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Decay rates for $1-d$ heat-wave planar networks
An epidemic model with nonlocal diffusion on networks
1. | University of Cergy-Pontoise, Department of Mathematics, UMR CNRS 8088, Cergy-Pontoise, F-95000 |
2. | University of Cergy-Pontoise, Department of Mathematics, UMR CNRS 8088, F-95000 Cergy-Pontoise, France |
References:
[1] |
V. Colizza, R. Pastor-Sattoras and A. Vespignani, Reaction-diffusion processes and meta-population models in heterogeneous networks, Nat. Phys., 3 (2007), 276-282. |
[2] |
V. Colizza and A. Vespignani, Invasion threshold in heterogeneous metapopulation networks, Phys. Rev. Lett., 99 (2007), 148701.
doi: 10.1103/PhysRevLett.99.148701. |
[3] |
V. Colizza and A. Vespignani, Epidemic modeling in metapopulation systems with heterogeneous coupling pattern: Theory and simulations, J. Theor. Biol., 251 (2008), 450-467.
doi: 10.1016/j.jtbi.2007.11.028. |
[4] |
O. Diekmann and J. A. P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, Wiley, New York, 2000. |
[5] |
S. N. Dorogotsev and J. F. F. Mendes, Scaling properties of scale-free evolving networks: Continuous approach, Phys. Rev. E, 63 (2001), 056125. |
[6] |
S. N. Dorogotsev and J. F. F. Mendes, Evolution of networks, Adv. Phys., 51 (2002), 1079. |
[7] |
I. Hanski, A practical model of metapopulation dynamics, J. Animal Ecology, 63 (1994), 151-162.
doi: 10.2307/5591. |
[8] |
I. Hanski, Metapopulation dynamics, Metapopulation Biology, (1997), 69-91.
doi: 10.1016/B978-012323445-2/50007-9. |
[9] |
H. W. Hethcote, The mathematics of infectious diseases, SIAM Review, 42 (2000), 599-653.
doi: 10.1137/S0036144500371907. |
[10] |
D. Juher, J. Ripoll and J. Saldana, Analysis and monte carlo simulations of a model for the spread of infectious diseases in heterogeneous metapopulation, Phys. Rev. E, 80 (2009), 041920, 9pp.
doi: 10.1103/PhysRevE.80.041920. |
[11] |
M. J. Keeling and K. T. D. Eames, Networks and epidemic models, J. R. Soc. Interface, 2 (2005), 295-307.
doi: 10.1098/rsif.2005.0051. |
[12] |
R. Levins, Some demographic and genetic consequences of environmental heterogeneity for biological control, Bull. Entomology Soc. of America, 71 (1969), 237-240.
doi: 10.1093/besa/15.3.237. |
[13] |
E. Logak and I. Passat, A nonlocal model for epidemics on networks in the case of nonlimited transmission, preprint. |
[14] |
M. E. J. Newman, The structure and function of complex networks, SIAM Rev., 45 (2003), 167-256.
doi: 10.1137/S003614450342480. |
[15] |
R. Pastor-Sattoras, C. Castellano, P. Van Mieghem and A. Vespignani, Epidemic processes in complex networks, Rev. Mod. Phys., 87 (2015), 925-979.
doi: 10.1103/RevModPhys.87.925. |
[16] |
R. Pastor-Sattoras and A. Vespignani, Epidemic spreading in scale-free networks, Phys. Rev. Lett., 86 (2001), 3200.
doi: 10.1103/PhysRevLett.86.3200. |
[17] |
J. Saldana, Continous-time formulation of reaction-diffusion processes on heterogeneous metapopulations, Phys. Rev. E, 78 (2008), 012902. |
[18] |
J. Saldana, Analysis and Monte-Carlo simulations of a model for spread of infectious diseases in heterogeneous metapopulations, Phys. Rev. E, 80 (2009), 041920, 9pp.
