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Epidemiology of complex networks

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Epidemiology of complex networks, disease spread in a globalized world, Phytophthora ramorum, Sudden Oak Death, California, England and Wales,

Epidemiology of complex networks, disease spread in a globalized world, Phytophthora ramorum, Sudden Oak Death, California, England and Wales,

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  • 1. Epidemiologyof complex networks Marco Pautasso, Division of Biology, Imperial College London, Wye Campus, Kent, UK Universität Bayreuth, 25 Jan 2007
  • 2. Disease spread in a globalized world number of passengers per dayFrom: Hufnagel, Brockmann & Geisel (2004) Forecast and controlof epidemics in a globalized world. PNAS 101: 15124-15129
  • 3. Phytophthora alni along water courses in Bayern 10 km From: Jung & Blaschke (2004) Phytophthora root and collar rot of alders in Bavaria: distribution, modes of spread and possible management strategies. Plant Pathology 53: 197–208Modified from: Holdenrieder, Pautasso, Weisberg & Lonsdale (2004) Tree diseases and landscapeprocesses: the challenge of landscape pathology. Trends in Ecology & Evolution 19, 8: 446-452
  • 4. Web of susceptible genera connected by Phytophthora ramorum (based ongenus co-existence in 2788 positive findings in England & Wales, 2003-2005) Viburnum Camellia Umbellularia Castanea Taxus Syringa Drimys Fagus Rhodo- dendron Festuca Hamamelis Quercus Kalmia Pieris Laurus Magnolia Parrotia LeucothoeFrom: Pautasso, Harwood, Shaw, Xu & Jeger (2007) Epidemiological modeling of Phytophthoraramorum: network properties of susceptible plant genera movements in the UK nursery sector.Accepted for the Sudden Oak Death Science Symposium III, Santa Rosa, CA, US
  • 5. Epidemiology is just one of the many applications of network theoryNetwork pictures from:Newman (2003) NATURALThe structure and functionof complex networks. food websSIAM Review 45: 167-256 cell metabolism neural networks Food web of Little Rock ant nests Lake, Wisconsin, US sexual DISEASE partnerships SPREAD family innovation networks flowsInternet co-authorship HIVstructure railway nets spread telephone calls networks urban road network electrical networks E-mail committees power grids airport Internet WWW patterns computing networks grids software mapsTECHNOLOGICAL SOCIAL
  • 6. Epidemic spread of studies applying network theory 2005 2005 2005 2005 2005 2004 2005 2006 2004 2004 2001 2005 2002 2006 2004 2003 2005 2004 2005 2003 2005 2005 2005 2006 2005 2003 2005Modified from: Jeger, Pautasso, Holdenrieder & Shaw (in press) Modelling disease spreadand control in complex networks: implications for plant sciences. New Phytologist
  • 7. Networks and Epidemiology1. Introduction: interconnected world, growing interest in network theory and disease spread in networks2. Examples of recent work modelling disease (i) spread and (ii) control in networks of various kinds3. Case study: Phytophthora ramorum and epidemiological simulations in networks of small size4. Conclusion: further potential work applying network theory in biogeographic modelling
  • 8. Different types of networks local small-world random scale-freeModified from: Keeling & Eames (2005) Networks and epidemic models. Interface 2: 295-307
  • 9. Epidemic development in different types of networks scale-free random 2-D lattice rewired 2-D lattice 1-D lattice rewired 1-D lattice N of nodes of networks = 500; p of infection = 0.1; latent period = 2 time steps; infectious period = 10 time steps From: Shirley & Rushton (2005) The impacts of network topology on disease spread. Ecological Complexity 2: 287-299
  • 10. Super-connected individuals in scale-free networks A reconstruction of the recent UK foot-and-mouth disease epidemic (20 Feb–15 Mar 2001). Vertices marked with a label are livestock markets, unmarked vertices are farms. Only confirmed infected premises are included. Arrows indicate route of infection. From: Shirley & Rushton (2005) Where diseases and networks collide: lessons to be learnt from a study of the 2001 foot-and-mouth disease epidemic. Epidemiology & Infection 133: 1023-1032
