , pp. 58701
    • Newman, M.E.J.1
  • 43
    • 0035794256 scopus 로고    scopus 로고
    • Epidemic spreading in scale-free networks
    • DOI 10.1103/PhysRevLett.86.3200
    • R. Pastor-Satorras, A. Vespignani. Epidemic spreading in scale-free networks. Physical Review Letters, 86 (2001), no. 14, 3200-3203. (Pubitemid 32317894)
    • (2001) Physical Review Letters , vol.86 , Issue.14 , pp. 3200-3203
    • Pastor-Satorras, R.1    Vespignani, A.2
  • 45
    • 79958045826 scopus 로고    scopus 로고
    • Maximum-entropy moment-closure for stochastic systems on networks
    • T. Rogers. Maximum-entropy moment-closure for stochastic systems on networks. Journal of Statistical Mechanics: Theory and Experiment, 2011 (2011), no. 5, P05007.
    • (2011) Journal of Statistical Mechanics: Theory and Experiment , vol.2011 , Issue.5
    • Rogers, T.1
  • 47
    • 33747656394 scopus 로고    scopus 로고
    • Percolation and epidemic thresholds in clustered networks
    • M. Serrano, M. Boguñá. Percolation and epidemic thresholds in clustered networks. Physical Review Letters, 97 (2006), no. 8, 088701.
    • (2006) Physical Review Letters , vol.97 , Issue.8 , pp. 088701
    • Serrano, M.1    Boguñá, M.2
  • 48
    • 84902176919 scopus 로고    scopus 로고
    • Interdependency and hierarchy of exact and approximate epidemic models on networks
    • In Press, available at
    • 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.
    • Journal of Mathematical Biology
    • Taylor, T.J.1    Kiss, I.Z.2
  • 49
    • 36749049140 scopus 로고    scopus 로고
    • SIR dynamics in random networks with heterogeneous connectivity
    • E. M. Volz. SIR dynamics in random networks with heterogeneous connectivity. Journal of Mathematical Biology, 56 (2008), no. 3, 293-310.
    • (2008) Journal of Mathematical Biology , vol.56 , Issue.3 , pp. 293-310
    • Volz, E.M.1
  • 50
    • 79959857702 scopus 로고    scopus 로고
    • Effects of heterogeneous and clustered contact patterns on infectious disease dynamics
    • 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.
    • (2011) PLoS Comput Biol , vol.7 , Issue.6 , pp. 1002042
    • Volz, E.M.1    Miller, J.C.2    Galvani, A.3    Meyers, L.A.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.