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Networks and epidemiology - an introduction

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network epidemiology, Phytophthora ramorum, network theory, plant pathology, epidemic spread, clustering, small-world, random, scale-free. Introduction: interconnected world, growing interest in …

network epidemiology, Phytophthora ramorum, network theory, plant pathology, epidemic spread, clustering, small-world, random, scale-free. Introduction: interconnected world, growing interest in network theory and disease spread in networks. Examples of recent work modelling disease (i) spread and (ii) control in networks of various kinds

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  • 1. Networks and Epidemiology Mike Jeger & Marco Pautasso,Division of Biology, Imperial College London, Wye Campus, Kent, UK APS, CPS & MSA Joint Meeting, Quebec City, Jul 31, 2006
  • 2. 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 kind3. Case study: Phytophthora ramorum and epidemiological simulations in networks of small size4. Conclusion: call for enhanced use of network theory in plant pathology
  • 3. Networks are formed by: • physical structures • associations/relationships • processes/flows on a structure
  • 4. Armillaria rhizomorph network near Wageningen, NetherlandsFrom: Lamour et al. (submitted to FEMS Microbiology Ecology)
  • 5. Plant-frugivores network in a Denmark forestfrom Lazaro et al. 2005, Bird-made fruit orchards in northern Europe:nestedness and network properties. Oikos 110: 321-329
  • 6. number of passengers per dayFrom: Hufnagel et al. (2004) Forecast and control of epidemicsin a globalized world. PNAS 101: 15124-15129
  • 7. 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 2003 2005 2005From: Pautasso & Jeger (submitted)
  • 8. Epidemiology just one of the many applications of network theoryNetwork pictures from:Newman (2003) NATURALThe structure and functionof complex networks. food websSIAM Review 45, 2: 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
  • 9. 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: call for enhanced use of network theory in plant pathology
  • 10. Different types of networks local small-world random scale-freeModified from: Keeling & Eames (2005) Networks and epidemic models. Interface 2: 295-307
  • 11. 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
  • 12. Clustering vs. path length local small-world random local small-world random Modified from: Roy & Pascual (2006) On representing network heterogeneitiesin the incidence rate of simple epidemic models. Ecological Complexity 3, 1: 80-90
  • 13. 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
  • 14. Epidemic control in networks with low vs. high clustering (a) low clustering (b) high clustering average number of connections per node = 10 From: Kiss et al. (2005) Disease contact tracing in random and clustered networks. Proceedings of the Royal Society B, 272: 1407-1414
  • 15. 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
  • 16. Degree distribution of nodes in a scale-free network The degree distribution of 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
  • 17. 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, in press
  • 18. 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
  • 19. Connectivity loss in the North American power grid due to the removal of transmission substations transmission nodes removed (%) From: Albert et al. (2004) Structural vulnerability of theNorth American power grid. Physical Review E 69, 025103
  • 20. 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: call for enhanced use of network theory in plant pathology
  • 21. Sudden Oak Death in California Marin County, CA, USPhoto: Marin County Fire Department (north of San Francisco)
  • 22. 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
  • 23. European garden & nursery findsPhytophthora ramorum infection on Rhododendron in Europe Photos: Hans DeGruyter, Netherlands Plant Protection Institute
  • 24. UK: records positive to Phytophthora ramorum; n = 2788 Jan 2003-Dec 2005Data source: Department for Environment, Food and Rural Affairs, UK
  • 25. UK, 2003-2005; n = 2788 250 Records positive to P. ramorum unclear which 200 n of records estates/environment 150 nurseries/garden centres 100 50 0 O 3 O 4 O 5 A 03 A 04 A 05 Ja 3 Ja 4 5 Ju 3 Ju 4 Ju 5 l-0 l-0 l-0 -0 -0 -0 -0 -0 -0 n- n- n- pr pr pr ct ct ct JaData source: Department for Environment, Food and Rural Affairs, UK
  • 26. Own epidemiological investigations in four basic types of directed networks of small size(a) (b) SIS-model; N nodes = 100; n links = 369; directed networks; probability of infection for the node x at time(c) (d) t+1 = Σ px,y iy where px,y is the probability of connection between node x and y, and iy is the infection status of the node y at time t; 20 replicates for each (a) local; (b) small world; type of network (c) random; (d) scale-free
  • 27. 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 1.2 80 1.6 60 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 iteration iteration
  • 28. Linear epidemic threshold on a graph of the probability of persistence and of transmission 1.00 epidemic local 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