  • 11. Degree distribution of nodes in a scale-free network based on a reconstruction of the UK foot-and mouth disease network. Fitted line: y= 118.5x -1.6, R2 = 0.87 From: Shirley & Rushton (2005) Where diseases and networks collide: lessons to be learnt from a study of the 2001 foot-and-mouth disease epidemic. Epidemiology & Infection 133: 1023-1032
  • 12. Fraction of population infected (l) as a function of ρ0 uniform degree distribution scale-free network with P(i) ≈ i-3 ρ0 is coincident with R0 for a uniform degree distribution; for a scale-free network, theory says that R0 = ρ0 + [1 + (CV)2], where CV is the coefficient of variation of the degree distribution From: May (2006) Network structure and the biology of populations. Trends in Ecology & Evolution 21, 7: 394-399
  • 13. Networks and Epidemiology1. Introduction: interconnected world, growing interest in network theory and disease spread in networks2. Examples of recent work modelling disease (i) spread and (ii) control in networks of various kinds3. Case study: Phytophthora ramorum and epidemiological simulations in networks of small size4. Conclusion: further potential work applying network theory in biogeographic modelling
  • 14. Sudden Oak Death Marin County, CA, USPhoto: Marin County Fire Department (north of San Francisco)
  • 15. Sudden Oak Death ground survey, Northern California, 2004 Map courtesy of Ross Meentemeyer
  • 16. Trace-forwards and positive detections across the USA, July 2004 Trace forward/back zipcode Positive (Phytophthora ramorum) site Hold releasedSource: United States Department of Agriculture,Animal and Plant Health Inspection Service, Plant Protection and Quarantine
  • 17. Vascular plant species richness as a function of human population size in US countiesFrom: Pautasso & McKinney (in review) The botanist effect revisited: plant species richness, county area, and human population size in the United States. Conservation Biology
  • 18. P. ramorum: an aggressive AND generalist pathogen Acer macrophyllum, Aesculus californica, Lithocarpus densiflorus, Quercus agrifolia, Quercus kelloggii, Quercus chrysolepis, Quercus parvula, Pseudotsuga menziesii, Sequoia sempervirens Modified from: Pautasso, Holdenrieder & Stenlid (2005) Susceptibility to fungal pathogens of forests differing in tree diversity. Scherer-Lorenzen, Körner & Schulze (eds) Forest Diversity and Function: Temperate and Boreal Systems. Ecological Studies, 176: 263-289
  • 19. England and Wales: records positive to Phytophthora ramorum n = 2788 Jan 2003-Dec 2005Data source: Department for Environment, Food and Rural Affairs, UK
  • 20. Own epidemiological investigations in four basic types of directed networks of small sizelocal small- world SIS-model N nodes = 100 constant n of links directed networks probability of infection for the node x at timerandom scale- t+1 = Σ px,y iy where free px,y is the probability of connection between node x and y, and iy is the infection status of the node y at time tfrom: Pautasso & Jeger (in review) Epidemic threshold and network structure:the interplay of probability of transmission and of persistence. Ecological Complexity
  • 21. Examples of epidemic development in four kinds of directed networks of small size (at threshold conditions)sum probability of infection across all nodes 1.2 40 1.2 25 35 % nodes with probability of infection > 0.01 1.0 1.0 20 small-world network nr 4; 30 0.8 0.8 25 starting node = nr 14 15 0.6 20 0.6 10 15 0.4 0.4 local network nr 6; 10 5 starting node = nr 100 0.2 0.2 5 0.0 0 0.0 0 1 51 101 151 201 1 26 51 76 1.6 iteration 60 1.2 iteration 80 1.4 1.0 scale-free network nr 2; 70 starting node = nr 11 50 1.2 60 40 0.8 1.0 50 0.8 30 0.6 40 0.6 random network nr 8; 30 0.4 starting node = nr 80 20 0.4 20 10 0.2 0.2 10 0.0 0 0.0 0 1 26 51 76 1 26 51 76 from: Pautasso & Jeger (in review) Ecological Complexity
