Geodesic
Epidemic Spread in Networks: Existing Methods and Current Challenges
J. C. Miller1 ; I. Z. Kiss2
1 School of Mathematical Sciences, School of Biological Sciences, and Monash Academy for Cross & Interdisciplinary Mathematics, Monash University, VIC 3800, Australia
2 School of Mathematical and Physical Sciences, Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, UK
Mathematical modelling of natural phenomena, Tome 9 (2014) no. 2, pp. 4-42

Voir la notice de l'article provenant de la source EDP Sciences

We consider the spread of infectious disease through contact networks of Configuration Model type. We assume that the disease spreads through contacts and infected individuals recover into an immune state. We discuss a number of existing mathematical models used to investigate this system, and show relations between the underlying assumptions of the models. In the process we offer simplifications of some of the existing models. The distinctions between the underlying assumptions are subtle, and in many if not most cases this subtlety is irrelevant. Indeed, under appropriate conditions the models are equivalent. We compare the benefits and disadvantages of the different models, and discuss their application to other populations (e.g., clustered networks). Finally we discuss ongoing challenges for network-based epidemic modeling.
DOI : 10.1051/mmnp/20149202

J. C. Miller 1 ; I. Z. Kiss 2

1 School of Mathematical Sciences, School of Biological Sciences, and Monash Academy for Cross & Interdisciplinary Mathematics, Monash University, VIC 3800, Australia
2 School of Mathematical and Physical Sciences, Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, UK 
@article{10_1051_mmnp_20149202,
     author = {J. C. Miller and I. Z. Kiss},
     title = {Epidemic {Spread} in {Networks:} {Existing} {Methods} and {Current} {Challenges}},
     journal = {Mathematical modelling of natural phenomena},
     pages = {4--42},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2014},
     doi = {10.1051/mmnp/20149202},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20149202/}
}
TY  - JOUR
AU  - J. C. Miller
AU  - I. Z. Kiss
TI  - Epidemic Spread in Networks: Existing Methods and Current Challenges
JO  - Mathematical modelling of natural phenomena
PY  - 2014
SP  - 4
EP  - 42
VL  - 9
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20149202/
DO  - 10.1051/mmnp/20149202
LA  - en
ID  - 10_1051_mmnp_20149202
ER  - 
%0 Journal Article
%A J. C. Miller
%A I. Z. Kiss
%T Epidemic Spread in Networks: Existing Methods and Current Challenges
%J Mathematical modelling of natural phenomena
%D 2014
%P 4-42
%V 9
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20149202/
%R 10.1051/mmnp/20149202
%G en
%F 10_1051_mmnp_20149202
J. C. Miller; I. Z. Kiss. Epidemic Spread in Networks: Existing Methods and Current Challenges. Mathematical modelling of natural phenomena, Tome 9 (2014) no. 2, pp. 4-42. doi: 10.1051/mmnp/20149202

[1] R. M. Anderson, R. M. May. Infectious Diseases of Humans. Oxford University Press, Oxford (1991).

[2] F. Ball, P. Neal Mathematical Biosciences 2008 69 87

[3] M. Boguñá, C. Castellano, R. Pastor-Satorras Physical Review Letters 2013 068701

[4] T. Britton, M. Deijfen, A. Lageras, M. Lindholm Journal of Applied Probability 2008 743 756

[5] S. Chatterjee, R. Durrett The Annals of Probability 2009 2332 2356

[6] O. Diekmann, M. C. M. De Jong, J. A. J. Metz Journal of Applied Probability 1998 448 462

[7] K. Eames, M. Keeling Proceedings of the National Academy of Sciences 2002 13330 13335

[8] K. T. D. Eames Theoretical Population Biology 2008 104 111

[9] J. Gleeson, S. Melnik, A. Hackett Physical Review E 2010 066114

[10] D. M. Green, I. Z. Kiss Journal of Biological Dynamics 2010 431 445

[11] L. Hébert-Dufresne, O. Patterson-Lomba, G. M. Goerg, B. M. Althouse Physical Review Letters 2013 108103

[12] M. A. Van Der Hoef, M. Van Sint Annaland, N. Deen, J. Kuipers Annual Review of Fluid Mechanics 2008 47 70

[13] T. House, G. Davies, L. Danon, M. J. Keeling Bulletin of Mathematical Biology 2009 1693 1706

[14] T. House, M. Keeling Journal of The Royal Society Interface 2011 67 73

[15] E. T. Jaynes Physical review 1957 620

[16] B. Karrer, M. E. J. Newman Physical Review E 2010 066118

[17] M. J. Keeling Theoretical Population Biolology 2005 1 8

[18] E. Kenah, J. M. Robins Journal of Theoretical Biology 2007 706 722

[19] A. N. Kolmogorov. Dissipation of energy in locally isotropic turbulence. In Dokl. Akad. Nauk SSSR, volume 32, pages 16–18.

[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.

[21] M. Kretzschmar, R. White, M. Caraël AIDS (London, England) 2010 313

[22] J. Lindquist, J. Ma, P. Van Den Driessche, F. Willeboordse Journal of Mathematical Biology 2011 143 164

[23] R. M. May, R. M. Anderson Philosophical Transactions of the Royal Society London B 1988 565 607

[24] R. M. May, A. L. Lloyd Physical Review E 2001 066112

[25] E. S. Mcbryde Clinical infectious diseases 2009 685 686

[26] S. Melnik, A. Hackett, M. Porter, P. Mucha, J. Gleeson Physical Review E 2011 036112

[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.

[28] L. A. Meyers Bulletin of the American Mathematical Society 2007 63 86

[29] L. A. Meyers, B. Pourbohloul, M. E. J. Newman, D. M. Skowronski, R. C. Brunham Journal of Theoretical Biology 2005 71 81

[30] J. C. Miller Physical Review E 2009 020901(R)

[31] J. C. Miller Journal of The Royal Society Interface 2009 1121

[32] J. C. Miller Journal of Mathematical Biology 2011 349 358

[33] J. C. Miller Bulletin of Mathematical Biology 2012 2125 2141

[34] J. C. Miller, A. C. Slim, E. M. Volz Journal of the Royal Society Interface 2012 890 906

[35] J. C. Miller, E. M. Volz PloS One 2013 e69162

[36] J. C. Miller, E. M. Volz Journal of Mathematical Biology 2013 869 899

[37] M. Molloy, B. Reed Random Structures & Algorithms 1995 161 179

[38] Y. Moreno, R. Pastor-Satorras, A. Vespignani The European Physical Journal B-Condensed Matter and Complex Systems 2002 521 529

[39] M. E. J. Newman Physical Review E 2002 016128

[40] M. E. J. Newman SIAM Review 2003 167 256

[41] M. E. J. Newman Physical Review Letters 2009 58701

[42] P.-A. Noël, B. Davoudi, R. C. Brunham, L. J. Dubé, B. Pourbohloul Physical Review E 2009 026101

[43] R. Pastor-Satorras, A. Vespignani Physical Review Letters 2001 3200 3203

[44] L. F. Richardson, S. Chapman. Weather prediction by numerical process. Dover publications New York (1965).

[45] T. Rogers Journal of Statistical Mechanics: Theory and Experiment 2011 P05007

[46] P. Sagaut. Large eddy simulation for incompressible flows, volume 3. Springer Berlin (2000).

[47] M. Serrano, M. Boguñá Physical Review Letters 2006 088701

[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.

[49] E. M. Volz Journal of Mathematical Biology 2008 293 310

[50] E. M. Volz, J. C. Miller, A. Galvani, L. A. Meyers PLoS Comput Biol 2011 e1002042

Cité par Sources :