Modelling the spread of    Phytophthora ramorumin complex directed networks         Marco Pautasso,        Division of Bio...
Sudden Oak Deathfrom Desprez-Loustau et multi al. (in press) Trends in Ecology & Evolution
Trace-forwards and positive detections across the USA, July 2004              Trace forward/back zipcode              Posi...
Simulation of disease spread in four basic  types of directed networks of small sizelocal              small-             ...
Examples of epidemic development in four kinds                                                           of directed netwo...
Linear epidemic threshold on a plot of                                       p(persistence) f p(transmission)             ...
2.0                                2.5infection probability across all nodes)             local                    2.0    ...
Marked variations in epidemic final size at threshold conditions       depend on the number of links of the starting nodes...
Spatially-explicit                            modelling frameworkClimate                      Long-distance tradesuitabili...
Network epidemiology                                    Natures guide for mentors                               number of ...
Epidemiology is just one of the              many applications of network theory                                NATURALNet...
AcknowledgementsPeter Weisberg,     Chris Gilligan, Univ.Univ. of Nevada,       of Cambridge   Reno, US                   ...
ReferencesDehnen-Schmutz K, Holdenrieder O, Jeger MJ & Pautasso M (2010) Structural change in the international horticultu...
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Modelling the spread of Phytophthora ramorum in complex networks

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Modelling the spread of Phytophthora ramorum in complex networks

  1. 1. Modelling the spread of Phytophthora ramorumin complex directed networks Marco Pautasso, Division of Biology, Imperial College London, Wye Campus, Kent, UK Wye, 14 Jul 2007
  2. 2. Sudden Oak Deathfrom Desprez-Loustau et multi al. (in press) Trends in Ecology & Evolution
  3. 3. 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
  4. 4. Simulation of disease spread 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 from: Pautasso & Jeger (in press) Ecological Complexity
  5. 5. Examples of epidemic development in four kinds of directed networks (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 press) Ecological Complexity
  6. 6. Linear epidemic threshold on a plot of p(persistence) f p(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 press) Ecological Complexity
  7. 7. 2.0 2.5infection probability across all nodes) local 2.0 small-world 1.5 Final size of epidemic (sum of 1.5 1.0 1.0 0.5 0.5 0.0 0.0 0 25 50 75 100 0 25 50 75 100 3.0 6.0 2.5 random 5.0 scale-free 2.0 4.0 1.5 3.0 1.0 2.0 0.5 1.0 0.0 0.0 0 25 50 75 100 0 25 50 75 100 Starting node of epidemic from: Pautasso & Jeger (in review) Journal of Theoretical Biology
  8. 8. Marked variations in epidemic final size at threshold conditions depend on the number of links of the starting nodesum at equilibrium of probability 2.0 3.0 local 2.5 small-world of infection across all nodes 1.5 2.0 1.0 1.5 1.0 0.5 0.5 0.0 0.0 0 2 4 6 8 0 1 2 3 4 5 6 3.0 6.0 random 5.0 scale-free 2.5 2.0 4.0 1.5 3.0 1.0 2.0 0.5 1.0 0.0 0.0 0 2 4 6 8 10 12 0 20 40 60 80 100 n of links from starting node n of links from starting node from: Pautasso & Jeger (in review) Journal of Theoretical Biology
  9. 9. Spatially-explicit modelling frameworkClimate Long-distance tradesuitability Local Trade Heathland Woodland
  10. 10. Network epidemiology Natures guide for mentors number of passengers per dayfrom: Hufnagel, Brockmann & Geisel (2004) PNAS
  11. 11. Epidemiology is just one of the many applications of network theory NATURALNetwork pictures from:Newman (2003) SIAM Review food webs cell metabolism neural Food web of Little Rock networks Lake, Wisconsin, US ant nests sexual partnerships DISEASE SPREAD family innovation networksInternet flows co-authorship HIVstructure railway urban road nets spread electrical networks networks network power grids telephone calls WWW computing airport Internet E-mail committees grids networks software maps patternsTECHNOLOGICAL SOCIALModified from: Jeger, Pautasso, Holdenrieder & Shaw (2007) New Phytologist
  12. 12. AcknowledgementsPeter Weisberg, Chris Gilligan, Univ.Univ. of Nevada, of Cambridge Reno, US Mike Jeger, Ottmar Imperial College, Mike Shaw, Holdenrieder, Wye Univ. of ETHZ, CH Reading Kevin Gaston, Mike Univ. of Sheffield Emanuele Della McKinney, Katrin Valle, Politecnico di Univ. of Boehning Milano, Italy Tennessee, -Gaese, US Univ. Mainz, Germany
  13. 13. 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

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