  • 22. Linear epidemic threshold on a graph of the probability of persistence and of transmission 1.00 local epidemic develops small-worldprobability of persistence 0.75 random scale-free 0.50 0.25 no epidemic 0.00 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 probability of transmission from: Pautasso & Jeger (in review) Ecological Complexity
  • 23. Lower epidemic threshold for higher correlation coefficient between links to and links from nodes 0.500 probability ofthreshold (p of transmission between nodes) 0.400 persistence = 0 0.300 0.200 local small world 0.100 random scale-free (one way) scale-free (two ways) 0.000 -0.500 0.000 0.500 1.000 correlation coefficient between number of links to and links from nodesfrom: Pautasso & Jeger (in preparation) Proceedings Royal Society B
  • 24. Marked variations in the final size of the epidemic at threshold conditions depending on the starting point 100 100 local network nr 2% nodes at equilibrium with probability of infection > 0.01 a b small world network nr 6 75 75 50 50 25 25 0 0 0 25 50 75 100 starting node 0 25 50 starting node 75 100 100 100 random network nr 9 c d scale-free network nr 8 75 75 50 50 25 25 0 0 0 25 50 75 100 0 25 50 75 100from: Pautasso & Jeger (in preparation) Proceedings Royal Society B
  • 25. Temporal development; England & Wales, 2003-2005; n = 2788 250 R ecords positive to P . ram orum unclea r w hic h 200n of records esta tes/env ironm ent 150 nurseries/ga rden centres 100 50 0 3 4 5 03 3 04 4 05 5 3 4 5 -0 -0 -0 l-0 l-0 l-0 -0 -0 -0 n- n- n- pr pr pr ct ct ct Ju Ju Ju Ja Ja Ja O O O A A AData source: Department for Environment, Food and Rural Affairs, UK
  • 26. Further developments of these simulations • effect on these relationships of number of links/size of networks • integration in simulations of different sizes of nodes and of a dynamic contact structure • migration of network theory into GIS with spatially explicit network modelling of epidemics
  • 27. Spatially-explicit modelling frameworkClimate Long-distance tradesuitability Local Trade Heathland Woodland
  • 28. Networks and Epidemiology1. Introduction: interconnected world, growing interest in network theory and disease spread in networks2. Examples of recent work modelling disease spread and control in networks of various kinds3. Case study: Phytophthora ramorum and epidemiological investigations in networks of small size4. Conclusion: further potential work applying network theory in biogeography
  • 29. Further potential work applying network theory in biogeographic modelling• conservation biology (e.g. meta-populations, reserve networks, botanical gardens)• invasion ecology (for exotic organisms particularly when spread by the nursery trade)• plenty of open questions of mathematical interest, to be addressed using theoretical analyses, but also numerical simulations
  • 30. AcknowledgementsPeter Weisberg, Chris Gilligan, Univ.Univ. of Nevada, of Cambridge, UK Reno, US Mike Jeger, Ottmar Imperial College, Mike Shaw, Holdenrieder, Wye, UK Univ. of ETHZ, CH Reading, UK Kevin Gaston, Univ. of Mike Sheffield, Emanuele Della McKinney, UK Katrin Valle, Politecnico di Univ. of Boehning Milano, Italy Tennessee, -Gaese, US Univ. Mainz
  • 31. ReferencesJokimäki J, Kaisanlahti-Jokimäki M-L, Suhonen J, Clergeau P, Pautasso M & Fernández-Juricic E (2011) Merging wildlife community ecology and animal behavioral ecologyfor a better urban landscape planning. Landscape & Urban Planning 100: 383-385Moslonka-Lefebvre M, Finley A, Dorigatti I, Dehnen-Schmutz K, Harwood T, Jeger MJ, Xu XM, Holdenrieder O & Pautasso M (2011) Networks in plant epidemiology: fromgenes to landscapes, countries and continents. Phytopathology 101: 392-403Pautasso M, Böhning-Gaese K, Clergeau P, Cueto VR, Dinetti M, Fernandez-Juricic E, Kaisanlahti-Jokimäki ML, Jokimäki J, McKinney ML, Sodhi NS, Storch D, Tomialojc L,Weisberg PJ, Woinarski J, Fuller RA & Cantarello E (2011) Global macroecology of bird assemblages in urbanized and semi-natural ecosystems. Global