Your SlideShare is downloading. ×
0
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Networks and epidemiology - an update
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

Networks and epidemiology - an update

283

Published on

Networks and epidemiology, sudden oak death, complex networks, small-world, random, scale-free, local connectivity, long-distance spread, clustering, plant pathogens. Phytophthora ramorum and …

Networks and epidemiology, sudden oak death, complex networks, small-world, random, scale-free, local connectivity, long-distance spread, clustering, plant pathogens. Phytophthora ramorum and epidemiological simulations in networks of small size Conclusion: further potential work applying network theory in plant sciences

Published in: Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
283
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
10
Comments
0
Likes
0
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. Networks and Epidemiology Marco Pautasso, Division of Biology, Imperial College London, Wye Campus, Kent, UK Wye, 8 June 2007 number of passengers per dayfrom: Hufnagel et al. (2004) Forecast and control of epidemics in a globalized world. PNAS 101: 15124-15129
  • 2. Relative concentration of Infections in case of ainfectious individuals in case smallpox outbreak starting of an influenza pandemic from London (5*5 km cells) t = 75 days in both casesfrom: Riley (2007) Large-scale spatial-transmission models of infectious disease. Science 316: 1298-1301
  • 3. Web of susceptible genera connected by Phytophthora ramorum (based ongenus co-existence in 2788 positive findings in England & Wales, 2003-2005)
  • 4. 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
  • 5. Epidemic spread of studies applying network theory 2005 2005 2005 2005 2005 2004 2005 2006 2004 20042001 2005 2002 2006 2004 2003 2005 2004 2005 2003 2005 2005 2005 2006 2005 2003 2005
  • 6. 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 plant sciences
  • 7. Different types of networks local small-world random scale-freeModified from: Keeling & Eames (2005) Networks and epidemic models. Interface 2: 295-307
  • 8. 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
  • 9. 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
  • 10. 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
  • 11. 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
  • 12. 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 plant sciences
  • 13. Sudden Oak Death in CaliforniaFrom Desprez-Loustau et al. (2007) The fungal dimension of biologicalinvasions. Trends in Ecology & Evolution, in press
  • 14. Sudden Oak Death ground surveys, Northern California, 2004 Map courtesy of Ross Meentemeyer
  • 15. 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
  • 16. England and Wales: records positive to Phytophthora ramorum n = 2788 Jan 2003-Dec 2005Data source: Department for Environment, Food and Rural Affairs, UK
  • 17. 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 t
  • 18. 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
  • 19. 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
  • 20. 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
  • 21. Spatially-explicit modelling frameworkClimate Long-distance tradesuitability Local Trade Heathland Woodland
  • 22. 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 plant sciences
  • 23. 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
  • 24. Further potential work applying network theory in plant sciences• conservation biology (e.g. meta-populations, reserve networks, botanical gardens)• invasion ecology (for exotic organisms particularly when spread by the nursery trade)• gene-for-gene interactions?
  • 25. Network of gene-for-gene relationships between rice and diverse avrBs3/pthA avirulence genes in Xanthomonas oryzae pv. oryzaeHR: High Resistance; R: Resistance; MR: Medium Resistance;MS: Medium Susceptibility; S: Susceptibility IRB IRB IRB Tet IR2Avr IRBB1 IRBB2 IRBB3 IRBB4 IRBB7 IRBB8 IRBB10 IRBB11 B13 B14 B21 ep 4gene Near isogenic lines of riceclones a b c d e f g h i j k l mPXO99 (p41) 1 MR R R HR HR R R MS MR HR HR MR HRPX099 (p51) 2 HR HR HR HR HR R HR HR R R HR HR HRPXO99 (p54) 3 S MR HR S MR MS R S MR MR R S MSPXO99 (p56) 4 MS S S MS R HR R MS R S R S SPXO99 (p58) 5 R HR R MR HR HR R HR R R R R RPXO99 (p65) 6 S HR S S MR MS R S R S HR S SPXO99 (p71) 7 MS MS S MS HR MR HR R MR MR HR HR HRPXO99(PUFR034) 8 MS S MS S MR MR MR S R MR HR S SPX099 9 MS S MS S MR MR MR S R MR HR S SJXOIII 10 MS MS HR MR HR R HR HR R S HR S MSData source: Wu et al. (2007) Plant Pathology 56, 1: 26-34
  • 26. Network of gene-for-gene relationships between rice and diverse avrBs3/pthA avirulence genes in Xanthomonas oryzae pv. oryzae(based on coexistence of High Resistance in the same isogenic lines ofrice for different gene clones; the number in the matrix is the number of isogenic lines with HR in the two gene clones connected)Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34
  • 27. Network of gene-for-gene relationships between rice and diverse avrBs3/pthA avirulence genes in Xanthomonas oryzae pv. oryzae(based on coexistence of High Resistance in the same isogenic lines of rice for different gene clones; the strength of the lines reflects the number of connections) JXOIII PXO99 PXO99 (p41) PXO99 (pUFRO34) PXO99 (p51) PXO99 (p71) PXO99 (p65) PXO99 (p54) PXO99 (p58) PXO99 (p56) N of links: 1 2 3 4 5Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34
  • 28. Frequency distribution of the number of links for isogenic lines of rice (based on coexistence of High Resistance in the same pathogen gene clone for different isogenic lines of rice) 7number of gene clones 6 5 4 3 2 1 0 0-5 6-15 16-25 n u m b er of c on n ec tion sData source: Wu et al. (2007) Plant Pathology 56, 1: 26-34
  • 29. Network of gene-for-gene relationships between rice and diverse avrBs3/pthA avirulence genes in Xanthomonas oryzae pv. oryzae (based on coexistence of High Resistance in the same gene clone for different isogenic lines of rice; the number in the matrix is the number of gene clones with HR in the two isogenic lines of rice connected)Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34
  • 30. Network of gene-for-gene relationships between rice and diverse avrBs3/pthA avirulence genes in Xanthomonas oryzae pv. oryzae (based on coexistence of High Resistance in the same gene clone for different isogenic lines of rice; the strength of the lines reflects the number of connections) IRBB1 IR24 Tetep IRBB2 IRBB21 IRBB3 IRBB14 IRBB4 IRBB13 IRBB7 IRBB8 IRBB11 IRBB10 N of links: 1 2 3 4Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34
  • 31. Frequency distribution of the number of links for Avr gene clones (based on coexistence of High Resistance in the same isogenic lines of rice for different pathogen gene clones) 8number of isogenic lines of rice 7 6 5 4 3 2 1 0 0 -5 6 -1 5 1 6 -2 5 n u m b er of c on n ec tion sData source: Wu et al. (2007) Plant Pathology 56, 1: 26-34
  • 32. Acknowledgements Mike Jeger, Imperial College, Wye Campus Mike Shaw & Tom Harwood, Univ. of Reading Xiangming Xu, East Malling Research Ottmar Holdenrieder, ETHZ, CH Sandra Denman, Forest Research, Alice Holt Judith Turner, Central Science Laboratory, YorkDepartment for Environment, Food and Rural Affairs
  • 33. 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

×