  • 29. Lower epidemic threshold for higher correlation coefficient between links to and links from nodes 0.500 probability ofthreshold (p of transmission between nodes) persistence = 0 0.400 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 nodes
  • 30. 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 0 25 50 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 75 100 starting node starting node
  • 31. 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? • applications in the control of Phytophthora ramorum spread?
  • 32. Spatially-explicit modelling framework
  • 33. UK- distribution centres of tree nurseries from Hort Week suppliers guide 2003; n = 476kindly providedby Tom Harwood
  • 34. Sites Distribution Centres Incoming material Outgoing material
  • 35. 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? • applications in the control of Phytophthora ramorum spread?
  • 36. Scale-free properties in the database of sites tested positive to Phytophthora ramorum, UK (2002-2005) 3.0log10 number of sites 2.5 2.0 1.5 1.0 0.5 0.0 1-4 5-49 50-284 n of positive P. ramorum records in database
  • 37. Scale-free properties in the database of sites tested positive to Phytophthora ramorum, UK (2002-2005) 4.0log10 of n of records 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 1-4 5-49 50-499 500-4999 5000- total amount plants affected by P. ramorum
  • 38. 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: call for enhanced use of network theory in plant pathology
  • 39. Where are the applications to plant pathology? LEGEND: PLANT no brackets = (plant application existing (mycorrhiza) metabolomics – (plant meta- cellular pathways) (…) = application existing, but not populations) strictly involving disease [nursery networks] […] = would involve plant pathology, but [quarantine] [plant-vector application of network interactions theory lacking [epiphytotics e.g. viruses] management & control] (plant- [recreation/ pollinator amenities interactions) (plant- landscape] frugivore (bats in networks of interactions)computer hollow trees) viruses Neisseria foot and fish diseases (rumor gonorrhoeae mouth diseasepropagation) Mycoplasma HIV Dengue avian flu bovine pneumoniae Rotavirus SARS raccoon rabies tuberculosis HUMAN ANIMAL
  • 40. Possible reasons for delay in the application of network thinking to plant pathology• Homogeneous mid-field conditions more than adequate for plant diseases? • Lack of data on network structure in plant epidemics relative to human and animal ones? • Just lagging behind? Clustering effects may have slowed down the spread of the concept into this meta-population?
  • 41. Acknowledgements Mike Shaw & Tom Harwood, Univ. of Reading, UK Xiangming Xu, East Malling Research, UK Ottmar Holdenrieder, ETHZ, CH Sandra Denman, Forest Research, Alice Holt, UK Judith Turner, Central Science Laboratory, York, UKDepartment for Environment, Food and Rural Affairs, UK
  • 42. ReferencesDehnen-Schmutz K, Holdenrieder O, Jeger MJ & Pautasso M (2010) Structural change in the international horticultural industry: some implicationsfor plant health. Scientia Horticulturae 125: 1-15Harwood 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: 3353-3361Jeger MJ & Pautasso M (2008) Comparative epidemiology of zoosporic plant pathogens. European Journal of Plant Pathology 122: 111-126Jeger MJ, Pautasso M, Holdenrieder O & Shaw MW (2007) Modelling disease spread and control in networks: implications for plant sciences. NewPhytologist 174: 179-197Lonsdale D, Pautasso M & Holdenrieder O (2008) Wood-decaying fungi in the forest: conservation needs and management options. EuropeanJournal of Forest Research 127: 1-22MacLeod A, Pautasso M, Jeger MJ & Haines-Young R (2010) Evolution of the international regulation of plant pests and challenges for future planthealth. Food Security 2: 49-70Moslonka-Lefebvre M, Pautasso M & Jeger MJ (2009) Disease spread in small-size directed networks: epidemic threshold, correlation betweenlinks to and from nodes, and clustering. J Theor Biol 260: 402-411Moslonka-Lefebvre M, Finley A, Dorigatti I, Dehnen-Schmutz K, Harwood T, Jeger MJ, Xu XM, Holdenrieder O & Pautasso M (2011) Networks inplant epidemiology: from genes to landscapes, countries and continents. Phytopathology 101: 392-403Pautasso M (2009) Geographical genetics and the conservation of forest trees. Perspectives in Plant Ecology, Systematics & Evolution 11: 157-189Pautasso M (2010) Worsening file-drawer problem in the abstracts of natural, medical and social science databases. Scientometrics 85: 193-202Pautasso M & Jeger MJ (2008) Epidemic threshold and network structure: the interplay of probability of transmission and of persistence in directednetworks. Ecological Complexity 5: 1-8Pautasso M et al (2010) Plant health and global change – some implications for landscape 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 ofhierarchical categories. Journal of Applied Ecology 47: 1300-1309Xu XM, Harwood TD, Pautasso M & Jeger MJ (2009) Spatio-temporal analysis of an invasive plant pathogen (Phytophthora ramorum) in Englandand Wales. Ecography 32: 504-516