Epidemics in networks of spatially correlated three-dimensional root-branching structures

Journal of the Royal Society Interface

Volumn 8, Issue 56, 2011, Pages 423-434

  Handford, T P ^a   Perez Reche F J ^a   Taraskin, S N ^a   Costa, L Da F ^b   Miazaki, M ^b   Neri, F M ^a   Gilligan, C A ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Correlated percolation; Epidemic outbreaks; Heterogeneity; Root systems

Indexed keywords

GEOLOGIC MODELS; NUMERICAL METHODS; SOLVENTS; THREE DIMENSIONAL;

ANALYTICAL AND NUMERICAL METHODS; BOND PERCOLATION; BRANCHING STRUCTURES; CORRELATED PERCOLATION; DEGREE OF BRANCHING; DIGITIZED IMAGES; EPIDEMIC OUTBREAKS; EPIDEMIOLOGICAL MODELS; HETEROGENEITY; HOMOGENEOUS SYSTEM; MORPHOLOGICAL COMPLEXITY; PLANT ROOTS; ROOT SYSTEM; SOIL-BORNE PATHOGENS; TRANSMISSION EFFICIENCY;

EPIDEMIOLOGY;

ANISOTROPY; ARTICLE; CONTROLLED STUDY; DISEASE TRANSMISSION; ECOSYSTEM RESILIENCE; EPIDEMIC; NONHUMAN; PATHOGENESIS; PLANT ROOT; SOIL POLLUTANT; SPATIAL AUTOCORRELATION ANALYSIS; SPATIAL SOIL VARIABILITY;

EID: 79251510855     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2010.0296     Document Type: Article

References (34)