Ecology &Biogeography 20: 426-436Barbosa AM, Fontaneto D, Marini L & Pautasso M (2010) Is the human population a large-scale indicator of the species richness of ground beetles? Anim Cons 13: 432-441Barbosa AM, Fontaneto D, Marini L & Pautasso M (2010) Positive regional species–people correlations: a sampling artefact or a key issue for sustainable development?Animal Conservation 13: 446-447Cantarello E, Steck CE, Fontana P, Fontaneto D, Marini L & Pautasso M (2010) A multi-scale study of Orthoptera species richness and human population size controlling forsampling effort. Naturwissenschaften 97: 265-271Chiari C, Dinetti M, Licciardello C, Licitra G & Pautasso M (2010) Urbanization and the more-individuals hypothesis. Journal of Animal Ecology 79: 366-371Dehnen-Schmutz K, Holdenrieder O, Jeger MJ & Pautasso M (2010) Structural change in the international horticultural industry: some implications for plant health. ScientiaHorticulturae 125: 1-15Golding J, Güsewell S, Kreft H, Kuzevanov VY, Lehvävirta S, Parmentier I & Pautasso M (2010) Species-richness patterns of the living collections of the worlds botanicgardens: a matter of socio-economics? Annals of Botany 105: 689-696MacLeod A, Pautasso M, Jeger M & Haines-Young R (2010) Evolution of the international regulation of plant pests & challenges for future plant health. Food Security 2: 49-70Pautasso M (2010) Worsening file-drawer problem in the abstracts of natural, medical and social science databases. Scientometrics 85: 193-202Pautasso M & Pautasso C (2010) Peer reviewing interdisciplinary papers. European Review 18: 227-237Pautasso M & Schäfer H (2010) Peer review delay and selectivity in ecology journals. Scientometrics 84: 307-315Pautasso M, Dehnen-Schmutz K, Holdenrieder O, Pietravalle S, Salama N, Jeger MJ, Lange E & Hehl-Lange S (2010) Plant health and global change – some implications forlandscape management. Biological Reviews 85: 729-755Pautasso M, Moslonka-Lefebvre M & Jeger MJ (2010) The number of links to and from the starting node as a predictor of epidemic size in small-size directed networks.Ecological Complexity 7: 424-432Pautasso M, Xu XM, Jeger MJ, Harwood T, Moslonka-Lefebvre M & Pellis L (2010) Disease spread in small-size directed trade networks: the role of hierarchical categories.Journal of Applied Ecology 47: 1300-1309Pecher C, Fritz S, Marini L, Fontaneto D & Pautasso M (2010) Scale-dependence of the correlation between human population and the species richness of streammacroinvertebrates. Basic Applied Ecology 11: 272-280Harwood TD, Xu XM, Pautasso M, Jeger MJ & Shaw M (2009) Epidemiological risk assessment using linked network and grid based modelling: Phytophthora ramorum and P.kernoviae in the UK. Ecological Modelling 220: 3353-3361Moslonka-Lefebvre M, Pautasso M & Jeger MJ (2009) Disease spread in small-size directed networks: epidemic threshold, correlation between links to and from nodes, andclustering. Journal of Theoretical Biology 260: 402-411
  • 32. References (bis)Pautasso M (2009) Geographical genetics and the conservation of forest trees. Perspectives in Plant Ecology, Systematics and Evolution 11: 157-189Pautasso M & Dinetti M (2009) Avian species richness, human population and protected areas across Italy’s regions. Environmental Conservation 36: 22-31Pautasso M & Powell G (2009) Aphid biodiversity is correlated with human population in European countries. Oecologia 160: 839-846Pautasso M & Zotti M (2009) Macrofungal taxa and human population in Italys regions. Biodiversity & Conservation 18: 473-485Xu XM, Harwood TD, Pautasso M & Jeger MJ (2009) Spatio-temporal analysis of an invasive plant pathogen (Phytophthora ramorum) in England and Wales. Ecography 32:504-516Jeger MJ & Pautasso M (2008) Comparative epidemiology of zoosporic plant pathogens. European Journal of Plant Pathology 122: 111-126Jeger MJ & Pautasso M (2008) Plant disease and global change – the importance of long-term data sets. New Phytologist 177: 8-11Lonsdale D, Pautasso M & Holdenrieder O (2008) Wood-decaying