doi: 10.1103/PhysRevE.80.041920. |
[19] |
J. Saldana, Modelling the spread of infectious diseases in complex metapopulations, Math. Model. Nat. Phenom., 5 (2010), 22-37.
doi: 10.1051/mmnp/20105602. |
show all references
References:
[1] |
V. Colizza, R. Pastor-Sattoras and A. Vespignani, Reaction-diffusion processes and meta-population models in heterogeneous networks, Nat. Phys., 3 (2007), 276-282. |
[2] |
V. Colizza and A. Vespignani, Invasion threshold in heterogeneous metapopulation networks, Phys. Rev. Lett., 99 (2007), 148701.
doi: 10.1103/PhysRevLett.99.148701. |
[3] |
V. Colizza and A. Vespignani, Epidemic modeling in metapopulation systems with heterogeneous coupling pattern: Theory and simulations, J. Theor. Biol., 251 (2008), 450-467.
doi: 10.1016/j.jtbi.2007.11.028. |
[4] |
O. Diekmann and J. A. P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, Wiley, New York, 2000. |
[5] |
S. N. Dorogotsev and J. F. F. Mendes, Scaling properties of scale-free evolving networks: Continuous approach, Phys. Rev. E, 63 (2001), 056125. |
[6] |
S. N. Dorogotsev and J. F. F. Mendes, Evolution of networks, Adv. Phys., 51 (2002), 1079. |
[7] |
I. Hanski, A practical model of metapopulation dynamics, J. Animal Ecology, 63 (1994), 151-162.
doi: 10.2307/5591. |
[8] |
I. Hanski, Metapopulation dynamics, Metapopulation Biology, (1997), 69-91.
doi: 10.1016/B978-012323445-2/50007-9. |
[9] |
H. W. Hethcote, The mathematics of infectious diseases, SIAM Review, 42 (2000), 599-653.
doi: 10.1137/S0036144500371907. |
[10] |
D. Juher, J. Ripoll and J. Saldana, Analysis and monte carlo simulations of a model for the spread of infectious diseases in heterogeneous metapopulation, Phys. Rev. E, 80 (2009), 041920, 9pp.
doi: 10.1103/PhysRevE.80.041920. |
[11] |
M. J. Keeling and K. T. D. Eames, Networks and epidemic models, J. R. Soc. Interface, 2 (2005), 295-307.
doi: 10.1098/rsif.2005.0051. |
[12] |
R. Levins, Some demographic and genetic consequences of environmental heterogeneity for biological control, Bull. Entomology Soc. of America, 71 (1969), 237-240.
doi: 10.1093/besa/15.3.237. |
[13] |
E. Logak and I. Passat, A nonlocal model for epidemics on networks in the case of nonlimited transmission, preprint. |
[14] |
M. E. J. Newman, The structure and function of complex networks, SIAM Rev., 45 (2003), 167-256.
doi: 10.1137/S003614450342480. |
[15] |
R. Pastor-Sattoras, C. Castellano, P. Van Mieghem and A. Vespignani, Epidemic processes in complex networks, Rev. Mod. Phys., 87 (2015), 925-979.
doi: 10.1103/RevModPhys.87.925. |
[16] |
R. Pastor-Sattoras and A. Vespignani, Epidemic spreading in scale-free networks, Phys. Rev. Lett., 86 (2001), 3200.
doi: 10.1103/PhysRevLett.86.3200. |
[17] |
J. Saldana, Continous-time formulation of reaction-diffusion processes on heterogeneous metapopulations, Phys. Rev. E, 78 (2008), 012902. |
[18] |
J. Saldana, Analysis and Monte-Carlo simulations of a model for spread of infectious diseases in heterogeneous metapopulations, Phys. Rev. E, 80 (2009), 041920, 9pp.
doi: 10.1103/PhysRevE.80.041920. |
[19] |
J. Saldana, Modelling the spread of infectious diseases in complex metapopulations, Math. Model. Nat. Phenom., 5 (2010), 22-37.
doi: 10.1051/mmnp/20105602. |
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