1. Nâsell, I. 2002 Stochastic models of some endemic infections. Math. Biosci. 179, 1-19. (doi:10.1016/S0025-5564(02)00098-6)
2. Pastor-Satorras, R. & Vespignani, A. 2003 Epidemics and immunization in scale-free networks. In Handbook of graphs and networks: from the genome to the internet (eds S. Bornholdt & H. G. Schuster). Berlin, Germany: Wiley-VCH.
3. Pastor-Satorras, R. & Vespignani, A. 2004 Evolution and structure of the internet: a statistical physics approach. Cambridge, UK: Cambridge University Press.
4. Liggett, T. M. 1985 Interacting particle systems. New York, NY: Springer.
5. Marro, J. & Dickman, R. 1999 Nonequilibrium phase transitions in lattice models. Cambridge, UK: Cambridge University Press.
6. Diekmann, O. & Heesterbeek, J. 2000 Mathematical epidemiology of infectious diseases: model building, analysis and interpretation. New York, NY: Wiley.
7. Murray, J. D. 2002 Mathematical biology. I. An introduction, 3rd edn. Berlin, Germany: Springer.
8. Keeling, M. J. & Rohani, P. 2007 Modeling infectious diseases in humans and animals. Princeton, NJ: Princeton University Press.
9. Jackson, M. 2008 Social and economic networks. Princeton, NJ: Princeton University Press.
10. Dybiec, B., Kleczkowski, A. & Gilligan, C. A. 2004 Controlling disease spread on networks with incomplete knowledge. Phys. Rev. E 70, 066145. (doi:10.1103/Phys-RevE.70.066145)
11. Hinrichsen, H. 2000 Non-equilibrium critical phenomena and phase transitions into absorbing states. Adv. Phys. 49, 815. (doi:10.1080/ 00018730050198152)
12. Ódor, G. 2004 Universality classes in nonequilibrium lattice systems. Rev. Mod. Phys. 76, 663. (doi:10.1103/RevModPhys.76.663)
13. Pérez-Reche, F. J., Taraskin, S. N., Costa, L. da F., Neri, F. M. & Gilligan, C. A. 2010 Complexity and anisotropy in host morphology make populations less susceptible to epidemic outbreak. J. R. Soc. Interface 7, 1083-1092. (doi:10.1098/rsif.2009.0475)
14. Sander, L., Warren, C. P., Sokolov, I. M., Simon, C. & Koopman, J. 2002 Percolation on heterogeneous networks as a model for epidemics. Math. Biosci. 180, 293-305. (doi:10.1016/S0025-5564(02)00117-7)
15. Gilligan, C. A., Brassett, P. R. & Campbell, A. 1994 Modeling of early infection of cereal roots by the take-all fungus: a detailed mechanistic simulator. New Phytol. 128, 515-537. (doi:10.1111/j.1469-8137.1994.tb02999.x)
16. Hornby, D. 1990 Biological control of soil-borne plant pathogens. Wallingford, UK: CAB International.
17. Gilligan, C. A. 1990 Mathematical modelling and analysis of soilborne pathogens. In Epidemics of plant diseases (ed. J. Kranz), pp. 96-142. Heidelberg, Germany: Springer.
18. Gilligan, C. A. 2002 An epidemiological framework for disease management. Adv. Bot. Res. 38, 1-64. (doi:10.1016/S0065-2296(02)38027-3)
19. Bailey, D., Otten, W. & Gilligan, C. A. 2000 Saprotrophic invasion by the soil-borne fungal plant pathogen Rhizoctonia solani and percolation thresholds. New Phytol. 146, 535-544. (doi:10.1046/j.1469-8137.2000.00660.x) (Pubitemid 30441923)
20. Grassberger, P. 1983 On the critical behavior of the general epidemic process and dynamical percolation. Math. Biosci. 63, 157-172. (doi:10.1016/0025-5564(82)90036-0)
21. Isichenko, M. B. 1992 Percolation, statistical topography, and transport in random media. Rev. Mod. Phys. 64, 961-1043. (doi:10.1103/RevModPhys.64.961)
22. Stauffer, D. & Aharony, A. 1992 Introduction to percolation theory, 2nd edn. London, UK: Taylor and Francis.
23. Newman, M. 2002 Spread of epidemic disease on networks. Phys. Rev. E 66, 016128. (doi:10.1103/PhysRevE.66.016128)
24. Kenah, E. & Robins, J. M. 2007 Second look at the spread of epidemics on networks. Phys. Rev. E 76, 036113. (doi:10.1103/PhysRevE.76.036113)
25. Miller, J. C. 2007 Epidemic size and probability in populations with heterogeneous infectivity and susceptibility. Phys. Rev. E 76, 010101. (10.1103/PhysRevE.76.010101)
26. Gilligan, C. A. 1995 Modelling soil-borne plant pathogens: reaction-diffusion models. Can. J. Plant Pathol. 17, 96-108.
27. Binder, K. & Young, A. P. 1986 Spin glasses: experimental facts, theoretical concepts, and open questions. Rev. Mod. Phys. 58, 801. (doi:10.1103/RevModPhys.58.801)
28. Heermann, D. W. & Stauffer, D. 1980 Influence of boundary conditions on square bond percolation near pc. Z. Physik. B: Condens. Matter 40, 133-136. (doi:10.1007/BF01295081)
29. Kuulasmaa, K. 1982 The spatial general epidemic and locality dependent random graphs. J. Appl. Prob. 19, 745-758. (doi:10.2307/3213827)
30. Cox, J. & Durrett, R. 1988 Limit theorems for the spread of epidemics and forest fires. Stochast. Proc. Appl. 30, 171-191. (doi:10.1016/0304-4149(88) 90083-X)
31. Otten,W., Bailey, D. & Gilligan, C. A. 2004 Empirical evidence of spatial thresholds to control invasion of fungal parasites and saprotrophs. New Phytol. 163, 125-132. (doi:10.1111/j.1469-8137.2004.01086.x) (Pubitemid 38826179)
32. Davis, S., Trapman, P., Leirs, H., Begon, M. & Heesterbeek, J. A. P. 2008 The abundance threshold for plague as a critical percolation phenomenon. Nature 454, 634-637. (doi:10.1038/nature07053)
33. Gilligan, C. A. 1983 Modeling of soilborne plant pathogens. Annu. Rev. Phytopathol. 21, 45-64. (doi:10.1146/annurev.py.21.090183.000401)
34. Sykes, M. F. & Essam, J. W. 1964 Exact critical percolation probabilities for site and bond problems in two dimensions. J. Math. Phys. 5, 1117-1127. (doi:10.1063/1.1704215)