fungi in the forest: conservation needs and management options. European Journal of Forest Research 127:1-22Pautasso M & Chiarucci A (2008) A test of the scale-dependence of the species abundance-people correlation for veteran trees in Italy. Annals of Botany 101: 709-715Pautasso M & Fontaneto D (2008) A test of the species-people correlation for stream macro-invertebrates in European countries. Ecological Applications 18: 1842-1849Pautasso M & Jeger MJ (2008) Epidemic threshold and network structure: the interplay of probability of transmission and of persistence in directed networks. EcologicalComplexity 5: 1-8Pautasso M & Weisberg PJ (2008) Density-area relationships: the importance of the zeros. Global Ecology and Biogeography 17: 203-210Schlick-Steiner B, Steiner F & Pautasso M (2008) Ants and people: a test of two mechanisms behind the large-scale human-biodiversity correlation for Formicidae in Europe. Jof Biogeography 35: 2195-2206Steck CE & Pautasso M (2008) Human population, grasshopper and plant species richness in European countries. Acta Oecologica 34: 303-310Jeger MJ, Pautasso M, Holdenrieder O & Shaw MW (2007) Modelling disease spread and control in networks: implications for plant sciences. New Phytologist 174: 179-197Pautasso M (2007) Scale-dependence of the correlation between human presence and plant/vertebrate species richness. Ecology Letters 10: 16-24Pautasso M & McKinney ML (2007) The botanist effect revisited: plant species richness, county area and human population size in the US. Conservation Biology 21, 5: 1333-1340Pautasso M & Parmentier I (2007) Are the living collections of the world’s botanical gardens following species-richness patterns observed in natural ecosystems? BotanicaHelvetica 117: 15-28Pautasso M & Gaston KJ (2006) A test of the mechanisms behind avian generalized individuals-area relationships. Global Ecology and Biogeography 15: 303-317Pautasso M & Gaston KJ (2005) Resources and global avian assemblage structure in forests. Ecology Letters 8: 282-289Pautasso M, Holdenrieder O & Stenlid J (2005) Susceptibility to fungal pathogens of forests differing in tree diversity. In: Forest Diversity and Function (Scherer-Lorenzen M,Koerner Ch & Schulze D, eds.). Ecol. Studies Vol. 176. Springer, Berlin, pp. 263-289Holdenrieder O, Pautasso M, Weisberg PJ & Lonsdale D (2004) Tree diseases and landscape processes: the challenge of landscape pathology. Trends in Ecology andEvolution 19, 8: 446-452
  • 33. Networks andEpidemiology Marco Pautasso, Division of Biology,Imperial College London, Wye Campus, Kent, UK Universität Bayreuth, 25 Jan 2007
  • 34. Clustering vs. path length local small-world randomclustering path length local small-world random Modified from: Roy & Pascual (2006) On representing network heterogeneities in the incidence rate of simple epidemic models. Ecological Complexity 3, 1: 80-90
  • 35. Reproductive ratio R0 in networks of differing degree of clustering Initial R0 Asymptotic R0 Simulations of a wide variety of networks with average of 10 contacts per individuals random (C/Cmax) localFrom: Keeling (2005) The implications of network structure for epidemic dynamics. Theoretical Population Biology 67: 1-8
  • 36. Epidemic control in networks with low vs. high clustering (a) low clustering (b) high clustering average number of connections per node = 10 From: Kiss, Green & Kao (2005) Disease contact tracing in random and clustered networks. Proceedings of the Royal Society B, 272: 1407-1414
  • 37. Critical tracing efficiency to control an SIS-type epidemic in a network with uniform degree distribution From: Eames & Keeling (2003) Contact tracing and disease control. Proceedings of the Royal Society B 270: 2565-2571
  • 38. Connectivity loss in the North American power grid due to the removal of transmission substations transmission nodes removed (%)From: Albert, Albert & Nakarado (2004) Structural vulnerability of the North American power grid. Physical Review E 69, 025103

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